Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

download Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

of 140

Transcript of Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    1/140

    Ancp~tnanh| ei clyn`|jeh chl p~tic`n!c|aepvbntn

    nr`bchkn jh `eavonr |nttcjh(

    Gnyjh B( Mehnp

    \bnpjp p~daj||nl iet |bn lnktnn ei Acp|nt ei Vbjoepevbz

    \bn ^hjyntpj|z ei Nljhd~tkb

    4662

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    2/140

    j

    Ln`octc|jeh

    J ln`octn |bc| |bjp |bnpjp tnvtnpnh|p az e{h {etg/ chl |bc| {bntn |bn {etg ei e|bntp

    bcp dnnh ~pnl j| bcp dnnh l~oz c``tnlj|nl( @bcv|nt 4 ei |bjp |bnpjp jp dcpnl eh c

    `eoocdetc|jyn nrvntjanh| {j|b @PJTE/ C~p|tcojc/ {bj`b tnp~o|nl jh |bn v~doj`c|jeh ei

    On~hjhk n| co( "4662*/ "pnn cvvnhljr |e |bjp |bnpjp*(

    Gnyjh B( Mehnp

    E`|ednt 4662

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    3/140

    jj

    C`ghe{onlknanh|p

    Achz |bchgp iet bnovi~o ljp`~ppjehp chl clyj`n l~tjhk |bn {etg iet |bjp |bnpjp ctn

    l~n |e=

    Vtei( Mebh Aeh`tjnii

    Lt( Tcz On~hjhk

    Lt( Ted @onanh|

    )

    Vtei( Mebh Ijhhjkch

    \bjp tnpnct`b {cp p~vvet|nl dz HNT@ ktch| HNT%P%M%466

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    4/140

    jjj

    Cdp|tc`|

    C``~tc|n edpntyc|jehp ei |bn `ctdeh `z`on ctn nppnh|jco cp jhv~|p |e koedco `ojac|n

    aelnop( Edpntyc|jehp acln dz |bn aj`tean|neteoekj`co |n`bhjs~n ei nllz

    `eyctjch`n/ {bjp| {jlnpvtncl/ acz dn jh`ettn`| ji cjt jp clyn`|nl c{cz itea dnoe{

    |bn pnhpet pzp|na( \bjp jp ve|nh|jcooz c pntje~p jpp~n iet IO^RHN\/ c koedco hn|{etg

    ei nllz io~r pj|np( \bn cvvtec`b jh |bjp |bnpjp |e jhynp|jkc|n |bjp vtedona {cp

    |{eieol=

    C i~oo aj`tean|neteoekj`co acpp dcoch`n ~pjhk ch jhp|t~anh|nl >6 a oehk dz >6 a

    {jln dz 9 a bjkb @ct|npjch `eh|teo yeo~an "@Y* `eyntjhk |bn ~hlntp|etnz

    ynkn|c|jeh ei c

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    5/140

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    6/140

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    7/140

    yj

    4(0 @eh`o~pjehp ;>

    0 Ktjiijh ietnp| {jhl |tchpn`| ) vteijon nrvntjanh|p ;;

    0(3 Jh|tel~`|jeh ;;

    0(4 Pj|n lnp`tjv|jeh ;:

    0(0 Nrvntjanh|co pn|~v chl tnp~o|p 23

    0(0(3 \bn betj}eh|co |tchpn`| nrvntjanh| 23

    0(0(4 \tchpn`| nrvntjanh| tnp~o|p chl ljp`~ppjeh 2 Ljp`~ppjeh ei |bn vteijon nrvntjanh| tnp~o|p 366

    0(0(9 \bn |e{nt vteijon `tepp `ettnoc|jeh p|~lz 363

    0(0(; Ljp`~ppjeh ei |bn vteijon `tepp!`ettnoc|jeh p|~lz 33:

    0(< @eh`o~pjehp 346

    @eh`o~pjehp (( 340

    Tnintnh`np (( 34;

    Cvvnhljr On~hjhk n| co( "4662* (( 300

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    8/140

    3

    3 \bn clyn`|jeh vtedona jh nllz io~r ancp~tnanh|p

    3(3 Jh|tel~`|jeh

    Tjpjhk c|aepvbntj` @E4 `eh`nh|tc|jehp jh |bn nct|bp c|aepvbntn itea

    ch|bteveknhj` pe~t`np ctn he{ ch np|cdojpbnl ic`| "Gnnojhk ) [beti/ 4663*( \bn nr`bchkn tc|n ei @E4 c`tepp |bn jh|ntic`n

    dn|{nnh |bn c|aepvbntn chl c voch| `chevz jp ancp~tnl cp |bn `eyctjch`n dn|{nnh

    io~`|~c|jehp jh ynt|j`co {jhl ynoe`j|z chl @E4 ajrjhk tc|je "Dcole``bj 4660*( \bn

    jh|ntic`n jh s~np|jeh jp c he|jehco betj}eh|co io~r vochn c| |bn pcan bnjkb| cp |bn nllz

    `eyctjch`n pzp|na/ {bj`b ~p~cooz `ehpjp|p ei c 0 `eavehnh| ~o|tcpehj` chnaean|nt

    chl |bn pcavojhk vejh| iet ch jhitctnl kcp chcozpnt "JTKC*/ cp lnp`tjdnl dz

    Aeh`tjniin| co( "3::;*/ chl joo~p|tc|nl jh ijk~tn 3(3( \bjp ns~jvanh| jp ~p~cooz

    pj|~c|nl eh c acp| et |e{nt cdeyn |bn n`epzp|na ~hlnt jhynp|jkc|jeh(

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    9/140

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    10/140

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    11/140

    * {ntn cdon |e ancp~tn p~`b c hn|

    betj}eh|co clyn`|jeh io~r ei @E4 `c~pnl dz c ietnp| nlkn( ^hiet|~hc|noz/ `~ttnh|

    nllz `eyctjch`n |e{ntp tnvet|jhk |e |bn IO^RHN\ hn|{etg ctn he| ns~jvvnl |e

    ancp~tn |bn lc|c tns~jtnl |e `co`~oc|n |bn betj}eh|co clyn`|jeh |nta( P~`b lc|c

    {e~ol |cgn |bn ieta ei @E4 `eh`nh|tc|jeh vteijonp ancp~tnl c| |bn ic`np et `ethntp

    ei |bn @Y/ vo~p c ynt|j`co vteijon ei betj}eh|co {jhl pvnnl {j|bjh |bn @Y/ de|b itea

    kte~hl onyno ~v |e |bn bnjkb|/ b (

    Onn "3::2* v~dojpbnl ch cvvterjac|n an|bel iet np|jac|jhk |bn ynt|j`co io~r |nta

    "|nta JJJ jh ns~c|jeh 3(4* c| ch nllz `eyctjch`n |e{nt/ ~pjhk m~p| |bn p|chlctl

    jhp|t~anh|c|jeh hetacooz ~pnl |e ed|cjh |bn nllz io~r "|nta JJ/ ns( 3(4* chl p|etckn

    |nta "|nta J/ ns( 3(4*/ j(n( |bn pehj` chnaean|nt chl JTKC/ chl |e{nt @E4

    `eh`nh|tc|jeh vteijon tnpvn`|jynoz( Onn ~pnp |bn javoj`j| cpp~av|jeh |bc| |bn ynt|j`co

    clyn`|jeh ynoe`j|z/ { / {joo ln`tncpn ojhnctoz itea |bn |ev ei |bn @Y c| bnjkb|/ b /

    le{h |e }nte c| kte~hl onyno( Onnp cvvterjac|jeh |e ynt|j`co clyn`|jeh jp kjynh jh

    ns~c|jeh 3(0=

    " *``{ bb " 3!0*

    {bntn b{ chl b` ctn |navetco anchp ei ynt|j`co ynoe`j|z chl @E4 `eh`nh|tc|jeh

    ancp~tnl eynt |bn cyntckjhk vntjel/ c| |bn pehj` chnaean|nt chl JTKC c| bnjkb|/

    b / chl ` tnvtnpnh|p |bn ynt|j`cooz jh|nktc|nl yco~np ei ` ancp~tnl eh |bn |e{nt

    @E4 vteijon( Ns~c|jeh 3(0 `ch dn ~pnl |e tnvoc`n |nta JJJ jh ns~c|jeh 3(4 chl bcp

    dnnh ~pnl jh pnyntco p|~ljnp jhyeoyjhk clyn`|jeh "Injknh{jh|nt n| co( 466*/ be{nynt |bn an|bel jp |bn p~dmn`| ei `eh|teyntpz jh |bn oj|ntc|~tn chl

    bcp dnnh `tj|j`jpnl dz Ijhhjkch "3:::*( On~hjhk n| co( "4662* `cttjnl e~| ch

    nrvntjanh| jhyeoyjhk c i~ooz jhp|t~anh|nl `eh|teo yeo~an "@Y* chl ie~hl |bc| Onnp

    ns~c|jeh "ns( 3(0* kcyn tnp~o|p icye~tcdoz `eavctcdon |e c yjkete~p h~antj`co

    javonanh|c|jeh ei |nta JJJ jh ns~c|jeh 3(4/ vteyjlnl |bc| |bn ynt|j`co clyn`|jeh

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    17/140

    36

    ynoe`j|z/ b{ / {cp np|jac|nl ~pjhk |bn betj}eh|co ljyntknh`n an|bel ei Yj`gntp chl

    Acbt| "4669* chl Bnjhnp`b n| co( "466;*(

    3(0 Ajppjhk io~rnp c| nllz `eyctjch`n pj|np

    Tnpnct`bntp p~`b cp Acobj n| co( "3::2* chl Chltncn n| co( "4664* tnvet|nl octkn

    ~v|cgnp @E4 dz |bn Cac}ehjch |tevj`co ietnp|/ jhlj`c|jhk |bnpn ietnp|p {ntn c octknt

    pjhg ei @E4 |bch bcl dnnh vtnyje~poz jhlj`c|nl dz `bcadnt ancp~tnanh|p( Ajoont n|

    co( "466

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    18/140

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    19/140

    34

    tnpvjtc|jeh aelnop ~pnl |e ed|cjh io~rnp dnoe{ |bn -~ |btnpbeol/ |bnh c pjkhjij`ch|

    eyntnp|jac|jeh ei he`|~thco tnpvjtc|jeh io~r `ch tnp~o|(

    \b~p |bn -~ |btnpbeol an|bel `ch pjkhjij`ch|oz eyntnp|jac|n chl pjkhjij`ch|oz

    ~hlntnp|jac|n HNN/ lnvnhljhk be{ j| jp cvvojnl et {bntn |bn-

    ~ yco~n jp ancp~tnl(

    C veppjdon {cz e~| ei |bjp javcppn jp |bn pe `coonl p~vnt!pj|n "Ebg~de n| co( 466;*

    {bntn yntz nr|nhpjyn |tclj|jehco ijnol ancp~tnanh|p ei n`epzp|na io~rnp "p~`b cp

    `bcadnt ancp~tnanh|p* ctn ~pnl |e `tepp `ehp|tcjh |bn yntz dnp| lcz|jan nllz

    `eyctjch`n io~r lc|c( ^hiet|~hc|noz/ |bn p~vnt!pj|n cvvtec`b jp yntz achve{nt

    jh|nhpjyn chl nrvnhpjyn/ |b~p dnjhk ~hp~j|cdon iet |bn acmetj|z ei IO^RHN\ pj|np(

    Che|bnt co|nthc|jyn cvvtec`b jp |e c||nav| |e ljtn`|oz ancp~tn |bn ajppjhk io~rnp

    cntelzhcaj`cooz/ j(n( |bn ynt|j`co chl betj}eh|co clyn`|jeh |ntap/ |ntap JJJ chl JY jh

    ns~c|jeh 3(4( Be{nynt/ cp {n pbcoo pnn oc|nt/ |bjp |ee jp vtedcdoz |ee achve{nt

    jh|nhpjyn chl nrvnhpjyn iet lnvoezanh| knhntcooz c`tepp IO^RHN\(

    3(< Nhntkz dcoch`n `oep~tn chl an`bchjpap iet ajppjhk io~rnp

    \bn nhntkz dcoch`n c| Nct|bp p~tic`n jp ei|nh he| `oepnl jh vtc`|jpn( Hn| tcljc|jeh

    chl kte~hl bnc| io~r |zvj`cooz nr`nnl |bn |e|co |~td~onh| io~rnp ei pnhpjdon chl oc|nh|

    bnc| dz cde~| 46. "Iegnh chl Eh`onz 3::>*( \bjp p|tehkoz p~kknp|p |bc| e|bnt

    |~td~onh| io~rnp p~`b cp @E4 ancp~tnl c| nllz `eyctjch`n |e{ntp acz p~iint itea c

    pjajoct oc`g ei `oep~tn |bc| acz achjinp| j|pnoi cp ajppjhk io~r( Iegnh "4662*

    tnyjn{nl v~doj`c|jehp `eh`nthjhk |bn nhntkz dcoch`n `oep~tn vtedona itea |bn vcp|

    46 znctp chl `can |e |bn `eh`o~pjeh |bc| |bn nhntkz dcoch`n `ch vtedcdoz ehoz dn

    `oepnl eh |bn octknt ochlp`cvn p`con jh bn|nteknhne~p ochlp`cvnp( \bjp jp p|tehkoz

    p~kknp|jyn ei |bn nrjp|nh`n ei octkn!p`con betj}eh|co clyn`|jyn vte`nppnp et octkn

    p`con nlljnp |tchpvet|jhk p`coctp c{cz itea nllz `eyctjch`n |e{ntp(

    C~djhn| "4662* ojp|p |btnn vtjh`jvco vte`nppnp cp dnjhk ojgnoz iet |bn ~hlntnp|jac|jeh

    ei io~rnp c| nllz `eyctjch`n pj|np/ aep|oz c| hjkb|(

    3* Jh|ntaj||nh| |~td~onh| nynh|p "J\Np*

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    20/140

    30

    4* Ochl dtnn}np0* Ktcyj|z%gc|cdc|j` ioe{p

    Jh|ntaj||nh| |~td~onh| nynh|p "J\Np*/ bcyn dnnh ljp`~ppnl nctojnt {j|b tnpvn`| |e |bn

    -~ |btnpbeol( Be{nynt/ dn`c~pn ei |bn pbet| l~tc|jeh ei J\Np |bnz acz he| pc|jpiz

    |bn p|c|jehctj|z tns~jtnanh| ei |bn nllz `eyctjch`n an|bel chl acz tns~jtn |bn ~pn

    ei yctjcdon onhk|b cyntckjhk vntjelp |e tnpeoyn |bn p`coct io~rnp |bnz ctn |tchpvet|jhk(

    Ochl dtnn}np ctn knhntc|nl dz c ljiintnh| vte`npp |e ktcyj|z ioe{p d~| bcyn c pjajoct

    niin`| jh tnaeyjhk p`coctp itea |bn yj`jhj|z ei ch nllz `eyctjch`n |e{nt dz

    clyn`|jeh "C~djhn| 4662*/ pnn ns~c|jeh 3(4/ |ntap JJJ chl JY(

    Ktcyj|z et gc|cdc|j` |zvn lnhpj|z ioe{p ctn dnojnynl |e dn |bn aep| javet|ch|

    an`bchjpa iet `c~pjhk |bn ajppjhk tnpvjtc|jeh io~r c| hjkb|/ chl jp vtedcdoz |bn

    aep| javet|ch| ic`|et jh |bn ~hlntnp|jac|jeh ei HNN {bnh cyntcknl eynt |bn {beon

    lj~thco z`on "Ke~olnh n| co( 4669/ Dno`bnt n| co( 4662*(

    L~tjhk hjkb||jan/ |bn c|aepvbntj` de~hlctz ocznt jp |zvj`cooz p|cdoz p|tc|jijnl/ {j|b c

    |navntc|~tn jhyntpjeh ei|nh nrjp|jhk {j|bjh c in{ 36p ei an|tnp ei |bn p~tic`n

    "Dno`bnt n| co( 4662*( \bjp jp npvn`jcooz |t~n ~hlnt ch|j!`z`oehj` `ehlj|jehp {j|b `onct

    pgjnp chl poc`g {jhlp "Acbt| 3:::*( Jh bjooz |nttcjh |bn lnhpnt cjt c| |bn de||ea ei |bn

    jhyntpjeh `ch ioe{ le{hbjoo ~hlnt ktcyj|z |e ieta c gc|cdc|j` ltcjhckn ioe{( Acbt|

    "3:23* bcp p~kknp|nl |bc| p~`b ltcjhckn ioe{p `ch ieta eh poevnp cp oe{ cp 3 lnktnn/

    chl Dno`bnt n| co( "4662* lnaehp|tc|n |bc| iet c ietnp|nl poevn |bn |nhlnh`z iet c

    ltcjhckn ioe{ |e ieta jp lnvnhlch| eh eyntcoo poevn onhk|b tc|bnt |bch poevn chkon/

    {j|b |bn `ehpns~nh`n |bc| coaep| coo ietnp|nl ochl p~tic`np ctn ve|nh|jcooz ciin`|nl dz

    betj}eh|co clyn`|jeh ei p`coctp c| hjkb| "|nta JY jh ns~c|jeh 3(4*(

    Gc|cdc|j` ioe{p {j|bjh ietnp|p ctn ei|nh `bchhnoonl dz |bn |t~hg pvc`n dnoe{ |bn

    `chevz "C~djhn| n| co( 4660/ C~djhn| 4662*/ cp {cp edpntynl jh |bn nrvntjanh|

    `cttjnl e~| jh |bn \~adct~adc ietnp|/ C~p|tcojc/ lnp`tjdnl jh `bcv|nt 4 ei |bjp

    ljppnt|c|jeh/ chl On~hjhk n| co( "4662*(

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    21/140

    3* `eoon`|nl 0> lczp ei lc|c jh |bnp~aant ei 4664/ tnp~o|jhk jh |bn anch lj~thco io~r `~tyn pbe{h jh ijk~tn 3(0d( \bjp

    `onctoz pbe{p |bc| clyn`|jeh leajhc|np |bn pj|n c| hjkb| "io~rnp ei dn|{nnh > chl 36

    aeo a!4

    p!3

    */ {j|b de|b betj}eh|co chl ynt|j`co clyn`|jeh io~rnp c`|jhk jh |bn pcan

    ljtn`|jeh "e~| ei |bn @Y*( \bn jh`o~pjeh ei |bn clyn`|jeh |ntap iet |bn Tnheh pj|n

    tnl~`nl |bn cvvctnh| `ctdeh pjhg ei |bn ietnp| dz 9>. "itea 0(4: |e 3(3> k @ a!4

    l!3

    *

    `eavctnl |e ~pjhk |bn p|chlctl N~teio~r -~ |btnpbeol an|bel(

    Ijk~tn 3(0` pbe{p c p`bnac|j` yjn{ ei c 0L tbeadejl pn|~v ~pnl dz Zj n| co( "4662*

    jh |bnjt nrvntjanh| |e ancp~tn |bn betj}eh|co chl ynt|j`co clyn`|jeh |ntap c| |bn

    Hj{e| Tjlkn Cantjio~r pj|n/ jh |bn Te`gz Ae~h|cjhp/ ^PC( \bn |evektcvbj` poevn

    ei |bn pj|n {cp < lnktnnp( Ehoz |btnn ei |bn ie~t |e{ntp pbe{h jh ijk~tn 3(0` {ntn

    ~pnl jh chz vct|j`~oct ancp~tjhk `cavcjkh/ d~| |bn ncp| |e{nt "|bn nllz `eyctjch`n

    |e{nt* {cp co{czp jh`o~lnl( \bn betj}eh|co clyn`|jeh io~r {cp `co`~oc|nl dz c ieta

    ei |tjchk~oc|jeh dn|{nnh @E4 `eh`nh|tc|jeh chl betj}eh|co {jhl pvnnl yco~np

    dn|{nnh |bn |btnn |e{ntp cp lnp`tjdnl jh Zj n| co( "4662*/ ~pjhk |bn chkonp chhe|c|nl

    jh ijk~tn 3(0`( Ynt|j`co clyn`|jeh {cp `co`~oc|nl c``etljhk |e Onn "3::2*(

    Iet |bn Hj{e| Tjlkn pj|n/ Zj n| co( "4662* ln|ntajhnl |bc| anch p~aant|jan

    clyn`|jeh io~rnp c| hjkb| {ntn/ 4(;9 aeo a!4

    p!3

    iet betj}eh|co clyn`|jeh "e~| ei |bn

    @Y*/ chl 3(

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    25/140

    32

    \bn ynt|j`co chl betj}eh|co clyn`|jeh |ntap c| |bn \bctchl| pj|n {ntn ie~hl |e bcyn

    evvepj|n pjkhp d~| pjajoct ackhj|~ln "anch 4(< k @ a!4

    l!3

    */ {j|b |bn ynt|j`co |nta

    pojkb|oz leajhc|jhk kjyjhk c anch io~r e~| ei |bn @Y ei 6(42 k @ a!4

    l!3

    iet |bn 46

    l~tc|jeh ei |bn nrvntjanh|(

    P|cndont n| co( "466* "`eo~ah 3/

    te{ * lenp jhlnnl jhlj`c|n

    aetn ynkn|c|jeh "chl bnh`n c octknt pe~t`n ei hjkb||jan @E4 tnpvjtc|jeh* |e{ctlp |bnle{h{jhl nhl ei |bn Tnheh @Y( Ijk~tn 3(< vtnlj`|p |bc| |bn pj|n ei |bn

    \~adct~adc clyn`|jeh nrvntjanh|/ lnp`tjdnl jh `bcv|nt 4 chl On~hjhk n| co(

    "4662*/ {joo bcyn c pjajoct vepj|jyn ktcljnh| ei tnpvjtc|jeh io~r pe~t`n lnhpj|z c`tepp

    |bn @Y( Be{nynt/ |bjp bcp zn| |e dn `bn`gnl(

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    26/140

    3:

    Ijk~tn 3!< C `ocppjij`c|jeh p`bnan iet ljiintnh| clyn`|jeh vc||nthp jh tnoc|jeh |e @E4 pe~t`n jh|nhpj|z

    ljp|tjd~|jehp chl acpp ioe{ `bctc`|ntjp|j`p( \cgnh itea C~djhn| "4662*(

    Cddtnyjc|jehp ctn= BC/ betj}eh|co clyn`|jeh7 YC/ ynt|j`co clyn`|jeh7 HNN/ djeoekj`co

    pe~t`n%pjhg7 D/ Dnokj~a7 L/ Kntachz7 @HL/ @chclc7 J/ J|coz7 chl I/

    Itch`n( Jh |bn pe~t`n jh|nhpj|z `eo~ah / R tnvtnpnh|p |bn le{h{jhl

    vepj|jeh( \cgnh itea C~djhn| "4662*(

    H(D tnintnh`n |e \~adct~adc bcp dnnh cllnl cp c aeljij`c|jeh(

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    27/140

    46

    Pj|np pbe{h jh ijk~tn 3(

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    28/140

    43

    3(9 @chevz ioe{ aelnop iet `eavonr |nttcjh

    Ijhhjkch "4662* ljyjlnp |bn teonp ac|bnac|j`co aelnop `ch vocz jh p~tic`n io~r

    ancp~tnanh| jh|e |{e ljp|jh`| kte~vp=

    3* Tnoc|jynoz pjavon chcoz|j`co chl h~antj`co aelnop |bc| `ch cppnpp |bn ojgnozpnyntj|z ei clyn`|jeh c| c kjynh io~r pj|n/ chl cope bnov jh |bn vochhjhk ei

    ancp~tnanh| p|tc|nkjnp(

    4* Lc|c cppjajoc|jeh aelnop(C| vtnpnh| ehoz aelnop ei |zvn 3 nrjp| pe {n {joo ljp`~pp |bna ijtp|( Jh`o~lnl jh |bjp

    ijtp| |zvn ctn c h~adnt ei pjavon `chevz ioe{ aelnop |bc| `ch lnp`tjdn cjt ioe{

    |bte~kb c lnhpn `chevz eynt knh|oz poevjhk 4!ljanhpjehco "4L* |nttcjh(

    Ehn nrcavon jp |bn chcoz|j`co aelno ei Ijhhjkch chl Dno`bnt "466c/ {bj`b pbe{p hetacojpnl betj}eh|co {jhl ynoe`j|z vteijonp

    c`tepp c 4L Kc~ppjch bjoo ei {jl|b 4O/ `eyntnl jh c lnhpn `chevz ei bnjkb|/ b( \bn

    cdeyn `chevz {jhl doe{p itea oni|!|e!tjkb| eynt |bn nh|jtn {jl|b ei |bn bjoo(

    Be{nynt/ l~n |e vtnpp~tn vnt|~tdc|jeh niin`|p/ |bn cjtioe{ jh |bn oe{nt vct| ei |bn

    `chevz dn`eanp tnyntpnl jh |bn jaanljc|n onn ei |bn bjoo`tnp|( \bjp tnyntpnl cjtioe{

    bcp |bn javet|ch| `ehpns~nh`n ei `c~pjhk ioe{ `ehyntknh`n c| |bn bjoo`tnp| chl |bn

    veppjdon nmn`|jeh ei p`coctp p~`b cp @E4 itea |bn ietnp| `chevz( \e lnaehp|tc|n |bjpvejh|/ ijk~tn 3(>d pbe{p e~|v~| itea c aelno dz Gc|~o n| co( "4669* |bc| ~pnp

    Ijhhjkch chl Dno`bntp {jhl ijnol itea ijk~tn 3(>c/ |e ltjyn ch nllz ljii~pjeh aelno

    ei |~td~onh| io~rnp "Dno`bnt c| co( 4662*( Ijk~tn 3(>d pbe{p ioe{ `ehyntknh`n coehk

    |bn bjoo`tnp| bcp jhlnnl `tnc|nl c vo~an ei @E4 |bc| cvvnctp |e dn nantkjhk itea |bn

    `chevz( @onctoz |bn bjoo`tnp| {e~ol he| dn c {jpn `bej`n ei oe`c|jeh iet ch nllz

    `eyctjch`n |e{nt/ cp j| {e~ol dn ojgnoz |e p~iint itea ynt|j`co clyn`|jeh( Jh cllj|jeh/

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    29/140

    44

    Ijk~tn 3!> Niin`|p ei ch jpeoc|nl Kc~ppjch bjoo eh {jhl pvnnlp chl p`coctp {j|bjh chl cdeyn c `chevz(

    "c* Hetacojpnl {jhl pvnnl vteijonp c`tepp |bn bjoo/ {j|b c `chevz ei bnjkb|/ b( \bn peojl ojhnp ctn {jhl

    pvnnl vteijonp cdeyn |bn bjoo `co`~oc|nl ~pjhk |bn aelno ei Ijhhjkch chl Dno`bnt "466

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    30/140

    40

    e|bnt tnp~o|p itea Gc|~op aelno "he| pbe{h* jhlj`c|n octkn `bchknp jh |bn |~td~onh|

    nllz `eyctjch`n io~r cp ehn `teppnp |bn bjoo `tnp|/ |bc| {e~ol tnhlnt |bn pj|n

    ~hp~j|cdon cp c pe~t`n ei tnvtnpnh|c|jyn n`epzp|na io~r yco~np(

    \bn Ijhhjkch chl Dno`bnt "466*(

    [jhl ioe{ chl p`coct |tchpvet| c| ietnp| nlknp bcp dnnh aelnoonl dz Pekc`bny n| co(

    "4662*( \bn aelnoojhk ei p~`b ljp`eh|jh~j|jnp jp vct|j`~octoz javet|ch| jh

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    31/140

    4

    ln|ntajhjhk |bn in|`b ei beaeknhne~p ietnp| |bc| ch nllz `eyctjch`n |e{nt a~p|

    bcyn jh etlnt |e cyejl clyn`|jeh ciin`|p itea |bn ietnp| nlkn "|bn in|`b a~p| dn c|

    oncp| * {j|b `ehyntknh`n c| |bn bjoo tjlkn( \bnh/ cp

    p|cdjoj|z jh`tncpnp |bn `ehyntknh`n }ehn pvoj|p chl p|ct|p |e aeyn le{h nc`b pjln ei

    |bn bjoo ~h|jo ch IO ei ehn jp tnc`bnl/ tnp~o|jhk jh |bn pj|~c|jeh ei gc|cdc|j` ioe{p

    lnp`nhljhk |bn nh|jtn onhk|b ei de|b pjlnp ei |bn bjoo/ {j|b `ehyntknh| }ehnp c| |bn

    dcpn chl c ljyntknh| }ehn c| |bn bjoo `tnp|( \bnh/ cp IO ln`tncpnp i~t|bnt |bn

    ljp|tjd~|jeh ei `ehyntknh| chl ljyntknh| }ehnp `eh|jh~np |e pbji|(

    \bn `ehpns~nh`n ei |bjp chcozpjp jp |bc| |bn oe`c|jehp c| {bj`b cjt jp nantkjhk itea

    |bn `chevz "`ehyntknh`n }ehnp*/ et dnjhk nh|tcjhnl jh|e |bn `chevz "ljyntknh`n

    }ehnp*/ {joo pbji| c`tepp c bjooz ochlp`cvn ji p|cdjoj|z yctjnp( \bjp anchp |bc| ji p~`b c

    `ehyntknh`n et ljyntknh`n }ehn `teppnp |bn oe`c|jeh ei ch nllz `eyctjch`n |e{nt/

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    33/140

    49

    Ijk~tn 3!;P`bnac|j` |cgnh itea Dno`bnt n| co( "4662*/ pbe{jhk iet`np cdeyn chl dnoe{ c `chevz ehc pjh~pejlco bjoo cp c i~h`|jeh ei Ite~ln h~adnt/ IO "jhlj`c|jhk p|cdjoj|z*( \bn |ev ei |bn ietnp| `chevz

    jp jhlj`c|nl dz |bn lcpbnl ojhn( Cdeyn |bn `chevz |bn ctte{p jhlj`c|n |bn bzltep|c|j` vtnpp~tn ktcljnh|

    ehoz( Dnoe{ |bn `chevz |ev "lcpbnl ojhn* |bn ctte{p tnvtnpnh| |bn dcoch`n dn|{nnh |bn bzltelzhcaj`

    vtnpp~tn ktcljnh| chl |bn bzltep|c|j` vtnpp~tn ktcljnh|( \bn ackhj|~lnp ei |bn iet`np ctn kjynh dz |bn

    onhk|bp ei |bn ctte{p( Ynt|j`co le||nl ojhnp pbe{ tnkjehp ei ljyntknh`n {j|bjh |bn `chevz/ {bjon

    ynt|j`co lcpb!le||nl ojhnp jhlj`c|n tnkjehp ei `ehyntknh`n {j|bjh |bn `chevz( Lnp`nh| c| |bn `chevz

    |ev jp nrvn`|nl eynt |bn tnkjehp ei ljyntknh`n/ chl cp`nh| c| |bn `chevz |ev jp nrvn`|nl eynt tnkjehp

    ei ehyntknh`n( Ijk~tn |nr| clcv|nl itea Dno`bnt n| co( 4662(

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    34/140

    4;

    |bc| |e{nt {joo dn p~dmn`| |e c octkn clyn`|jeh |nta "pnn |ntap JJJ chl JY jh ns~c|jeh

    3(4*( ^hiet|~hc|noz/ he p~`b aelno nrjp|p c| vtnpnh| |e vtnlj`| |bnpn niin`|p c`tepp c

    tnco 0L ochlp`cvn(

    \bn aelnop lnp`tjdnl pe ict/ co|be~kb ~pni~o jh `beepjhk oe`c|jehp iet ve|nh|jco hn{

    nllz `eyctjch`n pj|np/ cope tnjhiet`n be{ jh|tc`|cdon |bn clyn`|jeh vtedona acz dn

    iet |bn nllz `eyctjch`n an|bel(

    Ehn veppjdon {cz jh {bj`b |bn pjavon aelnop lnp`tjdnl pe ict/ `e~ol dn ~pnl jh c

    achhnt oncljhk |e s~ch|j|c|jyn clyn`|jeh np|jac|np iet c kjynh nllz `eyctjch`n |e{nt

    jp |e ~pn c lc|c ltjynh |n`bhjs~n lnp`tjdnl dz Acjlanh| "3::0*(

    Acjlanh| lnp`tjdnp |bn `ehp|t~`|jeh ei c lc|c ltjynh bzlteoekj`co aelno ~pjhk c

    knektcvbj`co jhietac|jeh pzp|na "KJP* |e `tnc|n c ~hj| bzltektcvb iet c `eavonr

    ochlp`cvn/ `ehpjp|jhk ei |evektcvbz "ljkj|co nonyc|jeh aelno/ LNA*/ ljyntpn

    ynkn|c|jeh chl pejo "ochl `eynt acv*/ chl tcjhicoo "tcjh kc~kn lc|c*( \bn

    ac|bnac|j`co t~onp et aelnop ~pnl dz Acjlanh| {ntn yntz pjavon/ d~| jh|ntc`|nl c|

    |bn ktjl!`noo chl bzlteoekj`co `c|`banh| onyno |e vtel~`n c `tnljdon tnp~o|( [e~ol j|

    dn veppjdon |e `tnc|n c pjajoct aelno iet gc|cdc|j` ioe{p5 @nt|cjhoz j| {e~ol dn c

    aetn `eavonr aelno/ cp |bn io~jl {e~ol dn `eavtnppjdon chl |bn vtedona aetn 0!

    ljanhpjehco jh hc|~tn( Be{nynt/ j| acz dn {et|b jhynp|jkc|jhk ehoz |e t~on j| e~|/ cp

    j| {e~ol ojgnoz dn ict onpp `eav~|nt jh|nhpjyn |bch c |tclj|jehco lc|c cppjajoc|jeh

    aelno(

    Ehn jh|tjk~jhk veppjdjoj|z jp |bc| co|be~kb |bn tnp~o|p ei p~`b c aelno vtedcdoz {e~ol

    he| dn c``~tc|n nhe~kb |e dn ~pni~o iet jhljyjl~co io~r pj|np/ |bnz ajkb| dn ~pni~o c|

    |bn tnkjehco p`con/ n`bejhk Iegnhp "4662* yjn{ |bc| |bn nhntkz dcoch`n `oep~tn

    vtedona jp ehoz peoycdon c| |bn tnkjehco p`con( \bn lc|c oczntp |bc| `e~ol dn ~pnl |e

    ltjyn p~`b c aelno ajkb| jh`o~ln/ jh cllj|jeh |e c ljkj|co nonyc|jeh aelno/ ochl

    `eynt lc|c/ chl pzhev|j` {jhl lc|c7 tnae|noz pnhpnl lc|c p~`b cp |bntaco tcljch`n

    jacknp |bc| ctn vteyjlnl dz |bn CP\NT pnhpet ehdectl |bn \nttc pc|nooj|n( CP\NT

    |bntaco jacknp {ntn ~pnl dz Keolnh n| co( "4669* jh |bnjt p|~lz ei he`|~thco

    ltcjhckn chl veeojhk jh |bn Cac}eh ietnp|/ chl `e~ol dn ~pnl dz c KJP dcpnl aelno

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    35/140

    42

    |e `ehp|tcjh `chevz chl p~tic`n |navntc|~tnp( Ji p~`b c aelno `e~ol dn acln |e

    {etg/ j| ajkb| dn veppjdon |e j|ntc|n j| |e cppjajoc|n |bn nllz `eyctjch`n lc|c(

    Be{nynt/ p~`b j|ntc|jeh {e~ol dn yntz jhniij`jnh| ji lehn ~pjhk c KJP(

    3(; Lc|c cppjajoc|jeh aelnop

    Nrcavonp ei lc|c cppjajoc|jeh aelnop jh ~pn |elcz ctn |bn koedco chl anpep`con

    h~antj`co {nc|bnt vtnlj`|jeh "H[V* N~ontjch aelnop ~pnl dz {nc|bnt ietn`cp|jhk

    cknh`jnp( P~`b aelnop ctn cdon |e `eh|jh~cooz jhknp| et cppjajoc|n {nc|bnt p|c|jeh

    edpntyc|jehp chl jhietac|jeh lntjynl itea {nc|bnt pc|nooj|n jacknp/ jh etlnt |e

    vteyjln c he{!`cp| ei `~ttnh| {nc|bnt `ehlj|jehp( \bnpn aelnop vteyjln {nc|bnt

    ietn`cp| jhietac|jeh dz pjavoz on||jhk |bnh t~h jh|e |bnjt e{h i~|~tn iet c in{

    lczp ei pja~oc|nl |jan(

    Ji lc|c cppjajoc|jeh aelnop ctn nynt `ehp|t~`|nl iet ~pn {j|b nllz `eyctjch`n |e{ntp

    jh `eavonr |nttcjh/ |bnz {joo vtedcdoz dn N~ontjch aelnop ~pjhk c @ct|npjch ktjl/

    {j|b nc`b ei |bn achz |be~pchlp ei `noop jh |bn aelno ktjl `ehp|j|~|jhk ch

    jhlnvnhlnh| `eh|teo yeo~an "@Y* c`tepp {bj`b |bn clyn`|jeh |ntap `ch dn nyco~c|nl

    "pnn ijk~tn 3(4*(

    \bn aelnop |cpg {joo dn pjavont |bch H[V jh |bc| ehoz bjhl!`cp|jhk/ j(n( |bn

    aelnoojhk ei vcp| `ehlj|jehp/ {joo dn tns~jtnl( Be{nynt/ e|bnt cpvn`|p ei |bn lc|c

    cppjajoc|jeh aelnop tns~jtnl |e clltnpp |bn vtedona ei clyn`|jeh c| nllz `eyctjch`n

    pj|np {joo dn ict aetn `bcoonhkjhk/ cp ctn ojp|nl dnoe{=

    3* \bn tns~jtnl aelno ktjl `noo pj}n {joo dn pacoo/ veppjdoz cp pacoo cp 36 |e366 a/ `eavctnl {j|b > |e 36 ga iet anpep`con H[V aelnop( \bjp pacoo

    `noo pj}n jp nppnh|jcooz c k~npp dcpnl eh c s~coj|c|jyn `ehpjlntc|jeh ei |bn

    aj`te!|evektcvbz edpntynl jh |bn yj`jhj|z ei |zvj`co nllz `eyctjch`n

    |e{ntp/ chl j|p niin`| eh gc|cdc|j` ioe{p(

    4* \bn tns~jtnl lc|c cppjajoc|jeh aelnop {joo vtedcdoz hnnl |e dn hnp|nl"Ijhhjkch 4662*/ tc|bnt ojgn c T~ppjch leoo/ {j|b c anpep`con H[V aelno

    bchljhk c|aepvbntj` ioe{ jhietac|jeh le{h |e c de~hlctz ocznt aelno

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    36/140

    4:

    chl |bc| aelno bchljhk lc|c |e c tnkjehco "pcz 36 ga |e >6 ga ps~ctn*

    clyn`|jeh aelno/ chl |bc| tnkjehco aelno ltjyjhk c yntz ln|cjonl

    clyn`|jeh aelno `nh|tnl eh |bn nllz `eyctjch`n |e{nt jh s~np|jeh( P~`b

    ch cvvtec`b {e~ol dn tns~jtnl |e cyejl acppjyn `eav~|c|jehco eyntbnclp

    `c~pnl dz |bn pacoo ktjl `noo pj}n( \bn de~hlctz `ehlj|jeh vtedonap

    dn|{nnh p~`b c aelno bjntct`bz {e~ol dn `bcoonhkjhk cp |bnz {e~ol dn

    jhbntnh|oz p`con lnvnhlch| jh de|b pvc`n chl |jan(

    0* \bn dc`gkte~hl ktjllnl lc|c oczntp p~`b cp |nttcjh "LNA* chl ynkn|c|jeh`eynt/ {e~ol hnnl |e ac|`b |bn pacoonp| aelno ktjl pj}n/ c| oncp| jh |bn

    yj`jhj|z ei |bn nllz `eyctjch`n(

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    37/140

    06

    voc`n l~tjhk 466> chl 4669 c| |bn Ktjiijh ietnp| nllz `eyctjch`n pj|n jh P`e|ochl/

    ^G/ tnp~o|jhk jh c s~coj|c|jyn aelno ei cdeyn `chevz chl jh `chevz cjt ioe{ iet |bc|

    pj|n "`bcv|nt 0*(

    Ijk~tn 3(2c pbe{p c `ct|eeh joo~p|tc|jeh ei |bn der d~lkn| `eh`nv| |bc| ancp~tnl

    |bn ynt|j`co clyn`|jeh/ betj}eh|co clyn`|jeh/ `bchkn jh p|etckn chl ynt|j`co nllz io~r

    ei `ctdeh ljerjln itea |bn `eh|teo yeo~an "@Y* et der pj|~c|nl dnhnc|b |bn |tnn

    `chevz c| |bn \~adct~adc ietnp| pj|n cp jp lnp`tjdnl jh `bcv|nt 4( \bn @Y tnvtnpnh|p

    c yjt|~co `bcadnt eynt c >6 dz >6 an|tn voe| |bte~kb |bn `co`~oc|jeh ei |bn hn|

    n`epzp|na nr`bchkn "HNN* ei `ctdeh ljerjln itea j|p cntelzhcaj` `eavehnh|p

    ancp~tnl eh |bn {coop ei |bn der "@Y* ~pjhk jhp|t~anh|c|jeh/ |bnpn `eavehnh|p

    dnjhk ljcktcaac|j`cooz tnvtnpnh|nl dz |bn tnl ctte{p jh ijk~tn 3(2c(

    \bn |{e Ktjiijh ietnp| nrvntjanh|p lnp`tjdnl jh `bcv|nt 0/ |eeg |bn ieta ei c

    betj}eh|co |tchpn`|/ chl ynt|j`co vteijon ei pehj` chnaean|ntp tnpvn`|jynoz jh cllj|jeh

    |e |bn nrjp|jhk io~r |e{nt( \bn cjt ynoe`j|z lc|c itea |bnpn |{e nrvntjanh|p {cp

    vte`nppnl |e jhynp|jkc|n {jhl ioe{ `e~vojhk niin`|p itea cdeyn |e dnoe{ |bn |tnn

    `chevz eynt knh|oz poevjhk |nttcjh/ ynt|j`co clyn`|jeh/ chl veppjdon ioe{ ljyntknh`n

    niin`|p {j|bjh |bn `chevz/ {j|b pvn`jco tnintnh`n |e |bn veppjdon vtnpnh`n ei gc|cdc|j`

    ioe{p( Ijk~tn 3(2d pbe{p c `ct|eeh tnvtnpnh|c|jeh ei |bjp pn| ei nrvntjanh|p(

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    38/140

    03

    Ijk~tn 3!2 "c* @ct|eeh tnvtnpnh|jhk |bn Der D~lkn| `eh`nv| navoeznl c| |bn \~adct~adc pj|n "|bn

    ln|cjo ei |bn ietnp| `chevz chl `nh|tco |e{nt ctn he| pbe{h*( "d* @ct|eeh tnvtnpnh|c|jeh ei |bn |{e

    Ktjiijh Ietnp| nrvntjanh|p "ehn ~pjhk c |e{nt vteijon chl |bn e|bnt c betj}eh|co |tchpn`| ei ~o|tcpehj`

    chnaean|ntp* jhynp|jkc|jhk `e~vojhk ei {jhl ioe{ itea cdeyn |e dnoe{ |bn `chevz "ln|cjop ei |bn |tnn

    `chevz bcyn dnnh eaj||nl*( Ln|cjonl ljcktcap ei de|b |bn \~adct~adc chl Ktjiijh Ietnp|

    nrvntjanh|co pn|~vp ctn kjynh jh `bcv|ntp 4 chl 0 tnpvn`|jynoz(

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    39/140

    04

    4 \bn \~adct~adc Clyn`|jeh Nrvntjanh|

    4(3 Nrvntjanh|co Pn||jhk

    Cp ljp`~ppnl jh `bcv|nt 3 ei |bjp |bnpjp/ `eh`nth bcp dnnh nrvtnppnl jh |bn nllz

    `eyctjch`n oj|ntc|~tn "Tc~vc`b chl Ijhhjkch 3::;/ Ijhhjkch/ 4660/ Gc|~o n| co/ 4660*

    |bc| betj}eh|co chl ynt|j`co clyn`|jeh niin`|p ~hlnt p|cdon `ehlj|jehp ctn c pjkhjij`ch|

    vtedona "`c~pjhk nttet ackhj|~lnp ei |bn etlnt ei 366. ei pjkhco* iet |bn koedco

    nllz eyctjch`n |e{nt hn|{etg/ IO^RHN\(

    \bn v~tvepn ei |bn nrvntjanh| tnvet|nl jh |bjp `bcv|nt/ {cp |e ljtn`|oz ancp~tn coo

    |bn @E4 io~r |ntap ciin`|jhk c >6 dz >6 a ctnc {j|bjh c N~`cozv|~p ietnp|/ ~v |e cbnjkb| ei 9a cdeyn kte~hl onyno "cko*/ bnh`niet|b tninttnl |e cp |bn `eh|teo yeo~an

    "@Y*(

    \bnpn io~r |ntap `ehpjp| ei c `bchkn jh p|etckn |nta/ betj}eh|co clyn`|jeh |ntap "iet

    |bn r chl z ljtn`|jehp*/ chl c |nta iet ynt|j`co nllz `eyctjch`n chl ynt|j`co

    clyn`|jeh( \cgnh |ekn|bnt |bnpn |ntap `ch dn ~pnl |e `co`~oc|n |bn hn| n`epzp|na

    nr`bchkn ei @E4 "HNN* dn|{nnh |bn ctnc ~hlnt `ehpjlntc|jeh "dnoe{ 9 a cko* chl

    |bn p~tte~hljhk c|aepvbntn( HNN `ch dn {tj||nh cp=

    6 6 6

    66 6

    6

    6 6

    + +

    6

    " * " * " * " *

    " * " * " * " *

    b b

    l` ` `

    | | |

    b b

    l b` `

    r O r

    b b

    l b` `

    z O z

    b

    `l `

    `I l} l}

    |

    ` ~P } } l} P } } l}

    O

    ` yP } } l} P } } l}

    O

    ` { { l}}

    1 1

    1 1

    1 1

    1

    '

    '

    ' '

    "4!3*

    {bntn `I tnvtnpnh|p HNN/ ` jp |bn aeon itc`|jeh ei @E4 "vva*/ l` jp |bn

    `eh`nh|tc|jeh ei ltz cjt "aeo a!0

    */ |tnvtnpnh|p |bn onhk|b ei |bn cyntckjhk |jan

    vntjel/ b jp bnjkb| ei |bn @Y "9 a*/O jp |bn onhk|b ei |bn @Y pjlnp et ic`np ">6 a*/ ~

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    40/140

    00

    Ijk~tn 4!3 Oe`c|jeh ei |bn \~adct~ac ijnol pj|n {j|bjh C~p|tcojc/ chl {j|b tnpvn`| |e hnctdz |e{hp

    chl `j|jnp "jhpn|*(Acv ei C~p|tcojc/ v~doj` leacjh/ `e~t|npz ei |bn ^hjyntpj|z ei \nrcp Ojdtctjnp/ \bn

    ^hjyntpj|z ei \nrcp c| C~p|jh( Jhpn| acv `e~t|npz ei |bn E}Io~r {ndpj|n

    "b||v=%%{{{(`act(`pjte(c~%e}io~r%*(

    Ijk~tn 4!4 P`bnac|j` ljcktca ei |bn betj}eh|co clyn`|jeh nrvntjanh|co pn| ~v jh tnoc|jeh |e |bn ietnp|

    `chevz%eynt!p|etnz chl |bn ~hlntdt~pb%~hlntp|etnz/ pbe{jhk |bn clyn`|jeh `eh|teo yeo~an "@Y*( \bn

    tn`|chk~oct yeo~an jp ietanl dz |bn ie~t @Y ic`np nc`b ei {bj`b jp >6 a jh onhk|b chl 9 a bjkb/

    `eavtjpnl ei vntietc|nl betj}eh|co pcavojhk |~dnp/ chl c ojl `ehpjp|jhk ei ch nllz `eyctjch`n

    pzp|na pj|~c|nl 9 a cdeyn kte~hl onyno( \bn |evektcvbj` poevn `eavehnh|p ei |bn kte~hl p~tic`n ctn

    jhlj`c|nl cp 0(> lnktnnp chl 0(6 lnktnnp jh |bn r chl z ljtn`|jehp( \bn chhe|c|jehp eh |bn @Y ic`np

    tnint |e ns~c|jeh 4(3( Itea On~hjhk n| co( "4662*(

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    41/140

    0 a

    chl bcl j|p |ev c| cte~hl

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    42/140

    0>

    Ijk~tn 4!0 \bn \~adct~adc clyn`|jeh nrvntjanh| `eh|teo yeo~an "@Y*/ pbe{jhk c ljcktcaac|j`

    tnvtnpnh|c|jeh ei |bn kcp pcavojhk {coop( \bn lcpbnl ojhnp tnvtnpnh| |bn vntietc|nl |~djhk |bte~kb

    {bj`b cjt {cp pcavonl( \bn acp| chl 9 a pehj` chnaean|nt jp pbe{h jh |bn `nh|tn ei |bn @Y( Cope

    pbe{h ctn pehj` 3(9> a chnaean|ntp hnct |bn ajllon ei nc`b ic`n ei |bn @Y( He|n= jh|ntanljc|n

    p~vvet| veonp bcyn dnnh oni| e~| iet `octj|z(Aeljijnl itea On~hjhk n| co( "4662*(

    Ijk~tn 4!< Chhe|c|nl vbe|ektcvb ei |bn `nh|tco 9 a acp|/ pbe{jhk ln|cjo ei |bn 4L pehj`

    chnaean|ntp vteyjlnl chl oekknl dz @PJTE/ chl |bn 0L pehj` chnaean|nt/ evnh vc|b JTKC

    `eadjhc|jeh "9 a cko* vteyjlnl dz @PJTE( 4L chnaean|nt bnjkb|p ctn 6(4/ 6(

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    43/140

    09

    @Y {ntn |bnh vcppnl jh |~th |bte~kb |bn kcp chcozpnt( \bn vtjh`jvco tncpeh iet

    ed|cjhjhk |bn {jhl vteijon pbe{h jh ijk~tn 4(>l {cp |e ed|cjh |bn {njkb|jhk

    i~h`|jehp/ [m/ ~pnl |e `eadjhn |bn cjtioe{ itea nc`b ei |bn pjr onynop eh nc`b @Y

    ic`n( Ijk~tnp 4(>c |e 4(>` pbe{ `tepp voe|p dn|{nnh 3> ajh~|n jh|ntyco edpntyc|jehpei betj}eh|co {jhl pvnnl ancp~tnl c| |bn oe{nt onynop eh |bn 9 a acp|/ chl {jhl

    pvnnlp ancp~tnl c| |bn |ev ei |bn acp| c| 9(< a( Cope pbe{h ctn tnktnppjeh ojhnp

    iet`nl |e vcpp |bte~kb |bn etjkjh iet nc`b ei |bn `tepp voe|p( Jh ijk~tn 4(>l |bn poevnp

    ei |bnpn tnktnppjeh ojhnp bcyn dnnh ~pnl |e ljtn`|oz voe| c hetacojpnl {jhl vteijon/

    P"}*/ ~v |e 9(< a( \bjp hetacojpnl {jhl vteijon jp aelnoonl ~pjhk ch nrvehnh|jco

    i~h`|jeh=

    " * W3 nrv" *QP } c d}1 "4!4*

    {bj`b knhntc|np |bn `~tyn |bte~kb |bn lc|c vejh|p jh ijk~tn 4(>l( Ijk~tn 4(>n pbe{p

    hetacojpnl {jhl pvnnl yco~np `co`~oc|nl ~pjhk ns~c|jeh 4(4 c| bnjkb|p `ettnpvehljhk

    |e |bn kcp pcavojhk |~dnp bnjkb|p "6(4/ 6(i pbe{p |bn tnp~o|ch| vteijon ei hetacojpnl [m yco~np {j|b bnjkb|( \bnpn

    hetacojpnl {njkb|jhk i~h`|jehp {ntn ~pnl |e pn| |bn ioe{ ycoynp eh |bn kcp ojhnp

    |cgjhk cjt itea |bn vntietc|nl pcavojhk |~dnp |e nc`b ei |bn pjr pcavojhk onynop "6(4/

    6(

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    44/140

    0;

    Ijk~tn 4!> [jhl lc|c `eoon`|nl eh |bn 9 a acp| jh |bn aeh|b dnietn |bn acjh nrvntjanh|/ |bc| {cp

    ~pnl |e `co`~oc|n |bn {njkb|jhk i~h`|jehp [m( "c* p`c||nt voe| ei betj}eh|co {jhl c| 6(> a ckcjhp| 9(< a/

    "d* 3(9 a ckcjhp| 9(< a/ "`* 0(0 a ckcjhp| 9(< a( "l* jp c hetacojpnl {jhl vteijon lntjynl itea |bn

    tnktnppjeh poevnp/ chl aelnoonl ~pjhk ch nrvehnh|jco i~h`|jeh( "n* jp hetacojpnl {jhlp c| |bn bnjkb|p

    ei |bn @Y ic`n pcavojhk |~dnp/ lntjynl itea |bn nrvehnh|jco aelno( "i* pbe{p |bn `ettnpvehljhk{njkb|jhk i~h`|jehp/ [m/ jh hetacojpnl ieta(

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    45/140

    02

    \bn ie~t kcp ojhnp "ehn iet nc`b ic`n* {ntn pcavonl jh |~th dz c pjhkon `oepnl vc|b

    jhitctnl kcp chcozpnt "JTKC* yjc c kcp ojhn p{j|`bjhk ~hj|( \bjp cvvtec`b tnp~o|p jh c

    kcp pcavojhk `z`on |jan ei m~p| ie~t ajh~|np chl pe tns~jtnp c p|nclz {jhl ljtn`|jeh

    ei m~p| |bjp l~tc|jeh( \bjp jp c djk javteynanh| eh vtnyje~p |n`bhjs~np |bc| tns~jtnl~v |e ajh~|np ei `ehp|ch`z ei {jhl ljtn`|jeh(

    Ijyn 4L pehj` chnaean|ntp eh |bn `nh|tco 9 a acp| c| |bn pcan bnjkb| cko cp |bn kcp

    pcavojhk |~djhk jh |bn @Y ic`np cooe{nl |bn pbcvn ei |bn ynt|j`co {jhl vteijon/ P"}*/

    {j|bjh |bn @Y |e dn aehj|etnl(

    \bn 4L pehj` chnaean|nt c| 9 a eh |bn `nh|tco acp| cooe{nl nyco~c|jeh ei |bn

    {njkb|nl jh|nktcop ei |bn @E4 `eh`nh|tc|jehp |e kjyn |bn betj}eh|co clyn`|jeh io~rnp(

    On~hjhk n| co( "4662* vteyjln ch nrvtnppjeh iet `I jh ijhj|n!ljiintnh`n ieta=

    9 9

    / /

    3 3 6

    9 9

    / /

    3 3 6

    9 9

    / /

    3 3 6

    + +

    6

    l

    ` ` m m ` m m

    m m| | |

    l bm ` m m ` m

    m mr O r

    l bm ` m m ` m

    m mz O z

    b`

    l lb

    `I } }

    |

    ` ~[ [

    O

    ` y [ [O

    ` { ` { l}}

    1 11 1

    1 11 1

    1 11 1

    1

    '

    '

    ' '

    "4!

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    46/140

    0:

    Jhp|t~anh|p/ C~p|jh/ \nrcp/ ^PC* chl |bn lc|c itea |bn |{e `oepnl vc|b JTKCPp

    tn`etlnl eh |e c @cavdnoo oekknt "@cavdnoo P`jnh|jij`/ Jh`(/ Het|b Oekch/ ^|cb/

    ^PC*(

    C 0L pehj` chnaean|nt chl evnh vc|b JTKC {ntn cope vteyjlnl c| 9 a cko eh |bn

    `nh|tco acp| |e vteyjln c ojl |e |bn >6 dz >6 dz 9 a @Y/ jh etlnt |e `co`~oc|n |bn

    nllz io~r ei @E4 |bte~kb |bn 9 a vochn( Lc|c itea |bjp 0L pehj` chnaean|nt chl

    evnh vc|b JTKC {ntn oekknl |e |bn Nljhd~tkb ^hjyntpj|z ocv|ev `eav~|nt yjc ch

    TP!

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    47/140

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    48/140

    / |bn cae~h| ei pehj` chnaean|nt lc|c oekknl eh |bn Nljhd~tkb

    ^hjyntpj|z ocv|ev {cp 3(< Kjkcdz|np/ `ehpjp|jhk ei NljPeo vtevtjn|ctz (po| djhctz lc|c

    ijonp( Ci|nt jhj|jco vtn!vte`nppjhk {j|b NljTn pei|{ctn "@onanh|( T(/ 466>7vntp

    `eaa(* et Ocd Yjn{ chl Iet|tch "iet |bn lc|c `eoon`|nl dz @PJTE*/ |bn lc|c {cp

    vte`nppnl ~pjhk c octkn pzp|na ei Aj`tepei| Nr`no pvtnclpbnn|p/ pnn ijk~tn 4(9 iet

    pean p`tnnh pbe|p(

    4(4 Nrvntjanh|co tnp~o|p

    C tnvtnpnh|c|jyn pehj` |navntc|~tn tn`etl iet |bn nrvntjanh|co l~tc|jeh/ ancp~tnl

    m~p| cdeyn |bn ~hlntdt~pb%~hlntp|etnz ynkn|c|jeh jp kjynh jh ijk~tn 4(;/ pbe{jhk c

    |navntc|~tn tchkn ei !0 |e '4; @nopj~p( \bn |{e acmet pzhev|j` iteh|co {nc|bnt

    pzp|nap |bc| `teppnl |bn pj|n l~tjhk |bn nrvntjanh| `ch dn `onctoz pnnh/ pnvctc|nl dz

    |nh lczp ei icjt {nc|bnt cppe`jc|nl {j|b c octkn bjkb vtnpp~tn pzp|na( Ijk~tn 4(2

    pbe{p |bn pzhev|j` {nc|bnt `bct| `ettnpvehljhk |e |bn vcppckn ei |bn ijtp| `eol iteh|

    eynt |bn pj|n eh |bn aethjhk ei |bn >|b

    Act`b 466>(

    \bn ctncp ei bjkb vtnpp~tn c{cz itea |bjp jpeoc|nl iteh| ctn jhlj`c|jyn ei |bn icjt

    {nc|bnt `ehlj|jehp vtnpnh| eynt |bn pj|n iet aep| ei |bn nrvntjanh|co l~tc|jeh(

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    49/140

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    50/140

    |b Act`b 466>/ pbe{jhk c `eol

    iteh| cvvtec`bjhk |bn \~adct~adc nrvntjanh|co pj|n "jhlj`c|nl dz |bn tnl le|*( @evztjkb| Hc|jehco

    An|neteoekj`co chl E`nchektcvbj` @nh|tn/ D~tnc~ ei An|neteoekz/ C~p|tcojc(

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    51/140

    |b

    ei Act`b chl 3;|b

    ei Act`b eh{ctlp/ {bj`b

    `ettnpvehl |e bjkb vtnpp~tn pzp|nap dn|{nnh {nc|bnt iteh|p( \bjp he`|~thco ltcjhckn

    ei cjt jh c het|bntoz ljtn`|jeh iet |bn {beon nrvntjanh|co yeo~an itea 6(4 |e 9

    an|tnp cko jp `ehpjp|nh| {j|b |bn nrvn`|nl gc|cdc|j` |zvn ltcjhckn {jhl ljtn`|jeh iet

    |bn \~adct~adc pj|n/ cp c tnp~o| ei |bn p~tte~hljhk |evektcvbz pbe{h jh ijk~tn 4(36(

    \bn nrvntjanh|co pj|n pbe{h jh ijk~tn 4(36 jp pj|~c|nl jh c octknt |evektcvbj` dcpjh ei

    cde~| > ga4

    jh ctnc/ de~hlnl eh |btnn pjlnp dz oe{ bjoop ei an|tnp tnoc|jyn

    nonyc|jeh( \bjp dcpjh jp evnh |e |bn Het|b chl bnh`n |bn nrvn`|nl ljtn`|jeh ei

    gc|cdc|j` |zvn ioe{ jp |e |bn Het|b(

    \bn itns~nh`z ljp|tjd~|jehp ei {jhl c}ja~|b pbe{h jh ijk~tn 4(: `eh|cjh coo |bn

    tns~jtnl jhietac|jeh |e voe| c `ehynh|jehco {jhl tepn iet chz lnpjtnl lcz l~tjhk |bn

    nrvntjanh|( Ijk~tn 4(33 pbe{p p~`b c {jhl tepn voe||nl iet |bn 30|b

    Act`b 466>/

    ~pjhk lc|c itea |bn pehj` chnaean|nt c| 3(9> a cko hnct |bn `nh|tn ei |bn ncp| ic`n(

    Itea ijk~tn 4(: j| `ch dn pnnh |bn het|bntoz he`|~thco cjtioe{p ctn c| |bnjt aep|

    ljp|jh`| cte~hl |bjp lc|n( \bjp jp `ehijtanl dz ijk~tn 4(33/ {bj`b pbe{p c `onctoz

    lnijhnl ojgnoz gc|cdc|j` ioe{ `eajhk itea c dnctjhk ei 392 lnktnnp l~tjhk |bn be~tp

    ei lctghnpp/ `eavctnl |e ch ~vbjoo ioe{ l~tjhk |bn lcz itea 009 lnktnnp( \bn ojgnoz

    gc|cdc|j` ioe{p c| 3: be~tp/ 40 be~tp chl 60 be~tp bcyn anch "eynt < be~tp*

    ynoe`j|jnp ei 6(0 chl 6(03 a p!3

    tnpvn`|jynoz/ {bntncp |bn ~vbjoo ioe{p c| 33

    be~tp chl 3> be~tp bcyn anch ynoe`j|jnp ei 6(:> chl 6(;: a p!3

    (

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    52/140

    Ijk~tn 4!: Itns~nh`z ljp|tjd~|jeh voe|p ei {jhl c}ja~|b iet |bn pehj` chnaean|ntp ei |bn Ncp|/

    Pe~|b/ [np|/ chl Het|b `~t|cjh {coop c| 3(9> a/ chl |bn `nh|tco acp| c| 9 a "h~adntnl 3/ 4/ 0/ < chl >

    tnpvn`|jynoz*( Lc|c itea chnaean|nt |btnn jp cdpnh| iet |bn hjkb| ei |bn 36 |b Act`b l~n |e ns~jvanh|

    acoi~h`|jeh(

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    53/140

    a(Aeljijnl itea On~hjhk n| co( "4662*(

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    54/140

    |b

    Act`b/ eh coo ei {bj`b nyjlnh`n ei gc|cdc|j` ioe{p{ntn pnnh(

    Be~toz {jhl lc|c itea ;6 a cko eh |bn hnctdz "4 a

    cko jh ijk~tn 4(33 iet |bn pcan |janp "60 be~tp/ 3: be~tp/ 40 be~tp*/ p~kknp|jhk |bc|

    |bnpn hnct p~tic`n ioe{p ctn jhlnnl ln`e~vonl p~d `chevz gc|cdc|j` ioe{p(

    Be~toz lcz|jan {jhlp iet ;6 a cko ancp~tnl eh |bn E}Io~r acp| iet 33 be~tp chl

    3> be~tp eh |bn 30|b

    Act`b ctn 0(; a p!3

    doe{jhk itea 06> lnktnnp/ chl 3(: a p!3

    itea 4;: lnktnnp tnpvn`|jynoz( Ijk~tn 4(33 pbe{p |bn 3(9> a cko {jhl doe{jhk itea

    dn|{nnh 422 lnktnnp chl 096 lnktnnp c| 33 be~tp chl 3> be~tp NP\ "{jhl pvnnlp

    dnjhk cte~hl 3 a p!3

    *( \bjp p~kknp|p |bc| |bn lcz|jan cjtioe{p pnnh jh ijk~tn 4(33 iet

    33 be~tp chl 3> be~tp ctn he| ~vbjoo chcdc|j` ioe{p/ d~| pjavoz ynntnl chl poc`gnl

    p~tic`n {jhlp ltjynh dz |bn eyntbncl knep|tevbj` {jhl(

    Ijk~tn 4(30 pbe{p c `eavctjpeh ei {jhl c}ja~|b bjp|ektcap ycojl iet 40 be~tp NP\

    eh |bn 30|b

    Act`b 466> "`tnc|nl ~pjhk lc|c iet |bn vntjel dn|{nnh 43 be~tp eh |bn

    30|b

    chl 63 be~tp eh |bn 3 a cko jh

    |bn ajllon ei |bn Het|b/ Ncp|/ Pe~|b chl [np| ic`np ei |bn @Y/ pnn ijk~tn 4(0( Cope

    pbe{h jp c bjp|ektca iet 9 a cko eh |bn acp| jh |bn `nh|tn ei |bn @Y(

    Coo |bn bjp|ektcap jh ijk~tn 4(30 pbe{ c vtedcdon gc|cdc|j` ioe{ jp e``~ttjhk/

    doe{jhk itea c Pe~|bntoz ljtn`|jeh iet |bn hjkb| ei |bn 30|b

    Act`b( \bn bjp|ektcap

    bcyn aep| ei |bnjt nhntkz dn|{nnh 3

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    55/140

    a hnct |bn `nh|tn ei |bn Ncp| @Y {coo/ iet |bn 30|b

    ei Act`b 466>(

    \bn {jhl lc|c {cp vte`nppnl ~pjhk |jan djhp ei ie~t be~tp(

    Ijk~tn 4!34 30|b

    Act`b 466> ve|nh|jco |navntc|~tn vteijonp iet |bn `nh|tco pjr an|tn acp|/ `co`~oc|nl

    itea |bntae`e~von lc|c iet bnjkb|p ei 6(4/ 6(

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    56/140

    lnktnnp chl 3:9 lnktnnp/ {j|b cppe`jc|nl p|chlctl lnyjc|jehp

    ei cte~hl 06 lnktnnp( Anch yn`|et {jhl ynoe`j|jnp {ntn dn|{nnh 6(0 chl 6(< a p!3

    {j|b c p|chlctl lnyjc|jeh ei m~p| eynt 6(3 a p!3

    ( Acrja~a yn`|et {jhl ynoe`j|jnp

    {ntn cte~hl 3 a p

    !3

    chl ajhja~a ynoe`j|jnp hnct }nte(

    Jh ijk~tn 4(30 coo |bn {jhl c}ja~|b ljp|tjd~|jehp cvct| itea |bn {np| {coo

    chnaean|nt/ bcyn acrjac iet {jhlp doe{jhk itea 392 lnktnnp( \bn c}ja~|b

    ljp|tjd~|jeh iet |bn {np| {coo dz `eh|tcp| bcp c acrjac iet {jhlp doe{jhk itea 3:4

    lnktnnp/ ehn c}ja~|b djh et 47vntp eaa(*( Be{nynt/

    lnpvj|n |bjp de|b io~rnp oeeg yntz hejpz/ chl j| {cp ln`jlnl |e cll |bn edpntynl lcjoz

    pjkhcop |e nc`b e|bnt/ iet |bn onpp hejpz vntjel dn|{nnh |bn |{e pzhev|j` {nc|bnt

    iteh|p "pbe{h eh ijk~tn 4(3>*/ jh ch c||nav| |e kn| c ~pcdon lj~thco io~r `~tyn(

    \bn tnp~o|jhk lj~thco io~r `~tynp ctn pbe{h jh ijk~tn 4(39/ {bj`b pbe{p |bn oc|nh|

    bnc| io~r `~tyn cp nrvn`|nl bcyjhk yco~np `oepn |e }nte c| hjkb| chl vepj|jyn yco~np

    l~tjhk |bn lczojkb| be~tp "vncgjhk c| cte~hl 34> [ a!4

    c| 3va NP\*( \bn pjkh

    `ehynh|jeh ~pnl jh ijk~tn 4(39 jp vepj|jyn yco~np jhlj`c|n c hn| ~v{ctl io~r itea |bn

    p~tic`n jh|e |bn c|aepvbntn( \bn pj|~c|jeh {j|b tnpvn`| |e |bn @E4 io~r jp aetn

    vtedonac|j` {j|b |bn lj~thco `~tyn pbe{jhk c le~don b~avnl cvvnctch`n/ vncgjhk

    cte~hl > chl m~p| ~hlnt 9 aeo a!4

    p!3

    jh |bn aethjhk chl ci|ntheeh tnpvn`|jynoz(

    \bn @E4 io~r `~tyn pbe{p c ajhja~a ei coaep| !0 aeo a!4

    p!3

    "c le{h{ctl io~r*

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    60/140

    >0

    Ijk~tn 4!3> @ctdeh ljerjln chl oc|nh| bnc| io~rnp `co`~oc|nl iet 9 a cko eh |bn `nh|tco |e{nt/ ~pjhk

    |bn nllz `eyctjch`n an|bel/ {j|b ch cyntckjhk |jan ei ehn be~t( Tnaeyco ei dcl lc|c vejh|p dcpnl

    eh aj`te!an|neteoekj`co `ehpjlntc|jehp bcp cotnclz dnnh `cttjnl e~|(

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    61/140

    >|b

    Act`b 466> jh`o~pjyn/ c| 9 a cko eh |bn `nh|tco acp|( \bn nttet

    dctp eh |bn jhljyjl~co @E4 chl oc|nh| bnc| `~tynp tnvtnpnh| vo~p chl ajh~p ehn p|chlctl nttet(

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    62/140

    >>

    cte~hl ajllcz( \bn hjkb| |jan @E4 io~r jp cte~hl 3 aeo a!4

    p!3

    iet aep| ei |bn

    hjkb|/ cvct| itea dn|{nnh 3: chl 43 be~tp {bnh j| jp dn|{nnh 4 chl 0 aeo a!4

    p!3

    (

    \bn anch @E4 io~r lntjynl itea |bn lj~thco `~tyn {cp 3(|b

    Act`b c hn| ~v{ctl aeynanh| ei @E4 e``~ttnl |bte~kb

    |bn 9 a io~r vochn "|bjp lenp he| hn`nppctjoz anch |bn {beon lnv|b ei |bn ietnp| {cp c

    @E4 pe~t`n l~tjhk |bjp vntjel*(

    Jhj|jcooz j| {cp |be~kb| |bc| c veppjdon nrvochc|jeh iet |bn oe{ edpntynl tnpvjtc|jeh

    io~r l~tjhk |bn hjkb||jan {cp |bc| |bn ietnp| p|t~`|~tn {cp c`|jhk cp c `eoojac|et

    cooe{jhk dtjkb| p~hojkb| |e joo~ajhc|n |bn ~hlnt p|etnz l~tjhk |bn ajllon ei |bn lcz

    d~| `c~pjhk lnnv pbcln jh |bn aethjhk chl ci|ntheeh "@onanh|( T(/ 466>7vntp`eaa(*(

    P~`b c pj|~c|jeh ajkb| tnp~o| jh |bn @E4 io~r `~tyn pnnh jh ijk~tn 4(39/

    vbe|epzh|bnpjp leajhc|jhk cte~hl ajllcz "hnkc|jyn%le{h{ctl @E4 io~r yco~np*/

    chl tnpvjtc|jeh leajhc|jhk "vepj|jyn%~v{ctl @E4 io~r yco~np* l~tjhk |bn {cta

    aethjhk chl ci|ntheeh/ {j|b hjkb| |jan tnpvjtc|jeh dnjhk p~vvtnppnl dz

    `eavctc|jynoz oe{ hjkb| |jan |navntc|~tnp(

    Be{nynt/ cp {joo dn ljp`~ppnl oc|nt jh |bjp `bcv|nt/ chcozpjp ei {jhl vteijonp

    ancp~tnl dn|{nnh 6(4 chl pjr an|tnp cko eh |bn `nh|tco acp| {j|bjh |bn @Y l~tjhk

    |bn nrvntjanh|/ p|tehkoz p~kknp| |bc| ln`e~vojhk ei |bn ietnp| ~hlntp|etnz itea |bn

    nllz io~r pzp|na c| pjr an|tnp {cp e``~ttjhk l~tjhk |bn hjkb||jan(

    Ijk~tn 4(3; pbe{p @E4 io~r ancp~tnanh|p `cttjnl e~| dz Doc`gn| co "3::9* l~tjhk

    M~hn 3::< jh c detnco cpvnh ietnp| jh @chclc kjyjhk tnp~o|p `eavctcdon {j|b ijk~tn

    4(39/ lnpvj|n |bn ljiintnh| |jan ei znct "ajl p~aant jhp|ncl ei nctoz c~|~ah* chl

    oc|j|~ln( Doc`g n| co( "3::9* acln io~r ancp~tnanh|p c| < a cko cdeyn c bc}noh~|

    ~hlntp|etnz cde~| 4 a |coo/ chl dnhnc|b cpvnh |tnnp ei bnjkb| 43 a "`chevz dcpn {cp

    c| 3> a*( Lcz|jan oc|nh| bnc| io~rnp "he| pbe{h* vncgnl c| yco~np dn|{nnh >6 chl

    3>6 [ a!4

    / chl {ntn `oepn |e }nte c| hjkb|( \bnpn oc|nh| bnc| tnp~o|p ctn ei c pjajoct

    ackhj|~ln |e |bepn pnnh c| 9 a cko c| |bn \~adct~adc pj|n "pnn ijk~tnp 4(3> chl

    4(39*(

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    63/140

    >9

    Ijk~tn 4!3; @eavctjpeh ei bcoi!be~toz nllz!`ettnoc|jeh @E4 io~rnp ancp~tnl cdeyn ch cpvnh

    eyntp|etnz "Ic* chl cdeyn c bc}noh~| ~hlntp|etnz "Ib*( Itea Doc`g n| co "3::9*(

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    64/140

    >;

    Iet @E4 io~r `~tynp c| < a cko eh |bn @chcljch pj|n/ ajhjac e``~ttnl hnct ajllcz

    {j|b io~rnp ei !3 |e !0 aeo a!4

    p!3

    ( Ci|ntheeh chl aethjhk io~rnp {ntn cte~hl 4

    aeo a!4

    p!3

    / chl acrjac e``~ttnl c| hjkb| {j|b io~rnp ei 0 |e > aeo a!4

    p!3

    ( Ckcjh

    |bn @chcljch chl \~adct~adc @E4 io~rnp dn|{nnh |bn ~hlnt p|etnz chl eynt p|etnzctn dtecloz pjajoct jh pbcvn chl ackhj|~ln {j|b ehn he|cdon nr`nv|jeh/ |bc| |bn

    C~p|tcojch @E4 io~rnp ltev dc`g `oepn |e }nte c| hjkb|/ {bntncp |bn @chcljch ehnp

    tnacjh bjkb chl jh ic`| c||cjh |bnjt acrja~a lj~thco yco~np(

    4(4(4 \bn ljp`eyntz ei c acrjac jh |bn hjkb||jan {jhl vteijon

    Ijk~tn 4(32 pbe{p be~toz betj}eh|co {jhl chl @E4 vteijonp ~v |bn `nh|tco acp| jh |bn

    @Y iet |bn hjkb| ei |bn 34|b

    Act`b 466>( C acrjac et mn| jh |bn betj}eh|co {jhl

    pvnnl ei 6(0 a p!3

    "3(> |janp |bn {jhl pvnnl c| pjr an|tnp* jp pnnh c| |btnn an|tnp

    cdeyn kte~hl onyno( @E4 aeon itc`|jehp jh |bn ietnp| ~hlntp|etnz "? 3a cko* jh`tncpn

    itea cte~hl 26 vva c| 6(4 a |e

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    65/140

    >2

    Ijk~tn 4!32 Ynt|j`co yctjc|jehp ei be~toz cyntckn betj}eh|co {jhl pvnnl ancp~tnl c| 6(

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    66/140

    >:

    Ijk~tn 4!3: Nrcavonp ei cyntckn @E4 aeon itc`|jehp/ ve|nh|jco |navntc|~tnp chl hetacojpnl

    {jhlpvnnl vteijonp edpntynl eh |bn `nh|tco 9 a acp| {j|bjh |bn @Y/ iet hjkb||jan "oni|bchl pjln ei

    ijk~tn* chl lcz|jan "tjkb|bchl pjln ei ijk~tn*(Aeljijnl itea On~hjhk n| co( "4662*(

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    67/140

    96

    On~hjhk n| co( "4662* bcyn aelnoonl |bn hetacojpnl {jhl pvnnl vteijon ~pjhk c oek!

    hetaco i~h`|jeh=

    4

    3

    oh" % *3" * nrv

    4``

    `

    } }P } c

    d

    1

    "4!;*

    |bc| jp cdon |e ij| de|b |bn acrja~a mn| {j|bjh |bn hjkb||jan {jhl vteijon/ chl |bn

    aehe|ehj`cooz jh`tncpjhk lcz|jan vteijon "pnn ijk~tn 4(3:*( [bntn P3"}* jp

    hetacojpnl {jhl pvnnl cp c i~h`|jeh ei bnjkb|/ }/ {j|bjh |bn @Y/ chl c`/ d` chl}` ctn

    vctcan|ntp ln|ntajhnl iet nc`b ehn be~t jh|ntyco( On~hjhk n| co( "4662* lnp`tjdnp

    be{ P3"}* {cp `co`~oc|nl iet nc`b be~t ~pjhk {jhl pvnnl yco~np ancp~tnl eh |bn

    `nh|tco 9 a acp|/ jh etlnt |e vteyjln c `ettn`|jeh ic`|et |bc| {cp cvvojnl |e |bn

    betj}eh|co clyn`|jeh |ntap "|bn pn`ehl chl |bjtl |ntap jh ns~c|jeh 4(

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    68/140

    93

    \bn hetacojpnl hjkb||jan {jhl vteijon pbe{h jh ijk~tn 4(3: pbe{p ch edyje~p

    acrjac et mn| c| cte~hl 4 a cko/ {j|b c yco~n P"}* ei cde~| 3(; |janp |bn {jhl

    pvnnl c| 9 a "ckcjh c pjajoct pj|~c|jeh jp pbe{h jh ijk~tn 4(32*(

    Ji {n tn`ehpjlnt |bn pbcvn ei |bn lj~thco @E4 nllz io~r `~tyn cp pbe{h jh ijk~tn

    4(39/ |bn oe{ yco~np ei ~v{ctl @E4 io~r pnnh c| hjkb| "cte~hl 3 aeo a!4

    p!3

    ci|nt

    ajlhjkb|* ctn vtedcdoz nrvocjhnl dz |bn vtnpnh`n ei |bjp p|cdon ocznt ei cjt |bc|

    `ehp|j|~|np |bn mn| jh |bn oe{nt vct| ei |bn @Y/ |bn niin`| ei {bj`b jp |e ln`e~von |bn

    9 a cko onyno itea |bn tnpvjtc|jeh ei |bn ~hlntp|etnz( \bn bjkbnt yco~np ei @E4 io~r

    ei dn|{nnh > chl 9 aeo a!4

    p!3

    pnnh cte~hl p~hpn| chl p~htjpn dnjhk nrvocjhnl dz

    |bn mn| bcyjhk zn| |e ieta/ et bcyjhk dnnh ljppjvc|nl dz bnc|jhk itea dnoe{/

    tnpvn`|jynoz(

    [n dnojnyn |bjp ljp`eyntz ei |bn niin`| ei c hjkb||jan p~d `chevz {jhl pvnnl

    acrjac et mn| eh |bn pbcvn ei |bn lj~thco @E4 nllz io~r `~tyn ancp~tnl cdeyn |bn

    ~hlntp|etnz d~| dnoe{ |bn ietnp| `chevz vtevnt "pnn ijk~tn 4(39c*/ jp aetn |bch c

    antn `~tjepj|z( \bjp jp dn`c~pn |bn vtnpnh`n ei |bn `bctc`|ntjp|j` le~don b~avnl

    lj~thco @E4 nllz io~r `~tyn ancp~tnl jh c pjajoct pj|~c|jeh jh |bn kcv dn|{nnh c

    {jlnoz ynt|j`cooz pnvctc|nl ~hlntp|etnz chl eyntp|etnz acz dn jhlj`c|jyn ei |bn

    vtnpnh`n ei c he`|~thco p~d`chevz mn| dnoe{ |bn ancp~tnanh| onyno( Doc`gn| co(

    "3::9* `cttjnl e~| m~p| p~`b nllz io~r ancp~tnanh|p jh |bn `chevz pvc`n ei c

    @chcljch cpvnh ietnp|/ d~| |bnjt @E4 io~r `~tynp p|cznl bjkb c| hjkb| "pnn ijk~tn

    4(3;* jhlj`c|jhk |bc| he p~d`chevz mn| {cp vtnpnh| dnoe{ |bn ancp~tnanh| onyno(

    Ijk~tn 4(46 pbe{p c ieojckn ctnc yeo~an lnhpj|z "ICYL* vteijon cp ancp~tnl ~pjhk c

    kte~hl dcpnl ojlct jh |bn yj`jhj|z ei |bn ;6 a |e{nt/ {bj`b ojnp 4 a cko/ chl c pojkb|oz pacoont ehn cte~hl ; a cko {j|b c

    yco~n ei 6(6; a!3

    "On~hjhk n| co( 4662*( \bn ojlct {cp ~hcdon |e vteyjln lc|c dnoe{ 4

    a cko chl pe |bn ~hlntp|etnz jp he| tnpeoynl jh ijk~tn 4(46(

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    69/140

    94

    Ijk~tn 4!46 Ieojckn ctnc yeo~an lnhpj|z "ICYL* vteijon ancp~tnl iet ietnp| {j|bjh |bn nllz io~r

    iee|vtjh| ei |bn ;6 a E}Io~r |e{nt ~pjhk c kte~hl dcpnl ojlct( Itea On~hjhk n| co( "4662*(

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    70/140

    90

    Jh|ntnp|jhkoz/ |bn vncg jh ICYL c| ; a cko {cp he| p~dmn`|jynoz nyjlnh| {bnh ehn

    {cp {etgjhk {j|bjh |bn >6 dz >6 a @Y/ co|be~kb ch ~hlntdt~pb%~hlntp|etnz ~v |e

    cte~hl 3 a bjkb `nt|cjhoz {cp/ cp {cp |bn N~`cozv|~p eyntp|etnz c| 0> a cko(

    \bn ieojckn ljp|tjd~|jeh pnnh jh ijk~tn 4(46 jp tnonych| |e |bn ietac|jeh ei tnoc|jyn

    {jhl pvnnl acrjac {j|bjh |bn ietnp| `chevz( Itj|p`bnh "3:2>* pbe{p be{ |bn

    cntelzhcaj` ltck ei ietnp| `chevz nonanh|p `ch `c~pn c tnoc|jyn {jhl pvnnl acrjac

    et mn| |e nrjp| jh |bn p|na pvc`n dnhnc|b c ietnp| `chevz( Itj|p`bnh lnp`tjdnp |bn

    ljp|tjd~|jeh ei cntelzhcaj` nonanh|p {j|bjh bjp ietnp| nrcavon jh |ntap ei vteijonp

    ns~jyconh| |e ICYL/ chl tnoc|np edpntynl tnoc|jyn mn|p jh |bn p|na pvc`n |e oe{

    ICYL yco~np `oepn |e |bn kte~hl(

    Ch javet|ch| ljiintnh`n dn|{nnh Itj|p`bnhp ICYL vteijonp chl |bn ehn pbe{h iet

    |bn \~adct~adc ietnp| jh ijk~tn 4(46/ jp |bc| Itj|p`bnhp joo~p|tc|jyn nrcavon jp c

    Le~kocp ijt p|chl {j|b c vncg ICYL yco~n ei cte~hl 4 a!3

    c| 36 |e 3> a cko/

    {bntncp |bn \~act~adc bcp c ICYL vncg ei ch etlnt ei ackhj|~ln onpp "6(3 a!3

    c|

    0> a cko*( Che|bnt `t~`jco ljiintnh`n dn|{nnh Itj|p`bnhp chcozpjp chl |bn pj|~c|jeh

    c| \~adct~adc jp |bc| |bn mn|p {j|bjh |bn \~adct~adc @Y "pnn ijk~tnp 4(32 chl

    4(3:* ctn ehoz pnnh c| hjkb| ~hlnt `ehlj|jehp ei |bnaco jhyntpjeh {j|bjh |bn oe{nt

    vct| ei |bn `chevz(

    Oeegjhk c| |bn ICLY vteijon iet |bn \~adct~adc ietnp| pbe{h jh ijk~tn 4(46 j|

    {e~ol dn |nav|jhk |e tnoc|n |bn he`|~thco mn|p pnnh c| 4 a |e 0 a cko "pnn ijk~tnp

    4(32 chl 4(3:* |e |bn ajhjac jh |bn \~adct~adc ICYL vteijon c| 4 a cko "pnn

    ijk~tn 4(46* |bc| {e~ol nrjp| ji |bn ICYL yco~np tnoc|nl |e |bn ~hlntp|etnz `e~ol dn

    cllnl dnoe{ |bn 4 a onyno(

    Be{nynt/ pjh`n |bn mn| jh |bn @Y jp ehoz pnnh c| hjkb| |bjp jhlj`c|np j| jp c gc|cdc|j`

    ktcyj|z |zvn ioe{ tc|bnt |bch ehn pjavoz `c~pnl dz |bn cntelzhcaj` ltck ei |bn

    ietnp| nonanh|p( \bntn jp p|joo |bn veppjdjoj|z |bc| lnpvj|n dnjhk c gc|cdc|j` |zvn ioe{/

    |bn mn| pnnh jh |bn @Y acz peanbe{ dn an`bchj`cooz chl%et |bntacooz `e~vonl |e

    |bn ietnp| ynkn|c|jeh nonanh|p |bc| kjyn tjpn |e |bn ICYL vteijon pbe{h jh ijk~tn

    4(46(

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    71/140

    9 lczp itea 62 be~tp NP\ eh |bn 9|b

    Act`b 466> ~h|jo 69 be~tp NP\

    eh |bn 43p|

    Act`b 466>( \bjp l~tc|jeh {cp `ehp|tcjhnl dz |bn cycjocdjoj|z ei lc|c iet

    |bn @Y ic`np chl 9 a `nh|tco acp| tn`etlnl dz |bn @PJTE ns~jvanh|( E|bnt |jan

    pntjnp p~`b cp oc|nh| bnc| chl @E4 nllz io~rnp/ chl pehj` |navntc|~tnp {ntn cycjocdon

    dn|{nnh |bn 0tl Act`b 466> chl 44hl Act`b 466> "pnn ijk~tnp 4(3> chl 4(;*(

    Ijk~tn 4(43 pbe{p |jan pntjnp ei lc|c `eoon`|nl itea |bn ic`np ei |bn @Y/ chl |bn 9 a

    acp| jh |bn `nh|tn ei |bn @Y( \bn l~tc|jeh ei |bn voe||nl |jan pntjnp jh ijk~tn 4(43 jp

    34 lczp itea oc|n aethjhk eh |bn 9|b

    Act`b 466> ~h|jo cte~hl heeh eh |bn 32|b

    Act`b 466>/ |bn ijhco |btnn lczp ei cycjocdon lc|c bcyn dnnh eaj||nl iet `octj|z d~|

    bcyn pjajoct `bctc`|ntjp|j`p |e |bn `coa hjkb|p jh ijk~tn 4(43`(

    Ijk~tn 4(43l pbe{jhk ve|nh|jco |navntc|~tn c| |btnn pnon`|nl onynop eh |bn 9 a acp|/

    jhlj`c|np |bc| iet coo hjkb|p `ehpjlntnl dz On~hjhk n| co( "4662*/ cvct| itea |bn oc|nt

    vct| ei |bn hjkb| ei |bn 3>|b

    Act`b {bnh c tcjh dnctjhk {nc|bnt iteh| {cp `teppjhk |bn

    pj|n/ |bntn {cp c |navntc|~tn jhyntpjeh dn|{nnh 6(4 a chl 9 a cko jh |bn @Y(

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    72/140

    9>

    Ijk~tn 4!43 \jan pntjnp iet |bn vntjel 9!32 Act`b 466>/ ei "c* {njkb|nl aeon itc`|jehp ei @E4 iet

    |bn het|b chl pe~|b {coop ei |bn @Y/ chl "d* |bn ncp| chl {np| {coop( Pbe{h jh "`* chl "l* ctn |jan

    pntjnp ei @E4 aeon itc`|jehp chl ve|nh|jco |navntc|~tnp ancp~tnl dn|{nnh 6(4 a chl 9 a cko eh |bn

    9a acp| c| |bn `nh|tn ei |bn @Y( Lc|n ocdnop ctn `nh|tnl eh ajllcz( \bjp jp ch nrvchlnl yntpjeh ei

    |{e ijk~tnp jh On~hjhk n| co( "4662*(

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    73/140

    99

    Ijk~tn 4(43l cope pbe{p |bn vtektnppjyn jh`tncpn jh lj~thco |navntc|~tnp dn|{nnh |bn

    9|b

    chl 3>|b

    Act`b cppe`jc|nl {j|b `coa bjkb vtnpp~tn {nc|bnt `ehlj|jehp "pnn cope

    ijk~tn 4(;*( \bn `ehlj|jehp {j|bjh |bn @Y eh |bnpn hjkb|p {ntn p|cdon chl p|tc|jijnl(

    Ijk~tn 4(43` pbe{p @E4 aeon itc`|jehp c| pjr bnjkb|p eh |bn 9 a acp|/ jhlj`c|jhk |bc|

    iet |bn `coa hjkb|p dn|{nnh |bn 9|b

    chl 3>|b

    Act`b/ |bntn {cp c ynt|j`co @E4 ktcljnh|

    ei cte~hl 4> vva a!3

    "@E4 aeon itc`|jehp jh`tncpjhk dz cte~hl 3>6 vva itea |bn

    |ev ei |bn @Y c| 9 a/ le{h |e 6(4 a cko/ cp cope pnnh jh ijk~tn 4(32*( L~tjhk |bn `coa

    lczp dz `eh|tcp|/ coo |bn @E4 aeon itc`|jehp c| |bn yctje~p bnjkb|p eh |bn 9 a acp|

    bcl pjajoct yco~np ei cte~hl 096 vva/ jhlj`c|jhk |bc| |bn lcz|jan @Y {cp {noo

    ajrnl ynt|j`cooz( Ijk~tn 4(43l iet |bn `coa lczp pbe{p |bc| lcz|jan ve|nh|jco

    |navntc|~tn ln`tncpnp {j|b bnjkb| {j|bjh |bn @Y/ {bj`b jp cope `ehpjp|nh| {j|b |bn

    @Y dnjhk {noo ajrnl l~tjhk |bn lcz(

    \bn hjkb| ei |bn 3;|b

    Act`b jp he|cdon iet |bn @Y dnjhk ciin`|nl dz {jhlz `ehlj|jehp

    ieooe{jhk |bn vcppjhk ei |bn {nc|bnt iteh|( Co|be~kb |bntn jp p|joo c he`|~thco

    jhyntpjeh jh ve|nh|jco |navntc|~tn {j|bjh |bn @Y/ |bn ynt|j`co @E4 ktcljnh| jp he{

    ehoz 0 vva a!3

    `eavctnl |e 4> vva a!3

    eh |bn `coa hjkb|p( \bjp jhlj`c|np |bc|

    l~tjhk |bn hjkb| ei 3;|b

    Act`b |bn @Y {cp dnjhk p~dmn`|nl |e {ncg ajrjhk `c~pnl dz

    {jhl pbnct jhl~`nl |~td~onh`n(

    Jh ijk~tn 4(43c chl ijk~tn 4(43d/ |bn {njkb|nl aeon itc`|jehp ei @E4 iet |bn het|b

    chl pe~|b/ chl ncp| chl {np| ic`np ei |bn @Y ctn pbe{h tnpvn`|jynoz( De|b pn|p ei

    |jan pntjnp pbe{ |bn nrvn`|nl lj~thco `z`ojhk {j|b bjkbnt aeon itc`|jeh yco~np

    vtnpnh| c| hjkb|( Cope |bn |jan pntjnp bcyn kcvp eh |bn 3>|b

    chl 39|b

    Act`b 466>/

    {bnh |bn cjt v~avp {ntn |~thnl eii |e cyejl tcjh {c|nt cppe`jc|nl {j|b |bn vcppjhk

    {nc|bnt iteh| dnjhk ltc{h jh|e |bn vntietc|nl pcavojhk |~dnp "ijk~tn 4(43` pbe{p

    kcvp iet |bn pcan tncpeh*(

    Jh ijk~tn 4(43c/ |bn ljiintnh`n jh {njkb|nl aeon itc`|jehp ei @E4 dn|{nnh |bn het|b

    chl pe~|b ic`np ei |bn @Y ctn pacoo c| hjkb|/ bcyjhk c acrja~a ljiintnh`n ei cte~hl

    > |e 36 vva eh |bn hjkb| ei |bn 33|b

    Act`b 466>/ {j|b |bn het|b ic`n bcyjhk |bn

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    74/140

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    75/140

    92

    Ijk~tn 4!44 P`c||nt voe| ei be~toz anch ynt|j`co ynoe`j|jnp " *"b{a * ancp~tnl c| 9 a eh |bn `nh|tco

    acp| ~pjhk c 0L pehj` chnaean|nt/ ckcjhp| "c* {jhl ljtn`|jeh c}ja~|b/ chl "d* ynt|j`co ynoe`j|jnp

    `co`~oc|nl ~pjhk |bn `eh|jh~j|z ns~c|jeh " *"b{` *( Ijk~tn 4(3:d jp |cgnh itea On~hjhk n| co( "4662*(

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    76/140

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    77/140

    ;6

    Ijk~tn 4(44d pbe{p c p`c||nt voe| ei |bn etjkjhco *"b{a yco~np itea |bn 9a pehj`

    chnaean|nt ckcjhp| |bn *"b{` yco~np lntjynl ~pjhk `eh|jh~j|z( P~tvtjpjhkoz/ |bn

    `ettnoc|jeh jp icjtoz keel iet coo voe||nl yco~np {j|b chT4

    ei 6( a p!3/ {bj`b jp

    veppjdoz `c~pnl dz ch ~hhe|j`nl lteev jh |bn cta c| 9 a cko |bc| bnol |bn pehj`

    chnaean|nt/ {bj`b acz bcyn e``~ttnl ci|nt jhj|jco onynoojhk( Dn`c~pn ei |bn octkn

    aeon itc`|jeh ktcljnh|p ei @E4 {j|bjh |bn @Y c| hjkb| |bjp ynoe`j|z eiipn| kjynp tjpn

    |e octkn hnkc|jyn yco~np ei ynt|j`co clyn`|jeh ei dn|{nnh 36 chl 46 aeo a!4

    p!3

    "On~hjhk n| co( 4662* iet coo |bn `coa hjkb|p( J| {cp `eh`o~lnl |bc| |bnpn octkn

    hnkc|jyn hjkb||jan ynt|j`co clyn`|jeh yco~np {ntn ch ct|nic`| ei |bn ynoe`j|z eiipn|

    chl he| tnoc|nl |e tnco ynt|j`co clyn`|jeh ynoe`j|jnp(

    \bntnietn/ {n ctn oni| {j|b m~p| *"b{` lntjynl itea `eh|jh~j|z/ cp c `chljlc|n itea

    {bj`b |e kn| ~pcdon ynt|j`co clyn`|jeh s~ch|j|jnp( Iet|~hc|noz/ |bn *"b{` yco~np

    pbe{h jh ijk~tn 4(44d bcyn ch cyntckn yco~n c| hjkb| ei `oepn |e }nte "6(666 a p!3

    c``etljhk |e On~hjhk n| co( "4662**( Cp anh|jehnl nctojnt jh |bjp `bcv|nt |bntn ctn

    |bnetn|j`co tncpehp |e nrvn`| *"b{` {joo vntieta dn||nt |bch chz ljtn`|oz ancp~tnl

    ynt|j`co ynoe`j|z ~pjhk c pjhkon 0L pehj` chnaean|nt/ de|b jh |ntap ei tnl~`nl pjkhco

    hejpn chl te|c|jehco `eetljhc|n pzp|na cadjk~j|z( \bntnietn/ ci|nt `eavctjpeh ei

    ynt|j`co clyn`|jeh s~ch|j|jnp iet coo |bn jhljyjl~co lczp chl hjkb|p l~tjhk |bn

    nrvntjanh| "he| pbe{h bntn d~| cycjocdon jh On~hjhk n| co("4662**/ `co`~oc|nl ~pjhk

    de|b *"b{a chl *"b{` j| {cp ln`jlnl |e ~pn m~p| |bepn lntjynl ~pjhk *"b{` jh |bn

    ijhco chcozpjp(

    4(4(> \bn ijhco @E4 io~r `eavehnh|p iet |bn @Y

    Ijk~tn 4(40c pbe{p c lj~thco `eavepj|n dct ktcvb ei coo |bn @E4 io~r eavehnh|p iet

    |bn @Y( \bjp {cp `co`~oc|nl dz |cgjhk |bn anch yco~np ei io~r iet nc`b be~t ei |bn

    lczp io~r yco~np itea |bn cycjocdon 3> lczp be~toz |jan pntjnp( Ijk~tn 4(40d pbe{p

    |bn `ettnpvehljhk p|chlctl nttet yco~np chl ijk~tn 4(40` pbe{p |bn tnp~o|ch| eyntcoo

    @E4 io~r iet |bn @Y(

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    78/140

    ;3

    Ijk~tn 4!40 Lj~thco dct ktcvbp ei |bn ie~t @E4 io~r `eavehnh|p iet |bn @Y/ `co`~oc|nl itea be~toz

    yco~np lntjynl iet |bn 3> lcz nrvntjanh|co l~tc|jeh itea |bn 9 |b |e |bn 4hl Act`b 466>( "c* pbe{p |bn

    anch be~toz lj~thco yco~np/ "d* |bnjt be~toz p|chlctl nttetp chl "`* |bn tnp~o|ch| eyntcoo @E4 io~r iet

    |bn @Y "{j|b nttet dctp ei '%! ehn p|chlctl nttet*(

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    79/140

    ;4

    Jh ijk~tn 4(40c |bn betj}eh|co clyn`|jeh io~r ei @E4 jp `oepn |e }nte l~tjhk aep| ei

    |bn lczojkb| be~tp "62 be~tp |e 3; be~tp NP\*/ {j|b pjkhjij`ch| betj}eh|co clyn`|jeh

    `eaanh`jhk cte~hl p~hpn| chl `ncpjhk c| p~htjpn( \bn betj}eh|co io~r c| p~hpn|

    pbe{p ch ci|ntheeh vncg ei cte~hl < aeo a

    !4

    p

    !3

    / {j|b yco~np |bnh dn`eajhkhnkc|jyn "|zvj`cooz 4 |e 0 aeo a

    !4p

    !3* ~h|jo 63 be~tp NP\( Iet |bn tnp| ei |bn

    hjkb|/ jh`o~ljhk p~htjpn/ betj}eh|co clyn`|jeh yco~np ctn vepj|jyn/ {j|b yco~np

    dn|{nnh 4 chl > aeo a!4

    p!3

    ( \bn lj~thco yco~np ei ynt|j`co clyn`|jeh ctn pjajoct/

    d~| {j|b lcz|jan yco~np ei 3 |e 4 aeo a!4

    p!3

    / chl |bn p~hpn| vncg e``~ttjhk cde~|

    ch be~t oc|nt( Cp {j|b |bn betj}eh|co io~r/ |bn ynt|j`co io~r dn`eanp hnkc|jyn jh |bn

    nctoz vct| ei |bn hjkb| "hnkc|jyn vncg yco~n/ !< aeo a!4

    p!3

    cte~hl 44 be~tp*/ d~| jp

    vepj|jyn itea 63 be~tp eh{ctlp {j|b anch yco~np cte~hl < aeo a!4

    p!3

    (

    Ch javet|ch| edpntyc|jeh {j|b tnpvn`| |e |bn betj}eh|co chl ynt|j`co clyn`|jeh io~rnp

    l~tjhk |bn hjkb| jp |bc| |bnz cvvnct |e dn jh vbcpn/ bcyjhk |bn pcan pjkh chl pjajoct

    ackhj|~lnp/ iet a~`b ei |bn hjkb|( Act`eooc n| co( "466>* cope edpntynl |bjp/ d~|

    e|bnt tnpnct`bntp bcyn nj|bnt edpntynl "Zj n| co( 4662*/ et `co`~oc|nl |bnetn|j`cooz

    "Gc|~o n| co( 4669* |bc| |bnpn clyn`|jeh |ntap pbe~ol dn e~| ei vbcpn/ j(n( bcyn

    evvepj|n pjkhp chl pjajoct ackhj|~lnp(

    Ijhhjkch "3:::* |bnetn|j`cooz `ehpjlntnl ioe{ jh |bn ieta ei pvch{jpn yet|j`np

    `c~pnl dz c oe{ bjoo chl `eh`o~lnl |bc|/ jh knhntco/ |bn clyn`|jeh io~r |ntap pbe~ol

    dn ns~co chl evvepj|n/ cvct| itea c| oe`c|jehp `oepn |e |bn |nttcjh p~tic`n {bntn

    ancp~tnanh|p ctn ~p~cooz acln( C| |bnpn `oepn |e |bn p~tic`n oe`c|jehp |bn pjkhp chl

    tnoc|jyn ackhj|~lnp ei |bn clyn`|jeh io~r |ntap ctn |bn tnp~o| ei `eavn|jhk niin`|p

    tnoc|nl |e |bn |evektcvbj` chl aj`tean|neteoekj`co pn||jhk ei |bn vct|j`~oct pj|n/ chl

    |bn clyn`|jeh io~r |ntap he oehknt hnnl dn ns~co chl evvepj|n(

    C| \~adct~adc/ ijk~tn 4(40c pbe{p |bn betj}eh|co chl ynt|j`co clyn`|jeh io~rnp

    {ntn jh vbcpn iet hjhn be~tp l~tjhk |bn hjkb||jan( Iet |bn be~tp ei p~htjpn chl

    p~hpn| |bn clyn`|jeh io~rnp bcl |bn pcan pjkh "de|b vepj|jyn*/ d~| {j|b ackhj|~lnp

    |bc| {ntn he{ he|j`ncdoz ljiintnh|( Iet |bn be~t dnietn p~htjpn |bn clyn`|jeh io~rnp

    {ntn e~| ei vbcpn( \bn ie~t be~tp ieooe{jhk p~hpn| "32 |e 44 be~tp NP\*/ bcl ehn

    ei |bn clyn`|jeh io~rnp dnjhk `oepn |e }nte/ et ei evvepj|n pjkh jh |bn `cpn ei |bn be~t

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    80/140

    ;0

    dn|{nnh 3: chl 46 be~tp NP\( \bn tncpeh iet dnbcyje~t ei |bn clyn`|jeh io~rnp jh

    |bn be~t vtn`nljhk p~htjpn chl |bn ie~t be~tp ieooe{jhk p~hpn| jp he| ghe{h(

    Be{nynt/ `ehpjlntjhk |bn be~tp ieooe{jhk p~hpn| "~v |e 44 be~tp*/ j| acz jhlj`c|n

    |bc| c `eh`nv|~cooz pjavon gc|cdc|j` ioe{ tnkjan jp he| np|cdojpbnl {j|bjh |bn ietnp|

    `chevz ~h|jo pean |jan dn|{nnh 44 be~tp chl 63 be~tp NP\/ cp dz 63 be~tp |bn

    clyn`|jeh io~rnp ctn de|b jh vbcpn chl ei vepj|jyn ackhj|~ln(

    Jh ijk~tn 4(40c |bn @E4 nllz io~r pbe{p c pjajoct vc||nth |e |bc| ljp`~ppnl nctojnt jh

    |bn `bcv|nt "pnn ijk~tn 4(39*/ {j|b pacoo et pojkb|oz hnkc|jyn yco~np l~tjhk |bn lcz/

    d~| bcyjhk vepj|jyn vncgp ei cte~hl > aeo a!4

    p!3

    c| lc{h chl l~pg( L~tjhk |bn

    hjkb| |bn nllz io~r jp vepj|jyn "cde~| 4 aeo a!4

    p!3

    */ d~| ~hcdon |e c``e~h| iet |bn

    onyno ei he`|~thco tnpvjtc|jeh itea |bn ~hlntp|etnz%~hlntdt~pb |bc| ehn {e~ol nrvn`|

    |bn nllz `eyctjch`n pzp|na |e edpntyn "pnn |bn ctk~anh| jh pn`|jeh 4(4(4/ p~kknp|jhk

    > aeo a!4

    p!3

    / `ettnpvehljhk |e |bn @E4 nllz io~r pnnh cte~hl l~pg chl lc{h*( Cp

    ljp`~ppnl nctojnt "pn`|jeh 4(4(4* |bjp ajppjhk @E4 tnpvjtc|jeh io~r ei cte~hl 0 aeo

    a!4

    p!3

    c| hjkb| jp |be~kb| |e dn tnoc|nl |e c p|tc|jijnl betj}eh|co cjt ioe{ et mn| dnoe{

    |bn 9 a cko onyno ei |bn nllz `eyctjch`n pzp|na( Ji {n `ehpjlnt |bn io~r `eh|tjd~|jeh

    ei |bn betj}eh|co chl ynt|j`co io~r `eavehnh|p c| hjkb| "pnn ijk~tnp 4(40c chl 4(40`*/

    |bn ajppjhk tnpvjtc|jeh he{ dn`eanp c``e~h|nl iet dn|{nnh 63 be~tp NP\ chllc{h/ {j|b |bn vteyjpe |bc| j|p |t~n yco~n cvvnctp |e dn `oepnt |e 2 aeo a

    !4p

    !3

    "tc|bnt |bch > aeo a!4

    p!3

    * eh`n clyn`|jeh io~rnp ctn jh`o~lnl(

    Act`eooc n| co( "466>* bcyn cope lnp`tjdnl edpntyjhk |bc| betj}eh|co chl ynt|j`co

    io~rnp c| hjkb| ctn octknt |bch |bn hjkb||jan nllz io~r/ chl |bjp jp jhlnnl {bc| ijk~tn

    4(40c pbe{p dn|{nnh 63 be~tp NP\ chl lc{h/ iet coo d~| ehn ei |bn be~tp( Jh

    ackhj|~ln |ntap/ |bjp jp |t~n iet coaep| |bn nh|jtn hjkb|(

    C vtedona tnacjhp jh |bc| |e|co @E4 io~rnp "ijk~tn 4(40`* ci|nt |bn l~pg vncg/ ltev

    chl dn`ean hnkc|jyn jh |bn nctoz vct| ei |bn hjkb| dnietn 63 be~tp/ chl {bc| |bjp

    tnvtnpnh|p jp p|joo ~hghe{h(

    \bn `bchkn jh p|etckn yco~np pbe{h jh ijk~tn 4(40c/ bcyn |bn nrvn`|nl lj~thco

    dnbcyje~t( \{e io~r v~opnp ei @E4 ctn nyjlnh|/ ehn c| lc{h chl ehn c| l~pg( J|

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    81/140

    ; aeo a!4

    p!3

    / {j|b c p|chlctl nttet ei lczp ei |bn nrvntjanh| {cp cte~hl 33666 aeonp et >66

    Gk "ns~jyconh| |e 30> Gk ei @ctdeh*( \bjp jp ns~jyconh| |e 30 | bc!3 zt!3 ei v~tn

    @ctdeh oncyjhk |bn ietnp| ~hlntp|etnz/ {j|b c p|chlctl nttet ei 39 | bc!3

    zt!3

    (

    Lc|c kjynh jh On~hjhk n| co( "466>* p~kknp| |bc| iet |bn \~adct~adc ietnp|/ |zvj`co

    |e|co n`epzp|na @E4 io~r yco~np "HNN* iet c~|~ah "Act`b!Cvtjo*/ lntjynl itea |bn

    ;6 a cko E}Io~r acp| ctn cte~hl 4 aeo a!4

    p!3

    "c le{h{ctl io~r*( E~t lntjynl

    yco~n ei 0(> aeo a!4

    p!3

    ~v{ctl e~| ei |bn ~hlntp|etnz iet |bn pcan |jan ei znct/ jp

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    82/140

    ;>

    p~kknp|jyn |bc| octkn @E4 io~rnp acz nrjp| {j|bjh |bn ietnp| `chevz dn|{nnh |bn

    ~hlntp|etnz chl eyntp|etnz `chevz( Be{nynt/ {n a~p| dn `c~|je~p cde~| m~avjhk |e

    p~`b c `eh`o~pjeh( Ijtp|oz/ |bn pbet| l~tc|jeh ei |bn nrvntjanh| ei ehoz 3> lczp

    acgnp j| ljiij`~o| |e acgn p~`b knhntcojpnl `eh`o~pjehp( Pn`ehloz/ chl vntbcvp aetn

    javet|ch|oz/ |bn nrvntjanh| ehoz pcavonl ltz `ehlj|jehp "{j|be~| tcjh*/ pe jp

    ~htnvtnpnh|c|jyn ei coo `ehlj|jehp {j|bjh |bn @Y(

    4(0 @eh`o~pjehp

    \bn lj~thco @E4 io~r d~lkn| iet |bn >6 dz >6 a dz 9 a bjkb nrvntjanh|co `eh|teo

    yeo~an "@Y* kjynp yco~cdon hn{ jhpjkb|p jh|e |bn @E4 io~r nr`bchkn vte`nppnp

    ciin`|jhk c ietnp| ~hlntp|etnz%~hlntdt~pb( Pvn`jij`cooz/ |bn nrjp|nh`n ei c p~d`chevz

    {jhl vteijon acrjac et mn| ~hlnt p|cdon p|tc|jijnl hjkb||jan `ehlj|jehp/ chl |bn

    niin`| p~`b c mn| `ch bcyn eh |bn pbcvn ei |bn lj~thco @E4 nllz io~r `~tyn ancp~tnl

    jh |bn p|na pvc`n dnoe{ |bn ~vvnt ietnp| `chevz chl cdeyn |bn

    ~hlntp|etnz%~hlntdt~pb( J| cvvnctp |bc| ji p~`b c lj~thco nllz io~r `~tyn bcp

    ~hnrvn`|nloz oe{ yco~np c| hjkb| |bjp acz jhlj`c|n |bn vtnpnh`n ei c mn| dnoe{ |bn

    ancp~tnanh| onyno(

    @eavctjpeh ei |bn tnoc|jynoz octkn anch ~v{ctl lj~thco @E4 io~r itea |bn

    ~hlntp|etnz "0(> aeo a!4

    p!3

    */ `eavctnl {j|b v~dojpbnl yco~np ei |zvj`co io~rnp jh

    |e |bn \~adct~adc ietnp| l~tjhk c~|~ah "4 aeo a!4

    p!3

    * acz jhlj`c|n |bc| octkn

    @E4 io~rnp acz nrjp| dn|{nnh |bn ~hlntp|etnz "~hlntdt~pb* chl eyntp|etnz "ietnp|

    `chevz* ei |bn \~adct~adc N~`cozv|~p ietnp|( Be{nynt/ aetn {etg {e~ol hnnl |e

    dn lehn |e `ehijta |bjp(

    \bn `co`~oc|jeh ei c ~pncdon ynt|j`co clyn`|jeh |nta {cp ehoz acln veppjdon dz |bn

    ~pn ei |bn `eh|jh~j|z an|bel |e `co`~oc|n |bn ynt|j`co ynoe`j|z {j|bjh |bn @Y( Ch

    co|nthc|jyn ljtn`|oz ancp~tnl ynoe`j|z np|jac|n {cp ie~hl |e dn ~hp~j|cdon(

    \bn `eadjhnl p|chlctl nttet yco~np ei |bn ynt|j`co chl betj}eh|co clyn`|jeh |ntap

    jhynp|jkc|nl dz |bjp nrvntjanh| {ntn octkn/ dnjhk |bn pcan etlnt ei ackhj|~ln cp |bn

    |e|co io~r pjkhco c| hjkb|( Lnpvj|n |bjp c anchjhki~o chcozpjp ei |bn lj~thco |e|co io~r

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    83/140

    ;9

    `~tyn {cp `cttjnl e~|/ d~| |bn octkn clyn`|jeh nttetp edpntynl {e~ol acgn ehn

    bnpj|c|n jh ~pjhk |bn pcan nrvntjanh|co cvvtec`b c| e|bnt pj|np(

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    84/140

    ;;

    0 Ktjiijh ietnp| {jhl |tchpn`| ) vteijon nrvntjanh|p

    0(3 Jh|tel~`|jeh

    Ieooe{jhk |bn clyn`|jeh nrvntjanh| `cttjnl e~| hnct |bn \~adct~adc E}Io~r pj|n jh

    C~p|tcojc l~tjhk Act`b 466> "pnn `bcv|nt 4*/ j| {cp ln`jlnl |e `cttz e~| nrvntjanh|p

    jh c |navntc|n ietnp| jh |bn ^G/ oeegjhk c| jpp~np ei io~r ljyntknh`n {j|bjh |bn ietnp|

    `chevz/ chl p~d `chevz cjt ioe{ ~hlnt p|cdon `ehlj|jehp( \{e nrvntjanh|p {ntn

    `cttjnl e~| c| ch nllz io~r |e{nt evntc|nl dz |bn ^hjyntpj|z ei Nljhd~tkb/ pj|~c|nl

    {j|bjh c Pj|gc Pvt~`n voch|c|jeh "Ktjiijh Ietnp|/ hnct Cdntinolz/ P`e|ochl*( \bn

    nrvntjanh|p ehpjp|nl ei=

    3* C |tchpn`| ei ~o|tcpehj` chnaean|ntp |e jhynp|jkc|n {jhl ioe{ ljyntknh`n{j|bjh |bn ietnp| `chevz/ jh etlnt |e tnoc|n j| |e |bn betj}eh|co clyn`|jeh |nta

    jh |bn nllz `eyctjch`n acpp dcoch`n ns~c|jeh "|nta JY jh ns~c|jeh 3(4*( C

    pn`ehlctz edmn`|jyn {cp |e jhynp|jkc|n |bn knhntco {jhl `ojac|n jh |bn oe{nt

    `chevz/ npvn`jcooz jh tnoc|jeh |e |bn veppjdon vtnpnh`n ei ktcyj|z ioe{p c|

    hjkb|(

    4* Ch ~o|tcpehj` chnaean|nt {jhl vteijon eh |bn nllz `eyctjch`n |e{nt |ejhynp|jkc|n |bn ynt|j`co cjt ioe{p tnoc|nl |e |bn ynt|j`co clyn`|jeh |nta jh |bn

    nllz `eyctjch`n acpp dcoch`n ns~c|jeh "|nta JJJ jh ns~c|jeh 3(4*( C

    pn`ehlctz edmn`|jyn {cp |e jhynp|jkc|n |bn knhntco {jhl `ojac|n jh chl cdeyn

    |bn `chevz iet |bn pj|n/ vct|j`~octoz jh tnoc|jeh |e he`|~thco `ehlj|jehp(

    \bn edmn`|jyn ei |bjp p|~lz {cp |e jhynp|jkc|n |bn vtevnt|jnp ei cjtioe{ {j|bjh chl m~p|

    cdeyn |bn ietnp| `chevz eh c pe `coonl clyn`|jeh hjkb|/ |zvj`cooz ~hlnt ch|j!

    `z`oehj` bjkb!vtnpp~tn c|aepvbntj` `ehlj|jehp {j|b `onct pgjnp chl ojkb| {jhlp c|

    hjkb| "C~djhn| n| co( 466>*( ^hlnt p~`b `ehlj|jehp c |navntc|~tn jhyntpjeh acz ieta

    {j|bjh chl%et m~p| cdeyn |bn ietnp| `chevz tnp~o|jhk jh ktcyj|z ioe{p |bc| l~n |e

    cppe`jc|nl niin`|p ei clyn`|jeh chl io~r `ehyntknh`n et ljyntknh`n/ clyntpnoz niin`|

    nllz `eyctjch`n ancp~tnanh|p ei p`coct s~ch|j|jnp eynt |bn ietnp| dz tnaeyjhk @E4

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    85/140

    ;2

    Ijk~tn 0(3C > ga dz > ga |evektcvbj` acv ei |bn Ktjiijh ijnol pj|n pbe{jhk |bn oe`c|jeh ei |bn nllz

    io~r |e{nt/ |bn acjh le{hpoevn crjp ei |bn @~o|~ooj`b ycoonz "chhe|c|nl C*/ chl |bn ljtn`|jeh chl

    onhk|b ei |bn bjoo poevn vtnpnh| c| |bn |e{nt "chhe|c|nl D*( Vtel~`nl ~pjhk Etlhch`n P~tynz 3=>6 666

    p`con `eoe~t tcp|nt lc|c itea NLJHC Ljkjacv7 b||v=%%ljkjacv(nljhc(c`(~g/ `te{h `evztjkb| tnpntynl(

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    86/140

    ;:

    itea dnoe{ |bn pnhpet dnietn j| bcp |jan |e dn ajrnl ~v{ctlp vcp| |bn nllz

    `eyctjch`n pzp|na "C~djhn| n| co( 466>*(

    0(4 Pj|n lnp`tjv|jeh

    \bn |evektcvbj` pn||jhk ei |bn nllz io~r%nrvntjanh|co |e{nt {j|bjh |bn Ktjiijh Ietnp|

    jp pbe{h jh ijk~tn 0(3( \bjp pbe{p |bn nrvntjanh|co |e{nt jp pj|~c|nl jh |bn ~vvnt

    pn`|jeh ei c pjln ycoonz "bnh`niet|b tninttnl |e cp |bn @~o|~ooj`b ycoonz* eh |bn pe~|b

    pjln ei |bn \cz ycoonz( \bn @~o|~ooj`b ycoonz jp > gjoean|tnp oehk chl etjnh|nl coehk

    ch crjp |bc| bcp c dnctjhk ei 006 lnktnnp/ dnjhk evnh c| j|p het|b{np| nhl {j|b |bn

    @~o|~ooj`b D~th ioe{jhk jh|e |bn Tjynt \cz( C| j|p pe~|bncp| ~vvnt nhl |bn ycoonz bcp

    |bn `bctc`|nt ei c `oepnl ycoonz bncl et betpnpben pbcvnl cavbj|bnc|tn/ 4(4 ga {jln

    chl 4(0 ga oehk "coehk |bn ycoonz crjp*( \bn nrvntjanh|co |e{nt jp pj|~c|nl te~kboz

    jh |bn `nh|tn ei |bjp ~vvnt pn`|jeh ei |bn ycoonz/ pnn ijk~tn 0(3/ {bj`b jp coaep|

    nh|jtnoz ietnp|nl cvct| itea c``npp teclp(

    Pnyntco |evektcvbj` poevn chkonp chl onhk|bp `ch dn jlnh|jijnl {j|bjh |bn @~o|~ooj`b

    ycoonz |bc| acz dn tnonych| {bnh `ehpjlntjhk he`|~thco gc|cdc|j` |zvn ioe{p( \bn

    ljp|ch`n itea |bn ojv ei |bn ycoonz bncl |e |bn Tjynt \cz jp > ga {j|b c `bchkn jh

    nonyc|jeh ei 0;6 a/ `ettnpvehljhk |e c anch poevn ei m~p| eynt < lnktnnp coehk |bn

    nh|jtn onhk|b ei |bn @~o|~ooj`b ycoonz "dnctjhk 006 lnktnnp*( Jh |bn yj`jhj|z ei |bn

    |e{nt j|pnoi |bn le{h poevn ljtn`|jeh bcp dnnh jlnh|jijnl itea Etlhch`n P~tynz acvp

    chl oe`co p~tynz |e dn 066 lnktnnp( \bjp oe`co poevn `ch dn ieooe{nl ~vbjoo "346

    lnktnnp dnctjhk* itea |bn nrvntjanh|co |e{nt iet c ljp|ch`n ei cte~hl 3(4 ga dnietn

    tnc`bjhk |bn ojv ei |bn ycoonz bncl jh |bn yj`jhj|z ei |bn pe~|bnth vct| ei Ktchl|~ooz

    Bjoo/ kjyjhk c `bchkn jh nonyc|jeh ei 34> a/ `ettnpvehljhk |e c anch poevn yco~n ei 9

    lnktnnp( Ji |bn oe`co poevn jp ieooe{nl le{hbjoo "066 lnktnnp dnctjhk* itea |bn |e{nt/

    @~o|~ooj`b D~th jp tnc`bnl ci|nt ehoz 066 a/ {j|b c ltev ei m~p| 46 a/ tnp~o|jhk jh c

    anch poevn ei < lnktnnp(

    Hnct |bn |e{nt |bn ietnp| `chevz bcl c tnvtnpnh|c|jyn bnjkb| ei cte~hl 3> a/

    voch|c|jeh te{p dnjhk etjnh|nl coehk ch ncp|!{np| crjp/ {j|b nyntz iji|b te{ ei |tnnp

    bcyjhk dnnh tnaeynl dz |bjhhjhk "@onanh|/ 4662/vntp `eaa*( \bn |evektcvbj`

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    87/140

    26

    Ijk~tn 0(4"c* P`bnac|j` ltc{jhk ei |bn 4> a bjkb vteijon nrvntjanh| |e{nt {j|bjh |bn Ktjiijh ietnp|(

    "d* Pjln yjn{ ltc{jhk ei |bn 36(2 a oehk ~o|tcpehj` chnaean|nt |tchpn`|( \bn het|b nhl ei |bn

    |tchpn`| {cp pj|~c|nl 3< a ncp| ei |bn vteijon |e{nt(

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    88/140

    23

    poevn ei |bn kte~hl p~tic`n {j|bjh c 46 a tclj~p ei |bn |e{nt dcpn {cp p~tynznl chl

    ie~hl |e dn < lnktnnp/ {j|b c le{h poevn c}ja~|b dnctjhk ei 066 lnktnnp(

    0(0 Nrvntjanh|co pn|~v chl tnp~o|p

    Dn|{nnh Heynadnt 466> chl E`|ednt 4669 |{e nrvntjanh|p {ntn `cttjnl e~| c| |bn

    Ktjiijh ietnp| io~r |e{nt pj|n( \bn pn|~vp iet |bn |{e nrvntjanh|p ctn pbe{h jh

    ljcktcaac|j` ieta jh ijk~tn 0(4( Vbe|ektcvbp ei |bn oe`c|jehp ei |bn nrvntjanh|p ctn

    pbe{h jh ijk~tn 0(0c/ |bn nllz io~r |e{nt/ chl ijk~tn 0(0d |bn ietnp| |bjhhjhk ojhn(

    Betj}eh|co dnctjhkp {ntn ancp~tnl ~pjhk c ackhn|j` pjkb|jhk `eavcpp/ c``~tc`z '%!

    4 lnktnnp( Coo ackhn|j` ljtn`|jehp {ntn `ehynt|nl |e Etlhch`n P~tynz ktjl

    ljtn`|jehp( Tnoc|jyn bnjkb|p {ntn ancp~tnl {j|b c ocpnt onyno chl an|tn t~on iet |bn

    |tchpn`| kte~hl vteijon chl chnaean|nt vep| bnjkb|p "c``~tc`z '%! > `a*/ chl |cvn

    ancp~tn iet bnjkb|p eh |bn nrvntjanh|co |e{nt "c``~tc`z '%! 46 `a*(

    0(0(3 \bn betj}eh|co |tchpn`| nrvntjanh|

    \bn ijtp| nrvntjanh| "pnn ijk~tnp 0(4d chl 0(0d* {cp ch c||nav| |e jhynp|jkc|n io~r

    ljyntknh`n niin`|p tnoc|nl |e |bn betj}eh|co ljyntknh`n |nta "pnn ns~c|jeh 3(4/ |nta

    JY*( C ojhnct |tchpn`| ei ijyn 0L Kjoo T0!>6 ~o|tcpehj` chnaean|ntp/ bnh`niet|b

    tninttnl |e cp pehj` chnaean|ntp/ {ntn pn|~v c| tjkb|!chkonp c`tepp c ietnp| |bjhhjhk

    ojhn 3> |e 46 a ~vpoevn ei |bn nllz `eyctjch`n |e{nt( \bn < a {jln |bjhhjhk ojhn

    {cp etjnh|c|nl coehk ch ncp|!{np| crjp/ pnn ijk~tn 0(0d( \bn ijyn pehj` chnaean|ntp

    |bc| `eavtjpnl |bn |tchpn`| {ntn pn|~v eh p|nno p~vvet| vep|p pe |bc| |bnjt ancp~tjhk

    yeo~anp {ntn 3(9> a cdeyn oe`co kte~hl onyno "cko*( Jh ijk~tn 0(4 |bn p~tynznl

    tnoc|jyn kte~hl onyno jp voe||nl coehk |bn |tchpn`|/ chl |bn |zvj`co voe~kbnl p~tic`n

    ei ch ct|jij`jco `ehjint voch|c|jeh jp pnnh/ cp jp |bn het|b!pe~|b `eavehnh| ei |bn

    le{hbjoo |evektcvbj` poevn "le{hbjoo poevn < lnktnnp/ le{hbjoo ljtn`|jeh 066

    lnktnnp itea het|b*( \bn |tchpn`| {cp etjnh|c|nl nrc`|oz het|b pe~|b/ |e {j|bjh |bn

    ancp~tjhk c``~tc`z ei |bn p~tynz ns~jvanh| ~pnl(

    [j|b tnintnh`n |e ijk~tn 0(4d/ |bn pehj` chnaean|nt jh vepj|jeh 3 "bnh`niet|b

    tninttnl |e cp pehj` chnaean|nt 3* {cp oe`c|nl {j|bjh |bn oe{nt vct| ei |bn 3> a

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    89/140

    24

    Ijk~tn 0(0"c* Vbe|ektcvb ei |bn 4> a bjkb nllz io~r |e{nt ~pnl iet |bn vteijon nrvntjanh|/ |cgnh

    itea j|p ncp| pjln dnietn |bn jhp|cooc|jeh ei |bn 4 a oehk chnaean|nt p~vvet| deeap( "d* Oeegjhk ncp|/

    ~v |bn poevn ei |bn < a {jln ietnp| |bjhhjhk ojhn `teppnl dz |bn nrvntjanh|co |tchpn`|( \bn `nh|tco Kjoo

    T0!>6 ~o|tcpehj` chnaean|nt ei |bn |tchpn`| "chnaean|nt 0*/ jp pbe{h jhp|coonl {j|b j|p ancp~tjhk

    yeo~an c| 3(9> a cdeyn kte~hl onyno(

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    90/140

    20

    bjkb Pj|gc Pvt~`n ietnp| `chevz/ m~p| ~hlnt < a het|b ei |bn |bjhhjhk ojhn nlkn( Pehj`

    chnaean|nt 4 {cp oe`c|nl c| |bn het|bnth nlkn ei |bn |bjhhjhk ojhn/ cte~hl 6(> a

    pe~|b ei |bn `chevz vtevnt/ d~| jh c vepj|jeh p|joo jh vterjaj|z |e pacoo dtch`bnp itea

    |bn `chevz( Pehj` chnaean|nt 0 {cp pj|~c|nl jh |bn ajllon ei |bn |bjhhjhk ojhn 3(> |e4(6 a c{cz itea chz `chevz nonanh|p( Pehj` chnaean|nt < {cp m~p| dnzehl |bn

    pe~|bnth nlkn ei |bn |bjhhjhk ojhn/ cde~| 6(> a jh|e |bn `chevz( Ijhcooz/ pehj` > {cp

    oe`c|nl jh c tnoc|jynoz lnhpn vct| ei |bn `chevz coaep| < a itea |bn |bjhhjhk ojhn

    nlkn(

    \bn tc|jehcon dnbjhl |bn pn||jhk e~| ei |bn pehj` chnaean|ntp coehk |bn |tchpn`| {cp

    |e pcavon |bn yctje~p {jhl nhyjtehanh|p ei `chevz/ `chevz nlkn chl evnh |bjhhjhk

    ojhn( J| {cp bevnl |e ancp~tn chz `tepp |bjhhjhk ojhn/ chl cvvterjac|noz c`tepp

    le{hpoevn ioe{ ljyntknh`n niin`|p |bc| ajkb| e``~t( \bn nrvn`|nl le{hpoevn

    ljtn`|jeh |bc| chz he`|~thco ktcyj|z ioe{ ~hlnt p|cdon `ehlj|jehp ajkb| dn jhio~nh`nl

    dz {cp 066 lnktnnp itea het|b "ioe{ itea 346 lnktnnp*( Co|nthc|jynoz |bn |bjhhjhk

    ojhn j|pnoi ajkb| p|nnt p~`b c ioe{ |e{ctlp 4;6 lnktnnp itea het|b "ioe{ itea :6

    lnktnnp*(

    [jhl ioe{ lc|c lntjynl itea |bn ijyn pehj` chnaean|ntp ei |bn |tchpn`| {ntn oekknl

    ~pjhk c ocv|ev `eav~|nt chl jh|ntic`n non`|tehj`p oe`c|nl jh |bn jhp|t~anh| pbnl c|

    |bn de||ea ei |bn nllz io~r |e{nt/ pnn ijk~tn 0(4c( \bn nrvntjanh|co ns~jvanh| chl

    ocv|ev {ntn ve{ntnl dz c 34 Y dc||ntz cttcz "`ehhn`|nl jh vctcoono*/ {bj`b {e~ol

    ve{nt |bn |tchpn`| nrvntjanh| iet c acrja~a ei cte~hl 3> be~tp eh`n i~ooz

    `bctknl(

    \bn nrvntjanh|co voch {cp |e aehj|et pzhev|j` {nc|bnt `bct|p ei |bn Het|b C|och|j`

    chl ^G ctncp/ jpp~nl dz |bn ^G An|neteoekj`co Eiij`n( Iet|b`eajhk ch|j!`z`oehj`

    `ehlj|jehp |bc| {ntn kejhk |e ciin`| |bn nrvntjanh|co pj|n c| hjkb| {ntn jlnh|jijnl(

    \bn acmetj|z ei p~`b ch|j!`z`oehj` `ehlj|jehp `ehpjp|nl ei tjlknp ei bjkb vtnpp~tn

    |bc| {e~ol |zvj`cooz `tepp |bn pj|n jh 4< be~tp et onpp( \bn pj|n {e~ol |bnh dn yjpj|nl

    chl |bn dc||ntz cttcz `bctknl ~pjhk c vn|teo knhntc|et/ {j|b |bn nrvntjanh| dnjhk pn|

    t~hhjhk jh |bn ci|ntheeh m~p| dnietn |bn tnpnct`bnt lnvct|nl |bn pj|n( \bjp tnp~o|nl jh

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    91/140

    2 ~h|jo |bn 33|b

    Indt~ctz 4669/ {j|b c |e|co ei 04; be~tp ei 0L 46 B} cjt ioe{ lc|c dnjhk `eoon`|nl

    itea nc`b ei |bn ijyn pehj` chnaean|ntp |bc| `eavtjpnl |bn |tchpn`|(

    Dz lnic~o|/ |bn lc|cpn| |bc| {cp ed|cjhnl {cp nrvn`|nl |e dn djcpnl |e{ctlp ch|j!

    `z`oehj` `ehlj|jehp/ jh {bj`b ktcyj|z ioe{p tnoc|nl |e p|cdon c|aepvbntj` `ehlj|jehp

    ajkb| dn ln|n`|nl(

    0(0(4 \tchpn`| nrvntjanh| tnp~o|p chl ljp`~ppjeh

    Ijk~tn 0(< pbe{p bjp|ektcap ei {jhl ljtn`|jeh chl |e|co yn`|et {jhl ackhj|~ln/ ^/

    lntjynl itea lc|c `eoon`|nl dz pehj` chnaean|nt 0/ {bj`b {cp vepj|jehnl `nh|tcooz

    jh |bn |bjhhjhk ojhn "pnn ijk~tnp 0(4d chl 0(0d*/ chl |bn pehj` chnaean|nt c| 4> a cko

    eh |ev ei |bn nllz io~r |e{nt( Jh etlnt |e `tnc|n |bn bjp|ektcap/ |bn tc{ 46 B} lc|c

    {ntn vte`nppnl |e `tnc|n anch bcoi be~toz yco~np ei {jhl ljtn`|jeh chl ackhj|~ln(

    \bnpn bcoi be~toz yco~np {ntn |bnh ~pnl |e `ehp|t~`| |bn itns~nh`z bjp|ektcap

    pbe{h jh ijk~tn 0( a* c| |bn pj|n ctn jhio~nh`nl dz de|b |bn oe`co poevn {bj`b p|tn|`bnp

    ~vbjoo iet c betj}eh|co ljp|ch`n ei cte~hl c gjoean|tn/ chl pean e|bnt inc|~tn eh c

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    92/140

    2>

    Ijk~tn 0(

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    93/140

    29

    dnctjhk `oepn |e |bn ycoonz crjp( Nrcajhc|jeh ei |bn |evektcvbj` `eh|e~tp jhlj`c|np

    |bc| |bn poevn cdeyn |bn nllz io~r |e{nt jp |ntajhc|nl c| j|p pe~|b{np| nr|nh| dz c

    pnyntco b~hltnl an|tn {jln he|`b jh |bn `oepnl ycoonz bncl |bc| ietap |bn ~vvnt

    vct| ei |bn @~o|~ooj`b ycoonz( \bjp inc|~tn jp eh c dnctjhk ei dn|{nnh 36lnktnnp itea |bn pj|n/ chl `e~ol nrvocjh |bn tnl~`|jeh jh |bn {jhl ljtn`|jeh

    itns~nh`z pnnh jh |bc| ljtn`|jeh(

    Javet|ch|oz/ ijk~tn 0(

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    94/140

    2;

    ljiintnh| |e |bn ns~jyconh| hjkb||jan inc|~tn cotnclz ljp`~ppnl {j|b tnpvn`| |e ijk~tn

    0( a cko {j|bjh |bn

    ietnp| chevz(

    Dz `eh|tcp|/ |bn vncg `ettnpvehljhk |e |bn le{h!poevn ioe{ pnnh c| 4> a cko "336 |e

    3>6 lnktnnp*/ `ettnpvehlp {noo |e |bn acjh {jhl ljtn`|jeh vncgp edpntynl c| 3(9> a

    cko iet de|b lcz chl hjkb| "366 |e 3 a cko "36 a cdeyn |bn ietnp|

    `chevz* acz dn `e~vojhk |e et nynh ltjyjhk |bn p~d!`chevz le{hpoevn%le{h!

    ycoonz ioe{ c| 3(9> a/ {bntncp ~v!ycoonz {jhl ioe{p c| 4> a le he| tnp~o| jh ~v!

    poevn ljtn`|nl cjt ioe{p c| 3(9> a cko(

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    95/140

    22

    [j|b tnkctl |e |bn |evektcvbj` acv pbe{h jh ijk~tn 0(3/ j| `ch dn pnnh |bc| |bn

    le{hpoevn ljtn`|jeh c| |bn nrvntjanh|co pj|n "chhe|c|nl D*/ chl `ehpns~nh|oz |bn

    nrvn`|nl ljtn`|jeh ei chz p~d!`chevz gc|cdc|j` |zvn ioe{p |bc| acz niin`| |bn pj|n/

    ctn jh |bn pcan ljtn`|jeh cp |bn le{h!ycoonz ioe{ edpntynl c| 4> a "ijk~tn 0( a ~hlnt p|cdon hjkb||jan `ehlj|jehp ctn jhlnnl gc|cdc|j` ktcyj|z

    |zvn ioe{p/ et antnoz cjt ioe{p ltjynh itea cdeyn |bn `chevz et c `eadjhc|jeh ei

    de|b(

    \bn nrvntjanh| lnp`tjdnl jh `bcv|nt 4 tnoc|jhk |e |bn \~adct~adc ietnp| {cp aetn

    p|tcjkb|iet{ctl jh |bjp tnpvn`|/ cp jh |bc| `cpn |bn nrvn`|nl chl ancp~tnl ljtn`|jeh ei

    p~d!`chevz ktcyj|z ioe{p {ntn ljiintnh| itea aep| ei |bn {jhl ljtn`|jehp ancp~tnl

    cdeyn |bn ietnp| `chevz "c| ;6 a cko*(

    Ijk~tnp 0( a p!3

    oe{nt(

    \bn anch ynoe`j|z/ ^/ bjp|ektca iet 4> a cko eh |bn |e{nt iet coo be~tp "hjkb| chl

    lcz* jp pbe{h jh ijk~tn 0( chl 3(6 a p!3

    ( \bn

    acrja~a yco~n ei bcoi!be~t anch {jhlp/ ^/ pnnh c| 4> a {ntn ;(6 |e ;(> a p!3

    (

    Ijk~tn 0(> pbe{p ch coehk |tchpn`| ljyntknh`n!ojgn s~ch|j|z |bc| bcp dnnh `co`~oc|nl

    dn|{nnh yctje~p chnaean|nt vepj|jehp coehk |bn het|b!pe~|b etjnh|nl onhk|b ei |bn

    |tchpn`| "pnn ijk~tn 0(4d*( \bjp ljyntknh`n!ojgn yco~n {cp `co`~oc|nl dz |cgjhk |bn

    ljiintnh`np dn|{nnh bcoi be~toz anch het|b ic`jhk yn`|et `eavehnh|p ei {jhl

    ynoe`j|z lntjynl itea c vcjt ei chnaean|ntp/ p~d|tc`|jhk |bna chl ljyjljhk |bn tnp~o|

    dz |bn ljp|ch`n dn|{nnh |bn |{e chnaean|ntp( \bjp tnp~o|nl jh c yco~n |bc| {cp

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    96/140

    2:

    Ijk~tn 0(>C `co`~oc|nl coehk |tchpn`| ljyntknh`n ojgn s~ch|j|z iet |bn nh|jtn 36(2 a onhk|b ei |bn

    3(9> a cdeyn kte~hl onyno |tchpn`|/ `co`~oc|nl itea lc|c kc|bntnl c| j|p het|b chl pe~|b nhlp/ iet "c*

    lcz chl "d* hjkb|( Vchnop "`* chl "l* pbe{h |bn coehk |tchpn`| ljyntknh`n ojgn s~ch|j|z `co`~oc|nl

    ~pjhk lc|c itea |bn nlknp ei |bn evnh |tchpn`|/ 0(:> a cvct|( Bcoi be~t anch yco~np ei |bn het|b

    ic`jhk yn`|et {jhl `eavehnh|p {ntn ~pnl cp |bn pe~t`n lc|c iet |bn `co`~oc|jehp( Coo |bn ljyntknh`n

    ojgn s~ch|j|jnp ctn voe||nl ckcjhp| {jhl ljtn`|jeh ancp~tnl c| 3(9> a cko c| |bn het|b nhl ei |bn

    |tchpn`|(

  • 8/9/2019 Jones K H 2008 MPhil Thesis Measurement of Advection and Sur

    97/140

    :6

    vepj|jyn iet `ehlj|jehp ei ioe{ ljyntknh`n coehk |bn |tchpn`|/ chl hnkc|jyn iet

    `ehyntknh`n coehk |bn pcan crjp( \bn ~hj|p ei |bjp s~ch|j|z ctn tn`jvte`co pn`ehlp

    "p!3

    *(

    \bn ljyntknh`np pbe{h jh ijk~tn 0(> ctn voe||nl ckcjhp| {jhl ljtn`|jeh ancp~tnl c|

    |bn het|b nhl ei |bn |tchpn`| "chnaean|nt 3*( Ijk~tnp 0(>c chl 0(> d pbe{

    ljyntknh`np `co`~oc|nl dn|{nnh |bn nr|tnan het|b chl pe~|b nhlp ei |bn |tchpn`|

    "chnaean|ntp 3 chl >/ {j|bjh |bn ietnp| `chevz/ pnvctc|jeh 36(2 a*/ iet hjkb| chl

    lcz tnpvn`|jynoz( De|b |bnpn hjkb| chl lcz|jan voe|p jhlj`c|n |bc| ioe{ `ehyntknh`n

    "hnkc|jyn yco~np* coehk |bn |tchpn`| acz dn cppe`jc|nl {j|b cjtioe{p `eajhk itea |bn

    ~vpoevn ljtn`|jeh "cte~hl 346 lnktnnp dnctjhk itea het|b*(

    \bn ijk~tnp 0(>` "hjkb|* chl 0(>l "lcz* pbe{ ljyntknh`np `co`~oc|nl dn|{nnh

    chnaean|ntp 4 chl a cvct| c| |bn het|b chl pe~|b nlknp ei |bn evnh

    |bjhhjhk ojhn "pnn ijk~tn 0(4d*( Bntn |bn ackhj|~ln ei |bn ljyntknh`n bcp c acrjac

    cppe`jc|nl {j|b |bn dnctjhkp ei :6 |e 3>6 lnktnnp/ {bj`b tchknp itea |bn ~v!|bjhhjhk

    ojhn/ |e ~vpoevn/ |e ~v!ycoonz ljtn`|jehp( Jh|ntnp|jhkoz be{nynt/ {bnh veoctj|z jp

    `ehpjlntnl/ |bntn jp c hnkc|jyn vncg "`ehyntknh`n* cte~hl 346 lnktnnp chl vepj|jyn

    vncg "ljyntknh`n* cte~hl 3>6 lnktnnp dnctjhk/ pnnh `onctoz jh 0(>` "hjkb|*/ d~|