The University of AdelaideDepartment of Geology and Geophysics

LONGITUDINAL DUNES:THEIR GENESIS AND ORDERING

George Kuang Yee Tseo

Volume Two(figures and plates)

January, 1986

A thesis submitted to the University of Adelaidein fulfilment of the requirements for the

degree ofDoctor of Philosophy

by

/tr.¿¡ødea1 ¡L- I - ¿9 ;

PIates

Liet of Plates

Plete 1. Landsat imagery of six linear dune fields'

Plate 2. Rub' al Khali, Yemen'

Plate B. Erg'Bilma, Niger.

Plate 4. Negev Desert, Israel.

Plate 5. Simpson Desert, Australia'

Plate 6. ,,Fishinghook" linear dunes of western china.

Plate 7. "Honeycomb" linear dunes of western China'

Plate 8. "Dendritic" linear dunes of western China'

Plate 9. Navajo Indian Reservation, U'S'A'

plate 1O. Linear dunes with barchanlike slip faces (Central Wahiba Sands,

Oman).

Plate 11. Snow barchans.

Plate 12. Linear dunes emerging from the leeward side of a debris ridge'

Plate 13. smoke-marked roll vortices in a shallow fluid chamber'

Plate 14. Rotation canister.

Plate 15.tank.

Longitudinal streaks recorded in the china-clay bed of a rotation

Plate 1o. Longitudinal features recorded in the sand bed of a rotation canister'

Plate 17. Stationary vortìces produced in a rotation tank while fluid was moved

radially across the bottom.

Plate 18. Single stationary vortex'

plate lg. Longitudinal features recorded in the sand bed of a rotation canister'

Plate 20. Notched linear dunes in northern Africa'

Plate 21. Notched linear dunes in central Australia'

Plate 22. Instrumented tower.

l

Plates

Plate 28. Smoke trails.

Plate 24. Airplane wing-mounted electrical field measurement device.

Plate 26. Instrumented airplane foremast'

Plate 2o. Landsat image of the area of the study linear dune'

Plate 27. Bare portion of the study dune eastern flank'

Plate 2t. vegetated portion of the study dune eastern flank.

Plate 29. StudY dune summits.

Plate 3o. study dune summits as viewed looking south along the crest.

Plate 31. Study dune surface ripples.

plate 82. TÌansition between dune and interdune corridor (study dune western

perimeter).

plate BB. Close-up view of transition between dune and interdune corridor

(study dune western Perimeter).

ptate 84. Two stage transition between dune and interdune corridor (study

dune western perimeter).

plate 85. "Clay leave" erosional structures (eastern perimeter)-

plate BO. Portion of interdune corridor covered by low vegetation (west of study

dune).

plate BT. Portion of interdune comidor covered by grass (east of study dune).

plate St. Portion of interdune corridor covered by sand and very sparse low

vegetation (west of studY dune)'

plate 3g. Portion of interdune corridor covered by pebbles (west of study dune).

Plate 40. Electronic wind vane'

Plate 41. Electronic wind vane mounted on a pole'

Plate 42. Grid of stakes.

plate 48. Tracking theodolite and balloons (close to study dune western perime-

ter).

Plate 44. tacking theodolite (- 200 m west of study dune)'

Plate 46. lr{eander in the Colorado River.

Plate 48. Covergent dunes that do not coalesce (South Australia).

Fígures

List of Figures

Figure l. Sectional profiles of typical and sharp-crested longitudinal dunes.

Figure 2. The Australian system of linear dune frelds'

Figure B. The northern African system of linear dune frelds and its associated

wind pattern.

Figure 4. The Australian arc of relict dunes and a hypothetical trace of ancient

summer anticyclones.

Figure 5. Prevailing winds of the modern summer anticyclone.

Figure O. Aerial trace comparing the trend of newly forming linear dunes and

,"ti.t linear dunes of the northeastern shore of Lake Flome, south Australia.

Figure Z. Longitudinal dune with shifting crest and vectors of causal storm

winds.

Figure B. Series of pictures depicting the transition from a barchan to a linear

dune as a result of bidirectional winds.

Figure g. Longitudinal sand strips deposited during a stor,m and the hypothet-

ical secondary circulation.

Figure lO. Roll vortices and their relationship to longitudinal dunes, soaring

birds and longitudinal clouds.

Figure 11. Computer plots of various forms of longitudinal dunes and their

internal structure.

Figore 12. Aerial trace of a portion of the Simpson Desert displaying a high

density of Y junctions.

Figure 13. Dune profiles in relation to Y junctions'

Figure 14. Flow and pressure gradient forces around parallel travelling ships.

Figure 15. Internal structure of Bénard convection cell.

Figure 16. Schematic diagram of smoke chamber'

Figure 17. Wind field of roll vortices simulated using Doppler radar data.

Figure 18. Theoretically derived flow parameter profrles ol roll vortices.

Figure 19. Theoretical secondary flow in the planetary boundary layer'

Figures

Figure 2O. Schematic diagram of rotation tank-

Figure 21. Schematic diagram of rotation canister'

Figure 22. Spiral axes of the two mutuaþ orthogonal sets of roll vortices'

Figure 23. The formation of spiral sediment bands by roll vortices.

Figure 24. Graph depicting the relationship between the measured and calcu-

latãd anguìar divergence of longitudinal roll vortices from the mean flow.

Figure 25. Itlustrations depicting the consequences of the unconditional stabil-

ity6t roll vortices situated with respect to longitudinal dunes such that surface

flow convergence zones coincide with dune crests.

Figure 26. Illustrations depicting the consequences of the conditional stability

of ioll vortices situated with respect to longitudinal dunes such that surface flow

divergence zones coincide with dune crests'

Figure 27. Spectra of velocity components derived from airplane measurements.

Figure 28. Ideal rectangular circulation, elliptical circulation and the zones of

turbulent entrainment associated with elliptical circulation.

Figure 2g. Variations of the vertical electrical potential gradient as measured

using aircraft.

Figure BO. Simultaneous records of the vertical electrical potential gradient

and relative humiditY.

Figure 81. The relationship between geostrophic wind and roll vortices.

Figure 32. tlorizontal fluctuations of lvind parameters'

Figure 38. Recommended flight patterns for aircraft measurement of wind

parameters.

Figure 34. schematic diagrams of reverse flow temperature probes.

Figure s5. Map of simpson Desert, Strzelecki Desert and environs.

Figure BO. Plan-view symbolic representation of study linear dune depicting

salient geourorphic features'

Figure BZ. Grid of stakes over the study dune and its topographic form lines.

Figure BB. Arc of ôolored sand aggregates on the study dune avalanche face

believed to indicate a leervard side rotor.

Fígures

Figure Bg. i{ite and ribbon configuration believed to indicate a windward side

rotor.

Figure 4O. Delta wing kite.

Figure 41. Kite configuration believed to indicate roll vortices.

Figure 42. Kite confrguration believed to indicate roll vortices.

Figure 48. Array of tethered kites needed for full wavelength roll vortices

observations in linear dune fields.

Figure 44. Kite configuration believed to indicate quasi-laminar flow.

Figure 46. Kite configuration believed to indicate quasi-laminar flow.

Eigure 40. Peculiar kite configuration.

Figure 47. Horizontal plane wind directions across the southern perimeter of

the study site.

Figure 4E. Vertical plane wind directions across the southern perimeter of the

study site.

Figure 4g. Relative wind speed measurements across the southern perimeter

of the study site.

Figure 5O. Horizontal flow divergence/convergence pattern over the study lin-

ear dune.

Figure 61. Streamlines during oblique flow.

Figure 52. Study site deposition/erosion record for the period from December

16, 1982 to December 18, 1982.

Fígure 58. Study site deposition/erosion record for the period from December

14, 1982 to December 24, 1982'

Figure 54. Study site deposition/erosion record for the period from December

24,1982 to February 11, 1983.

Figure 55. Study site deposition/erosion record for the period from December

14, 1982 to February 11, 1983.

Figure 56. Study site deposition/erosion record for the period from February

11, 1983 to April 10, 1983.

Figure 57. Study site deposition/erosion record for the period from December

14, L982 to April 10, 1983.

Figures

Figure 58. Deposition/erosion records for the head of the study dune-

Figure 69. Study site firmness record for December 22, 1982

Figure 6O. Study site firmness record for January 30, 1983

Figure O1. Change in firmness record for the study site for the period fromDecember 22, 1982 to January 30, 1983.

Figure 62. Study site deposition/erosion record for the period from December

22, 1982 to January 30, 1983.

Figure 03. Lines along which topographic change was monitored over the studysite

Figure 64. Topographic change in the study site northern perimeter between

December 8, 1982 and January 29, 1983.

Figure O5. Topographic change in the study site southern perimeter between

December 8, 1982 and January 29, 1983.

Figure 66. Topographic change in the study site crestal axis between December8, 1982 and januan{ 29,1983.

Figure 67. Flow and sediment transport convergence and divergence zones

across a gridded area.

Figure 6t. Stake with vaseline-covered file cards for sand collection duringsaltation.

Figure 69. Distribution of colored grains over the study site on December 16,

1982.

Figure 7O. Inferior mirage of a mountain.

Figure 71. Optically deduced vertical temperature profile for Gershoj, Den-

mark.

Figure 72. Solar radiative heating of a linear dune

Figure 73. Comparative diagram of parabolic, sine, circular and sine-generatedcurves

Figure 74. River meanders.

Figure 75. FIow asymrnetry for channel bends of various shapes

Figure 78. Idealized flow patern of a typical meander.

Figures

Figure 77. Idealized shear pattern for turning flow if transverse flow is to be

prevented.

Figure 78. Linear sand banks of the Norfolk Banks area in the North Sea-

Figure 79. Flow and sediment transport deflection in the shallow water over a

linear sand bank.

Figure 8O. Flow momentum over a linear sand bank and far from it"

Figure 8L. Momentum vector and its components.

Figure 82. Illustration depicting the relationship between the parameters lr

and $f and the bottom toPograPhY'

Figure 88. The relationship between lateral flow speed variation and topogra-

phv.

Figure 84. Linear sand bank growth rate contours

Figure 85. Inflection point vertical velocity profile and vertical profiles of asso-

ciated parameters.

Figure E6. Curves for neutral stability for a two- dimensional boundary layer

with two-dimensional disturbances.

Figure E7. Sketch of Lake Phitlipi area, near the eastern margin of the Simpson

Desert in western Queensland.

Figure E8. Map of southwestern margin of Lake Eyre, central South Australia

and map of northern shore of Lake Gregory, central South Australia.

Figure tg. Map of the Diamantina flood plain near Birdsville, Queensland.

Figure gO. Stagnation pressure over the windward face of an obstacle and the

associated flow vertical velocity profile'

Figure 91. Pressure gradient generation of vortical fl.ow around an obstacle

Figure g2. Roll vortìces generated around a namow obstacle and around the

ends of a wide obstacle.

Figure 93. Görtter instability over a concave surface.

Figure 94. The development of a series of longitudinal deposition ridges froma single mound.

Figure g5. The development of longitudinal dunes from a clebris riclge.

Figures

Figure 96. Leeward secondary flow and the resultant longitudinal deposition

in wind tunnel trials using plasticene obstacles'

Figure 97. wind rotor between two converging linear dunes.

Figure 9t. Sine-generated curve.

Figure 99. Ekman sPiral.

Figure 1OO. centriÍugal instabitity for fl.ow over a concave slope.

1 8'30'l 26"30',

/o"^ro,

?3'00

1 5"00'

e-

zf3oi-&ihÞI

N

t

@ 'ta¿ 24'30'

KM

M

plate l. ,,Landsat imagery sample areas on which measurements of linear width, length,

and wavelength were *id". Nornbers in parentheses refer to the regions listed in table

36. Each sariple is an area 50 km by 50 km, or 2,500 km2 (1,550 mi2) in a sand sea. A)

Kalahari Desert southern Africa; simple dunes B) Great Sandy Desert, Australia; simple

dunes C) Southwestern Rub' al Khali, Saudi Arabia; compound dunes D) Southwestern

Sahara; áompound dunes E) Namib Desert, South-west Africa; complex dunes F) Western

R.b' ai Khaii, Saudi Arabia; complex dunes." (Flom BREED and GR9W, 1979).

N

I

B DP:948ANNUAL

DP=96FEB.

DP:119APR.

DP:71JUNE

DP=25AUG.

DP:49 DP:55DEC.ocT

Plate 8. "Landsat imagery of linear dunes A) in the Erg Bilma. Both simple andcompound linear dunes occur near Bilma in the same regìonal wind environment. B)Annual and six monthly sand roses for Bilma, Niger, illustrate a wide unimodal high-energT wind regime near the dunes. Arrow indicates resultant drift direction. Number incenter circle of rose is reduction factor. DP (drift potential, in vector units) is given foreach rose." (Fbom FRYBERGER, 1979).

Plate 6. SimPson Desert dunes'

ó"pu.t-.ot of Linds, South Australia)(Poolowanna 1:250,000 photograph' SVY' 2445'

Plate 6. "Fishinghook" linear dunes of

rvestern China. (From CHINA TAMES HER

DESBRTS, 1977).

ÇT

t\þ

,i

\I

t

,s

Þ--Plate 7. "Honeycomb" linear dunes of

*".t"* China. (From CHINA TAMES HER

DESERTS, 1977).

Plate 8. "Dendritic" linear dunes of

ru".tã.o China. (From CIIINA TAMES HER

DESERTS, 1977).

+t

l.

a

,

+Josh

()

.r') Í?gD

3 5'5 5'

.({.a\ù

4

,'1\\\\\\ '

[/¡r]r nk{) [¡¡

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:ì l\ll

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0

t"

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q*

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Klv'l)1*

Plate 9. simple linear dunes from the Navajo Indian Resewation, northern Arizona,

U.S.A. (Flom BREED and GROW, 1979)'

Ptate lO. Linear dunes "with barchan-

like slip faces developed on their western

flanks as a result of gentle eastern wtn-

t-". *i"at. Central Wahiba Sands' Oman'"

(From GLENNIE, 1970')

Plate 11. Snow barchans of the Lake

E.i" .no." linked by the elongation of ole of

it " t oto. of the windward barchan' (FTom

HANNES and HANNES, 1982)'

rvhìtc to rcd sand.

t1234Scrn

!!È

a - _.-.

>

j.=:¡-

CIIANDRA, 1938).

Plate 14. Rotation canister set uP for

photography' (Flom HORST, 1970b)'

III

I

Plate 16. "china-clay record of instability." The direction of disk rotation was

counterclockwise, the roiation rate was 3200 rev/min and the disk radius was 4.35 in'

(From GREGORY, STUART and WALKER, 1955)'

Plate 16' Longitudinal features developed on the bottom sand bed the rotation canister.(trÌom HORST, te70b).

tlit\

Plate 17' Stationary vortices produced jn a rotation tank while fluid was moved radiallyacross the bottom. (From FALLER and KAYLOR, f966).

Plate 19. Longitudinal features in

bottom sand bed of the rotation canister'

Note that in this instance only the fluid

near the fringe of the canister seems to have

succombed to an organìzed instability' (From

HORST, l97ob).

Twidale)'

¡

Þ

:

ii

I

B

Þ 4.,T

lt?

Ptate 22. A) 100 rn tower instrurnented for the observation of turbulant eddies over the

low canopy of a forest in central Eyre Penninsula, south Australia. Note that the pairs

of short extension arms, mounted with a cup anemometer and a shielded temperature

sensor, are logarithmicaily spaced. This is configuration is promptgd by the logarithmic

vertical variatlon in wind rp""a toa temperature. B) Long horizontal boom mounted with,

from right to left, wind vane and propellor anemometer, vertical wind component rotor

anemorieter, and hygrometer. The encasement for the thermometer mounted on the short

arm, of whici a ct"ir"r view is afforded in this image, is designed to shield the sensor from

direct solar radiation and wind. (chen Fa Zu, Chinese Academy of science).

a

I

Plate 28. "Smoke laid parallel to the

wind by a plane flying horizontally. Note

the vertical development of points A and

B. Elapsed time between (i) and (ii) is 88

seconds." (Taken from WOODCOCK and

WYMAN, 1947).

Plate 24. "Installation of potential gra-dient probes on wing of Tlipacer aircraft."(From VONNEGUT, MOORE and MÄLLA-HAN, 196l).

Plate 26. The instrumented fo¡emastor noseboom of the de Ilavilland Buffalo air-craft N326D of the N¿tional Center for At-mospheric Research (NCAR), Boulder, Col-

orado, U.S. (tlom LENSCHOW, 1972).

Bout¡n0

-tUZ

l

I

I1

I

I

I

8d

i

fl*

\I

!

^I

)

(!

'¡1:

Plate 26. Landsat image of the area just to the south of Moomba ga,s camP. The study

ã""ã i",rrrr.ed ,,s,,. (stizelecki l:250,ó00 photograph, svY. 2548, Department of Lands,

South Australia).

\Ja.

'î

i

-it

Plate 27. Eastern flank of the study dune'

,,, -#-

,{.\,,.r#

J-- .

t\,L^ y'-'. -,4¡-,. ', *' ,,.:_i.,_,

î'- .

-r"fu

;r' !L;.

.É¿tfir,

-".r&

-nrw

Plate 2t. The comparatively well vegetated eastern flank of the study dune

Plate 31. RiPPles on the studY dune

,ottu." as viewecl looking south and into the

wind.

Plate 33. A close-up view of the transi-

tion betrveen the dune and the interdune cor-

ridor (See Pt. 32).

Plate 32. A Point along the western

perimeter of the study dune at r¡vhich ^the

iransition between the dune and the firmmaterial of the interdune conidor is abrupt'

Plate 86. "Clay leave,"erosional struc-

turesjust beyond the eastern perimeter of the

study dune.

Ptate 96. Interdune corridor area tothe west of the study dune consisting mainlyof low vegetation.

Plate 87' Grassy interdune area to the

east of the studY dune'

Plate 8E. Sandy interdune corridorarea just to the west of the study site witha very sparse population of low vegetation'

Plate 89. Pebbly interdune corridor area to the west of the study dune with some low,

woody debris.

Plate 4O. Variable resistance wind vane utilizing a styrofoam tail and a DC 100

microampere meter.

,.{

i

gl t?

Electronic wind vane mounted on top o1 a - 2.5 m wooden pole forPlate 41.measurements

)

I

IIt'

t.

ll

I

-.\--- rli

',i

._q t

'¡{-.

Plate 42.monitoring

Grid of stakes planted over the study site for use in deposition/erosion

Plate 43. tacking theodolite and balloons before launching close to the western

perimeter of the study dune.

-..r4ff

Plate 44. Tracking theodolite - 200 m west of the dune.

Plate 46. Several examples of dunes that converge but do not coalesce can be foundin this image, most notably the three convergent dunes in the center. (Gason l:250,000photograph, ïVY.2473, Department of Lands, South Australia. )

Sectiou

A

-ôo

Poroll€l lonq¡rudinol

fiì Lons¡rud,ñol dunes ol

"..,dblc lrcñd.

B

SVONEY

E Simpson Desert

F Sturt's Stony Desert

[TWIDALE, lesll

Figure l. A) Section throügh a typical longitudinal dune. .B) Section through the sharp-crested

lc,n"gituclinal clunes founcl in the vicinity of Qinghai, central china

PER

o 1oo 200 l@ ¡00 H

l-,-+çl-È_U0 100 200 100 ¡00 xM

A Great Sandy Desert

B Tanami Desert

C Gibson Desert

D Great Victoria Desert

BR IS

N

.I

ì\

Spnngs

Figure 2. The continental system of Australian linear dune fields.

o too aoo

/)'-.lN

.? \Ir

¡l \ Au

¡o

to

zI

t'

\'E-

t-

IIl" IIr_Fo

-þ'N

Cap Jby

Ircpc

,o'w

to

t to'E 20'

Cilllol

I

,1,i

jfiI

30'

II

,ùi

lrrft¡lIIt.d(I

- 'r74t

I

III

ù

r$

--I

¡ aE

II

a-..

III

III

a tIt

ItI

Y

E

ç !I +t

Figure S. A) Saharan and Sahelian linear deposition and deflatïon feature patterns

as ãerived from satellite data. Dashed lines represent what are Presumably deposi-

tion features, and sotid lines represent what are presumably deflation features' B)

Saharan wind patterns based on satellite data'

t-

::-

a

N

'4

,a

=?t."'¿

ù

--\.\

¿

Figure 4. The Àustralian cont¡nental arc of relict linear clunes and an approximation ofthe mean trace of anc¡ent summer anticyclones (surface high pressure systems).

J

\

.,,

Figure 6. Prevailing winds of thc modcrn surnnrer anticycbnc

ISPRIGG, lesol

4 U I mile

1

l'tl

,/

(rl

ir 'i..) ¿

^(r

,

ti\Tù

I

*,Á

)

llI

(^:,Iì

LATE FâOAIT \."$

\ I

)/l

ISPRIGG, 19801

Flgure 6. present ¡rrevaìling winds, as ìndicateri by the thick arrow, freshly forming longìtudinal

rlunes on the northeastern shore of Lake Frome. The forming dunes are greatly dìvergent from the

preexisting ones.

\AI

:;ùi¡iË .p-F=- -:'

Plan

[BAGNOLD, rOltl

J/

Section

A E

FlgurcT.Longitudinaldunewithshiftingcrest,Arrowsarestormwindvectors.

Plan

(b)

A

A9

s

(el

lcl

Plan

cB

A

B

(o) s

g -...+

III (dl s

I A

,s

[BAGNOLD, le4llI

Flgure 8. Transition from barchan to linear dune as a result of bidirectional winds.

ù

tYtJ

\-^

Ur..i

I..

t-Sectlon

[BÀGNOtD, 19411

\)

J

,:J,,lu1.Y

.::

,.J:;ì

\-.:i.:,, *)

D

Flgure 9. strips of fine sand deposited during a storm and the hypothetical secondary circulation

r{Plan Section

IWIPPERI\,I4N, t9691¿, l!,

B///E

A

Figure fO. A) Roll vortices anrì longitudinal dunes. B) Roll vortices, longitudinal dunes, soaring

birds and longitudinal clouds or clouclstreets'

IRI-lI]lN, r9851

Figure 1la. Laterally stationary rvindrift-type linear dunes. llere clunes are presumably

aligned with mean sediment transport.

IRUBIN, t98sl

Figure 1lb. Linear clunes that cause dorvnward scouring during lateral migration' l)unes

.*"not aligned rvith tnean sediment transport'

IRUI]IN, 19851

Figure llc. Linear dunes that neither scour or clirnb during lateral migration

uìtJBlN, 19851

Figure lld. Linear dunes that climb at a slight angle during lateral migration

IìUBIN, le85]

Figurelle.I,inearclunesthatclimbatasubstantialangleduringlateralmigration

IRUBIN, 19851

Figure 1lf. Linear dunes "that accrete vertically without migrating laterally'" Ilere

dri", .." either alignecl wittr sedi¡nent transport, or deposition rate is unusually high'

IRUBIN, 1985]

Figure l1g. Liuear dunes that both accrete vertically and migrate laterally.

135'oo' 135?o'

23"6r

2525IFOLK, 1e711

Flgurc lZ. ..Tlacing of the northwest corner of Mcf)ill's topographìc sheet' showing dune trends

typical of the central Simpson desert. Observe the fantastic parallelism of the dunes, and the

systematic opening of the tuning-fork junctures üo the SSE. A count on the original map showed 8lout of 83 junctures opening to the south."

S¡l! I (o

Scolrr

Widlñ ¡n M.tr.troo 200 300 {oo

SllrL INSEI

Sir. I

S¡ tc I¡ o

\

s

zoi.g

,oEÌ@

IMABBUTT and SULIVAN, 1968l

Flguro lS. "Dune proflles in relation to junctions as shown inset."

Plan

,l

t

Irs

ft

17o

Plan

v" Ío

F2

I

l7o = velocity vector of the ambient

flow relative to the shiPs' and

f" = velocity vector of the constricted

flow relative to the shiPs'

Él > Y"l

F¡ and F, = no.mtl pressure gradient forces,

Po = ambient fluid Pressure, and

P" = fluid pressure in the region of contricted flow'

A

4P"

PoPo

PolP"

B

Flgurc l{. A) Flow around ships travelling in parallel. B) Pressure ffeld and normal pressure

gradient forces upon ships travelling in parallel'

Sectíon

IBRUNT, 19511

a

I

Flgurc 16. "Circutation in the Bdnard convection cell"'

Sectlo¡

Coldp

lron

21456Eo¡l¡o¡tal dtrtancc (Lm)

.tù

,t

¡ìþ

I

tt!:

'{

'l

ïI

I

,

iIGRAHAM, le33l

Flgurc lO. Smoke chamber for the <¡bservation of microscale roll vortices' The convective fluid

tayir is between the hot iron plate and the cold glass plate'

2

I

fl

Ë

IN

F¡fÁÐ'õtr

0

789x->

IKROPFI and KOIIN, 1978]

Figure 17. Wind field over an urban topography simulatcd qsing f)oppler radar data. The

win{ is {irected orthogonally out of the plane of the paper, towards the vierver, Note that the

wavelength of these roll vortices is approximately twice as large as ustral.

Return

t-11-I

\

\ I ¡ +r+¡lI f ,r..r.*,I f t.- -ttú,/r/K'l +r,. . ! r ll?,t, . | { llt".- .ttlIttar-

etJ { !.rî ì r*.* Ft J ! t t .

¡ Êa- ? , . y ì

I IIII

IIa

,q

Þ?.o

IE1ñ

o5E

o. r.o 1.5 2.O 2.ay' km

3.5 4.O 4.53.0

2.O

E!

N

t.oIBROWN, l98ol

2.O 5.5 4.5

I' km

Flgurc 18. "Theoretical secondary flow parameteni, stream function ty', and lateral

velocity u for latitude 45o, Ekman depth 6 = 400 m, Us = l0 m/s, and ^Rc =U06lK - 486, where I{ is the eddy viscosity."

€Wind

Hodoqroph

IBROWN, l98o]

05 LO 30

t.,

11

p

(

A

B

c

-.o2

.o4

oû

.o2

.o812

.o6I

to

-.04

Ó)

-.o35

vlUg

.o36

02

Figure 19. 'I'heoretical secondary flow in l,he planctary botlndãry layer

o

T

I

I

I

|-.

SrrtiooerTro¿lã

Orohr plúric

Sectio¡

Slor, 2 m

?!! od

200 @ ---{

chmbcr

¡i

hFlo¡r

Cammtrci.i0¡3¡dl

IFALLBR and I(AYLOR, 19661

Figure 2O. "schematic diagram of the rotating tank and mechanism"

Section

r -1r = can¡ster radius

7cm(r!22cmplexiglass tube

turntable flIl = fluid depth

rlIIl4r

brake plexiglass bottom plate

brake ring

clutchrotation rate

measuring device

motor

mounting plate

level adjusùment screw level adjustment screw

ulonsT, leTobJ

?

PUP

I

Figure 21. schenrat,ic. {iagrarn of t,he rqt,ating canist,cr an(l lllccllanisnl'

1l 2Iaaa aaa aaaaa

¿o6O4.-

a ab.- a_u4s - 'ol

.a-o3 4t

[wIPPERMAN, l96el

Flgure 22. Axes of the two mutually orthogonal sets of roll vortices. d¡ E zlxes of transverse

rotl vortices, and lf¡ = ilX€s of longitudinal roll vortices

a

[IlORST, loTobl

Flgure 23. The formatìon of spiral sediment bands by roll vortices.

e

!o2

r

C

¿ta.

o.å

o

3¡LL¡¡

o6 o., or o.9 r.o

IHORST, leTob]

ã = l3oll' ãl¡ = lSoll'

ø:experimental value of the angular difference between longitudinal roll vortices and the mean flow

c¡¡ =theoretical value of the angular difference between longitudinal roll vortices and the mean flow

äf =* inwIPPERMAN.

1¡ =wavenumber of transverse roll vortices

¿Iv :wavenumber of longitudinal roll vortices

Flgure 24. The ratio of the measured to calculated angular divergence of longitudinal roll vortices

from the mean flow as a function of the ratio of longitudinal roll vortices wavelength to transvetse

roll vortices wavelength.

i

,Sectlo¡

V¡

.- '. 'r.:,:, ..'l : .::.i j.i'.;'."1,'.1

A.

l"

c

c

BIt

dune.i ',

unconditioDal stabilitY As the vortices shift to the left at rate

l7r, a force /] towards the left is exerted

by the right-hand side vortice upon the

right-hand side flank of the dune.

D

The roll vortices shift back towarcls

the left al ratei2.

Figure 26.

A

Sectlo¡

unconditional stabilitY

l7l --.

B

......:

The roll vort¡ces continue to shift

towards the right.

D

As the vortices shift to the right at

rate fr, a force /'¡ towards the right isexerted by the left-hand side vortice upon

the left-hand side flank of the dune'

conditional stabilitY

%..t;

i:.

E

) Lterorlgln¡l dunc

disruption

Flgure 20.

unconditional stability

otlo!þ

o

ra

¡IIL'lYI

E

ot¡lt

o90

oa3

ort

oro

oott

aa

TIIE¡J'

L

aatax

E

¡r

ùtlr

20

ta

¡a

t.a

t2

to

olotoa

o2

roE-ol

tg¿-ot2 roc -ol r0c +oo

FREOUEÎICY III HZ

toE- 02 roE - or roE.oo

FREOU€IICY ril ltzoiþ

oat

oao

o!5

o¡¡o

o2!

o20

oltoro

roel0r

roc -o2 roE -o ro€ +oo

FRcorr€ircY rlt HZ

108-02 roE-or rof+oo

FiEqUEtlCY rf't HZ

oot

oooro€ -cEl roE +0t

tc+ot

ro€ -o! to€+o¡

rc +ot

ILEMONE, 19761

¡(,o

ooza

og¿2

oo20

oor to ora

o ola

o.ort

o oro

oooa

oooc

oooa

ooo?

ÎLa¡¡$ oooor

ttoooo"5

o(þta

ooort

ooora

ooor2

oooþ

ooooa

oooot

ooooo

5Þ

ttll

tc-ot toc-o2 loc-ot rG+ooFRÉOUE¡ICY IX }IZ

I oc -ol

Flgure 22. Spectra of velocity components of u, u and u (roll coordinates), temperatl¡re f'anã absolute humidity po from the NCAR Buffalo aircraft flying normal to roll axis at l0O-170 m

above un¿ulating terrain, near llaswell, Colo., meteorological tower. Airspeed 70 rn/s. Spectra

computed from 5 min of data.

u

T Po

Sectlon

Flow convergence and divergencejunctions are perfect.

Section

Convergence and rlivergence zones

are zones of apparent fìow decompression

A Ideal rectangular circulation B Elliptical llow

Sectloaac)

C Turbulerrtetìtrainnlent

Figure ZB. ,À) I{eal rectangular circulation in which the flow convergence and divergence zones

"x[eri"nce neither llow deconrpression or tttrbttlent entr¿inntent. B) Natural elliptical circulation

rvith apparent florv decompression ancl therefore apparent violation of mass conservation in flow

convergence and divergence zorìes. C) Turbulent entrainment of air in the convergence and

divergence zones mãintain Ina^ss conservation,

t0 20 ¡10 50 70 80

Distancc (kmI

20 ¡10 50 ,0 80

O¡slanc¡ (kml

[NfARI(SON, le75]

Ftgure 29. "Variations of the vertical potential gradient during me:Lsurement periods of extended

duration and constant height close to the sea east of Eleuthera, Bahamas, on lg December lg7l."

?35

Eg!

oi-=ao'-zCOoo-

c.9!o=d\lo:>E0oA.

0

235

0 6030

06030l00

1&þAA.#"./,rü t-t 2 [*-u*gParalhl lo wind C¡osswind

Height = ¡50 m

Parallcl to wind Crosswind

Height = 46 m

Parallcl to wind

HeiShl = 5 m

Crosswind

Ave:'::_2

;E=or:ÀEJ

400

00

0

l0

l0 20 40

50

50

60

60

4020 30

D'stance (km )

30

Distancr (km)

o.ì 85

;:tso=É1

6s

Figure 3O. "simultaneous records of the vertical potential gradient (A) and relative humidity(B) showing correlation. Data were obtained at an altitude of 16 m over the ocean off Eleuthera."

cloud streets e¿f

A

O.d., Ð

€)'

longitudinal dunes 3/[as modified from LEIr{OND, 19721

plan

ioto = vector of the geostrophic windc-= vector of the plane's motion

c ,<900d+e=90oc- l3o

Figure Sf . A) The relationship between geostrophic wind Ío an<l roll vortices. B) Thc orientation

of potential roll vortices during strong winds and the crossflotv direction for observation flights.

v

B

b

0

q"

r'o

A

B

=ã

ÊJ

l{U

VU

É.

8FäE

x Ê

É

¡l5

^¡+

ô

riåp

ã f

-ô-É

-Y-.

Èj-ã

.ãi

' ::-

\t +

r :i'

ão-

å-:

ØÐ

X'

Èi¿

J4

ØO

fl'ß

ort

xäñ

ö :€

X >

Q ã

Ë ;'

r* o

-Ø

-^õ:

< Þ

N^i

.{ i 1ã'

€-

z7-il

a

ìI^

ll t

: >

ã{

ãú_s

I F

.oå

EF

- É

rE,

-?

ã'1

ã¡

=P

É! 9=

tlt<

1

-.8

!ìã

='

or5

iãe

Eoi

vãâ

, I

-.-;

/F

9Ë 1¿tl

ô<ã

toÐ

Ø =

+Y

Oã

Pãô zË

'¡Þ

F'Ë

-*-

E t Þ

Q¿

Q¡

ré tÉ

Сl = 0t

¡öÉ ãf

l Þô

FC

'X

c,o f> äv Ù

Q Bõ -= è, c

-

voQ

g:

(r,

å*

ll:.

Iè)

9 T

OF

J 4+!a

=

9E^: ã^/

ä'E

=

aÉ

3'5

O.

-â-

Í.ò Øâ

ô; ?3 ê, f. H o ô õ'

f-_

n/se

c

Y rVsê

c¡y

'sec

TT

Iw

r3

Li.L

Li'

a-xi

s of

not

enti¿

l¿

- -

-lo

ngitu

dina

l rol

ls

- o <L ã z = 7- ÈL ã s f. a b

- rt z -trJ \¡

¡i t Ë

q¡ol

¡eur

pnlr8

uo¡

¡cr1

ua¡o

d ¡o

s¡x

e

A llight direction

platinum sensing element

Side Rear

IF\ 72.

supporting struf

flow-7

supporting struts

flight direction

\

aspiration holes I

RearB

platinum sensing elementsupporùing strutSide

supporting strut

flow

tubes

exhaust tubes

[after RODI and SPYDRS-DURAN, l97ll

I

Ij

_r

L

Flgure S4. ^)

Reverse-flow temperature probe. B) Improved reven¡e-flow temperature probe.

.t\o i

I

OELAIOE

\\n

[after TïVIDALE, l972aldunefields

I'lgure 36. Simpson f)esert, Strzelecki Desert and environs.

I1.2 km

continrred next Page

l.l km

lmplied <limensions, such as dune width,are approximate.

Ë lo'J

Section I

- 0.5 km

- 0.4 km

- 0.3 km

- 0.2 km

0.1 km

,L' ..1,.?.''-i'¡.,{t.:¡lfá::í;.:i.

'i;sectionstudy

longitudindune from thto - 0.1 km

50

N

ii{i * vegetation

,:t',jji,'

ii'# Peaked summit

rounded summit

¡í9" avalanche slope

small trees,#,

clay flatj ',t,

l"i r'-"1."..;:'

.. lr'r .a

liv

sandy, grassyrise in flank

Flgure 3O. Plan-view symbotic representation of süudy lincar dune dcpicting salient geomorphic

featr¡res. Due to insuffìcient information, the outline of the e¿stern dune flank in secton I is

above the base of the dune, and the peak of

is perhaps the highest point along the dune'

dune at - 5o, and at point p2, the dttne base

longiturlinal axis of the dtrne shifts towards the

.2 km south of the dune heacl'

1;',¿.,'(i'

Beyond this Pointt,he dune narÌows.

Section

Planef

2.5 km

2.3 km

2.1 km

- 2krn

1.9 km

1.8 km

1.7 km

1.5 km

1.4 km.?.i

- 3.0 km

- 2.8 km

- 1.3 km

track

2.7 km

Plan

oo

oo

Qo

o tt, t

oo

.oo

oo

II

crestalsummit

ephemeralavalanche

faces

o oo

o.n

.:r o r:lÐo

(dÊ.

.i. .i. .i.

. r'¡:',':' I f'!'t ':'

subsidiarysuntmit

¡'-i .r-r:;r¡r

\tra \o

(Ë

Ë\':'9

contour lines indicatea height difierence ofabout half a meter

4m

rd,Þ.t.. ã.2,

o.oq.

È'

o

o

À

È .)

N

. stakes plantcd on December 8' 1982

o stakes planted on Deceurber 10, 1982

'i' stakes planted on December 11, 1982

topographic contours sketchetl on l)ccc¡¡tl¡er 10, 1082

Flgure 37. Grid of stakes and topographic form lines'

original

colored patches

r 3 r.. ¿ .'. .\.{,

:' i"': " I /_.

"tìïîri..-,,,

\ \avalanche slope \ dune

i;.-;J.::..,r:. '; 'r.::'.b.r'\

colored arc!.¡

'::l i *-,i,r.:i.i.r.i J ::. :j"i:

interdune corridor

Flgure 38. 'I'hc ìeewarrl sirle l'otor arrrl I,he resultant anc of colorcd sand aggncgates

on t,he asalanche face. The highest point of the strrrly site is - 5 m above the castern

sirle intcrdune corrirìor. 'l'he avalance face is - 2 nr deep, an<l the high point of the

colorccl arc is atrout t/3 rvay up the greatest depth of the avalanchc face

¿-

---> 1

gust occurrence

; 500

SectlonE

dune

Plan

-l0m

ji N

N

A: :' ::,i.

¿

ôRô

:.'dune .

Pla¡

.:'dun"l

3

Figure 8g. I(ite and ribbon configuration believed to indicate a windward side

roiár. Mainstream wind in all frames wa"s from - 22Oo SSW. Mean wind speed

was È l3 knots, and gust speed was )15 knots. Time for all frames was around

5:00 PM, Dece¡nber 17, 1982. Exact angular orientation for the ribbon in the plan

frames is unknown. Kite cord length was -,50 m. symbols as in Fig. 37

Sectlon

- 30o - {0o

ì,*1::'{ lr:{ìq.:,.-.,:..:..... ':.:dune

-l0m

nroderate winds

Plan

N

- l00o

U - l80o

Figure 42. Tethered kitcs configural,ion bclievecl to indicate roll vortices âround the stucly

rlune. N{ean wincl was from - 14" NND at - 7 knots. The clbservation was made around

2:80 PN{ on December 19, 1982. Convergent kite flight lasted for several nì¡nutes.

Section

ki tes

dune dune

Flgure 43. Ârray of tethered kites for the observation of roll vortices in a linear dune field.A large numt¡er of kites distribr¡t,cd ovcr a clistance enconrpassing at teast trvo arljacentdunes is necessary if a complete wavclength of the secondary circulation is to Ìre observe{.The nlainstrcam is dincctcrl into thc ¡rlane of the paper.

\

\

200è

/

dune

kite will not staY uP Seetlon

dune

Plan

kite will not staY uP

- 45o

' "

t.j¡ -,;...):r: I .:...,-!

- 40o

-l0m

- 310'

-20o--40"

f'J

- 20"

À

-l0m

-280o - -310o _3200 - -g401

unsteady flier

- 30o

10"É3-3400'-3600

hypothetical streatnlines

Figure 44. Tcthere¿ kites confìgurat¡on bclieved to inclicate quasi'laminar florv over the

,t,irv ¿unn ¿uring oblique w¡n(ls. Mean winrl wtus from - 160o SSll an¿ at - l3 knots'

'IheobservationwasmadeduringtheafternoonofDccenlberl9'1982.

Sectlon

- 30o - 43o- 25"

û

:{t

dune

N

\

ì

- 330o

- 201¡o

Figure 46. 'fcthenecl kites confìgurat¡on believed to indicate qrta'si-larninar llow over the

J-u'.ry a*o rlrrring oblir¡rre winrls. I\{ean winrl was from - 1600 ss¡l an¿ at - l2 knots'

The observation wis ma(le at about 9:30 ÂN{ on f)ecenrber l8' 1982.

- 33.1o

Sectlon

9-¿O- 85' ENE

oo

U a

a

l0m

N

t

Figure 46. A peculiar tethered kites configrrration during oblique flow' Angl.e

measurements were not taken for this configuration, The figure derives from a field sketch

in which line vertical inclinations and hoiizontal orientations were purely qualitatively

estimatecl. Mean wind was from - l50o ssE and at - 12 knots. The observation was

made during the morning of December l9' 1982'

',.',,: ..'.r:i': .

iì'..'ri.:iÍ:

:'

,,

__-->o- 85' ENE

o

. . _-Z'.

- 85' ENEaaa

ì-->. J--l- .

- 100' ESE - 90'E| õ ---. -.---.

- 100. ESE - 94' ESE-. -'. O -O- 80" ENE - 105' ESE

. . .O Oa

tooo o

aa

a o

{m1l

-"=+- 85' ENE

mea"strrement porrrt

- 40 m west of study site

a

a

t

/lPlar

symbols as in Fig' 37

N

.trigure 47. Ilorizontal plane rvind directions across the southern perilììetcr of the study

site. Thc measurcments were made at 8:00 Âlr{ on Deccmber ll, t982' Ât 7:35 AM, the

wind was measured at - 2 knots from - l20o DSÐ at a point - 40 m wcst of the dune.

At 8:J0 ÂM, at this same point, the wincl wa^s at -7 knots and from - 9,'¡o llSFl. Ilecar¡se

of the similar wind <lircctions at 8:00 and 8:30 at - 40 m wcst of the dune, thc wind speed

at 8:00 is thought to be close to 7 knots.

Plan

- *5"o

- *5o

- tl3ooo

- +l0ooa

- *l0oaa

a

a

- +9caa

- *5o -0o --4o -0oa

I

-0'

a

a

oo

OOOr. a .,OO

a

aa

oo

.¡.

o

'¡.

oo

.t.

't.

4m

aa .¡.

a

- +5'

+

measurement polnt

- 20 m east of study site

Sectlon

4mLJ

- +90 -*5n -0.

_0. _0.

/lsymbols as in Fig. 37

N

- +13' - +10' - +l0c - -4'

6m

:--' j .''

- +5'

: ' .:.- ' -

measurement point

- 20 m east of study site

Flgure tt. Vertical plane direction vecton¡ of llow across the southern perimeter of sturlysite during oblique winds. Measurements made at 8:45 ÂN{ on December ll, 1982.

,{

trwE

(o

(,l

oC't

-l

CN

gl

o

o(¡

qtl

o

'l

ïII

II

ú

Ð',

p

-4m

Ttial I

Sectiou

slow

E w

fast ¡""¿ faateetmoderate fast moderate

5m elow

4m

Figure 4g. Relative wind spced nleasurenìents across the southern perilìleter of thc study

sit,e. N{easurenìent.s taken at 8:30 Alr{ on Decelnber ll, 1982. lr{can wind rvas at - 7 knots

and from - gbo []SE, making it ahnost pcrpenrlicrtlar rvith respect to the stucly site's

l,r¡rgilurlinal axis. 'l'hc ancnl.¡r]reter rvas helrl at a lreight of - 1.4 nl. The range of win¿

*¡r"",t, for each trial is stlnrrnarized at the far righthanrì sirle of lhe taþle, an<l as a general

iilrrstration of rvi.rl spccrl variat,ion, thc resttlts of of 'lrial I are shorvn in rclation to a

scc.t,ion of the dune in thc loruor portion of the fìgure'

rvalking

fromlower flank upper tlank cresl upper tlank lower tlank

DtoWTrial I

oo{

ilE

Tooo¡tÞo

Føoo

ÞÐ

D'0

lloCLo|lpo

!o{

\!toDTrial 2

oo4.

IoÈo¡tPo

to1.

IoÈIDãÞo

IoÈoIÞo

DtoW

Trial S

go{

òo(

øo{

Ioo@

Db

ooonIo

Þo

Eo{

WtoDfial 4

3oo.ôÈtÞr!

Þhoq

ãoooãIô

doÊo4Fo

aoI

DtoW

Tnial 5

oaoIÞo

!tbÉ

JoÊ.oIÞo

fb

fboÐ

IoÈorlÞo

3oÈo.lpo

Wtolù

Trial6

3oÈoãFr!

øot

øo{

ã3& F&ô*oiôaóoÞôô

!toÈoIFo

ÞoÀôãFo

wE

//

t

tÞ

Plau

inlerdune'.'corridor : .

flou'divergence

. tlank

flowconvergence

intertlunecorridor

Figure 6O. Ilorizontal fìorv divergence/convergence pattern over the stucly linear dune

Section

'r. '.j '

t{r

A

a:l

Section

:.'.' : i'.:.."'j'.:":

Figure 61. A) Streamlinc during oblir¡ue florv incirlent upon the broacl llank of thestrrcly dune. Maxirnrr¡n rr¡rwarrl flow cornponent occurs jrrst to winrlward of thc crcst.B) Strcamline during oblir¡ue flow incident u¡ron the avalanche flank of the study dune.Nfaximum uprvard flol conrponent occurs just to lecrvard of the crest.

B

5lÉ6È

o 'i.

-i. .:.

';'

5l.:.\

8o)ot.a.Ê.

t.l'+toìo

t.ñ{.:.l.

r..;.

t.1.T.

rù.¡.

t.i.

\.¡Ê.'i.

f,.!.

1..

S.l,

ì.i.

+ ':'

t.;.

+':'

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[.Sr{.l..{¡tfrta

t.i.

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1.

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14qo-Ê;

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-:. .:.

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':- ';'

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l.i. g'.i. ì.:'

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t'¡ I o \':'

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ra -:. I

.:. ñl .:.

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a.i- \.:. ì.:-

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r':'

r..i.É6È

te 10

o

o

o

\o o

O\ O

Plan

o

Pla¡

O1i\

. -/.---> . r... t .!, .:.\ .:, 4mlrìI

\

.i. ¡

sand ev¡r.cuation ) 25 cm

approximate contour lines

symbols as in Fig. 37

's-' ':' \

o

o

o

N

Figure 64. Deposition/erosion pattern over the stucly site for f)ccentber 24, 1982 (8:30

nU¡ t" February ll, lgSA (6:30 Alr{). Southeasterly winds bclieved to have prevailed

during the observation interval.

o \o\o o\

oo

\

4mfl

I

symbols as in Fig' 37sand evacuatlon ) 50 cm

(great erosion)

sand accumulation 2 50 cm

(great deposition)

N

Flgure 66. Deposition/erosion pattcrn over thc strrdy'site for l)ecernber l'1, 1982 (3:1,'r

Plrt) to l¡cbruary tl, 1983 (6:30 Âlr{). South southcastcrly winrls belicved to have prevailed

during the ol¡servation interval.

¡^

o o o

o o o

.i.

-i.

'i.

'?'

'i'

o o lol

I I )

1 à f u -¡

fú Ê Þ

,ì { 'l :rl

lr :õ 2. I

g. ê

toa 69

. a

Sô :ì= Êr

Ê,

U

a t I

o! =o pl =o do ir k6 C,¡

-

@Þ

cD5

a¡t ô o P o

/

=.?

=îg

aÇ:-

- _

¿

- È

vl

='e

=Z

a=--

-Å-

Ò

q _2

+

: Ë

: f

=l

¡. Ë

t ,ó

=19

ã'5

=!

>g

¡r -o

=

=:"

3af=

F

€<

=.,

I ?¿

ã 1

r 3.

=¿

3 =

Z i 1

E ?

'=-

=.>

,4G

=p:

=x

3:t

?: q

'Ê.æ

+=

'i=-Ê

--ã^

5'::.

iÉai

s!É

ìo=

d=á-

-:=

zlË

i i F

;i.È

ãî=

'1^=

=9-

iJ-^

vP

]:Ã-'v

a ã!

='Þ

J åa

.ã

,--

-z,

t=--

=7a

á 1

_.

6 -1

Ò =

î*î?

zë.?

.3?

T =

ã?

e =

'9=

.Ð*\

2Å'a

l+=

--

€ ^;

J

- -

7--"

Ñ

¿5

^ ã

_=2^

Ø-Ò

u)t

= -

¿

ô-¡

-+

:, :

vt.a

4l

s

a7,ë

=2*

úai

=o

c -

r=<

'' o

f ô-

=o

ã'Ø

==

3 €

=i

= ä

o f

P o

q ?

¿--

øá=

2.=

.Llro

'r-

"x=

?='T

ã'?

Fó

27,

9. =

'=.1

s-;'7

-*îõ

'c^

!¡

Ð

':a

3 Ð

i---À

=-a

ó2=

fíã?'

<=

!1

=

-'<

+!-

sÒ--

îráç

=âl

='

sãlii

aag

; o

ã *?

-¡

ðe

â c

ê, ¿

-â

a^

rl;€"

7FãË

hd I F

a/'i

- -'r

.

a-¿

a

.---

---')

a

\ \

a :\

\'Q

¡

\I

'2'

-úal

)

.!a

a{

)

z:.

.;\

-)...

.'--"

'a

) \

U) :t êt o o { o o - q o N o

\o

l\

--

_ )

\O

O

'v/o

[;

Plan

ooo\

O O rO

o

o

o

':'

,z]o or

\4m

\

symbols as in Fï9. 37

sir,nd accumulation ( 75 cm.

December 17, 1982'December 22,1982

4-3 +l +6.aaa

+l -4 +5 +2 +3'a a a a .

avalanche face

I

sand evacuation ) 75 cm

JanuarY 14, 1983

Janrrary 27, 1983

-l -2 0 -5+7aaaaa

N

Figure 67. Deposition/erosion pattern over the study site for l)ecember 14, 1982 (3:15

fni¡ to April 10, 1983 (12:40 PM). South ancl southeasterly winds believed to have pre-

vailed during the observation interval.

. '.:;a:.'- "'il:;¿'r "':!",)i'

" ";a

:'

: ," .:::.;i!. r ,1;11.... irr.'{"

. r"..t;q..... trll..:' .'.t¡i;:,.¡ii.4ï":J:l:,,|i

l.'

Pla¡

+l -5 -l

,. -.Íl:ir

.'rrí:':i i.j

¿ .'.':i-.'

",',iitÌ'

t,. . ,'.'

.Vj: ''ll

ww

"rú V

\vvN

wv"8m Yl

úú

vl.tl fl v ltrl'q

gra"s8

shrubs

4v

+23

, 19821983

t7l,

emberDec

+qt2-l

-6

eroslon

Fe

-5

bruary

I

vÚc+

dep osition

w\,

Figure 68. I)cposition/crosion patterns

ncar thc rlr¡ne l¡ea<|.

v 11

¿:ul

+3

IPlan

o

l0

l9.\l0

ephemeral avalanche faces

meral avalanche face

I

a

8't

o

o

o

,¡.

o1l

o ao

rÀ

taaa

6

28.

6'

: .'.:.:'l¡:.:

a

/.

t'"

II

o

o

o

o

o

ooo¿

a

4m

.:. .:. .:, .:. a

I.:. ,:. .'.. .:. .:.

16 I.:. .i- .i. .i' ':'

I

symbols a"s in Fig. 37penetraùion ( 20 cm

LJ (highest degree of penetration)

Ú penetration ) 20 cm

D penetration 2 50 cm

O penebration 2 100 cmN

Figure 69. Fir¡nness of study site sunface as gauged l>y penetration pattern' Penetronteter

readings taken on December 22, 1982'

Plan

oo

o

o

a

a

24)

l5I

o

o

o

t(.

40

!.t'73

o

o25

o

ò/Io

o

\9. l5:

i.{

26 1

a

(--.€ -/6

a28

.l

4m

G

16

\

synrbols as in Fig. 374 ¡n--l

N I4m

I

l3l3ll5

r4

8 l0

7

7(l

Flgure OO. Firmness of study site sllrface on 'lanuary 30' 1983'

Pla¡o+4o Io

o

o

o'r/6 a

ìI

)

o*8 o

\

face

4m

.i. 'i' 'i' ':' 'i'

a(

3 't¡

A

o

o

o

o

o

o

I

I

+l9l .

/':'t ! '\:1-i'

':. I -_,,

s)'mbols a;s in Fìg. 37

O change in penetration ilepth<5 cm

f--l increase in penetrat'ion depth I 5 cm. ^'mness)(slight decrea"se tn ttr

Ú increase ìn penetration depth 2 25 cmN

DD

tlE

increase in penetration depth 2 50 cm

decrea.se in penetration depth I 5 cm

(slight increase in firmness)

rlecrease in penetration de¡rth 2 25 cm

tlecrea"se in penetration depth ) 50 cm

Figure 61. change in lìrmness of the study site surface as gauged by change in penetra-

t¡oi. nrr"*ment feriocl is from December 22, 1982 to January 30, 1983'

Pla¡ 0 -8 l7 +15

61 o o(

o \o\_oo

.,. \it.i- \

i<o

0

':.

a a

/ ':'

I ':,:

4m

I lr..'i1

-i(ri/'ilt'l

r2

II

I

.--l

./

\:l

symbols as in Fig' 37

N

Figure 62. Deposit'ion/crosion ¡lattern ovcr t,lre strr<l¡' site ftlr Dccclnl¡cr 22, 1982 (9:00

ÀN{) to January 30, 19'83 (l:55 Plrl). Dast to eastsoutlteastcrìy s'in<ls ìrelicvtrd to have

prer;a,iled during the obscrvat'ion intcrval'

'g80I '62 Ártnut¡ Puq U86I

.g.requrera6l uaÐ,r,lfaq lolouttlod uJÐtllJou e'¡ts '(pn1s aq¡ u¡ eEutql elqdurSodo¡ '79 ernE¡g

algord 9961 '6¿ 'ut¡ -- -a¡gord ¿g61 tg 'raq "" c ÁÀ

,<=la-.-"-'ï='¿--<"""

rVo1*

¿y

't

J - - -<'t'3t'-"-:-'-"Ð'i-: : r. - .= t.a -t'a'1 :':': ":"7''--'a {'ii..l,

lur í,EollÐÐs

(gg pu* gg ,Þg s'ElJ) pÐJolluotll sta,r aSutqr rrqtltrEodo¡ qetqa'r 8uo¡e sÐurl '80 ernt¡¡

N

¿S 'ålJ ut * s¡oqu,(s

¡tt

:.-

tv

a a

ir!v

0 o o

t

a

a

t

t-I

a

o

o

a

o

rQOOsg

ooooo

u'

a

tC

rgD

EBId

Sectlon

Dec. I, 1982 proflle

2m

,""'- Dec. 8, 1982 prolìle

- -- Jrn. 29, 1983 proflle

B¡

J

t 2m

wE_:-

Flgure 66. Topographic change in the study site southern perimeter between l)ecember

8, 1982 and January 29, 1983.

Sectlon

2ml-¡

crc2

I

c2

2m

/,/

sN

Cr

I

-læ------L.

Jan. 29, 1983 ProflleJ

Flgure 6O. Topographic change in the crestãl axis between Decomber 8, 1982 and Jan'

uary 29, fg83. Note that the crãstal topography seems to translate with minor ¿istortion'

In a southwarcl migration of - 6 m, the separaiion betwccn thc two sunìnlits increa"sc¿ by

only æ I m,

^B

PlauI

I

--è __.1--I

flow vectors

sediment transportvectors

Figure 67. A) Flow and sediment transport convergence in a zone centered on thewindrvard perimeter of the grid of stakes resulting in deposition. B) Florv and sedimenttransport divergence in a zone centered on the leeward perimeter of the grid of stakesresulting in erosion. Note that while florv changes linearly, transport changes cubically.

wooden stake

\s

rubber band -ì*

stake number

vaseline-smeared fìle card

EN

w

-t

dune surface

of stakes

Flgure GB. Stake with vaseline-covcred fìlc cards for sand collection during saltation.

green patch (half-exposed, Dec. 10, 1982)Pla¡ blue patch

,- l--.( .I

u

Lt'. t..,:.,,

L rjl'it

v1.tt

4.m

l. ooOOO'

ooo

ooo(

rrì

-l

IIra

iL

L

La

o

o

o

o1, 1

.\ -!

.¡ .i. /..

¡.

La

L

L

a

a

L\.t .!. .i. .i .i.l;/.f

.rl¡l

t

l.r 'l A !: .

!¡ ;r;.:

symbols as in Fig. 37

base trench

Iy-

lines normal to form line

dashed lines in the above plob demarcate regions

in rvhich colored grain aggtegates ìYere found

N

Flgure 6g. Distribrrtion of colored grain aggregates over the study site on Decelllber 16,

lgS2. Stakes with colored aggregates in the trenches excavated around their bases are

marked "L", The original colored sand patches were - 0.5 m X - 3 m x - 0.0015+0'005

lìr.

Sectlon

Flgurc 7O. Inferior ntiragc of a nlorrntain

optical horizon

2.2

2.O

t,8

t.6

l.a

s r.2

Fü ,.o

s.0

.6

.4

.2

-,t -,6 '.5 '.4 -,! "2T 'T3 ('c,

t

ROSKILDEFIORO

l-l- llñ

to

Plan

nrsl

[FRASER, lsl791

Flgure Zl. A) "O for Gershoj deduced from two different heìghts (marked

rvilh x's) plotted o ßive a single line." B) "A map of a portion of Roskilde

Fiord in Denmark. was on the shore at Risø." The target Gershoj (7220 m)

is shown.

Sectio¡

solar rays

linear dune

-_- PARABOLIC CURVE

-

stNE cuRvE__ CIRCULAR CURVE

-

S|NE.GENERATED CURVE

Flgure 22. The comparative rates of solar radiat,ive heating of a linear dune's flanks

defend upon the orientalion of the incoming solar rays with respect to the slopes of the

duìe flanlr. This is ultimateìy determined by the position in the sky of the sun.

\I

I

I

I

Figure 73. ,,variation in curvature of a sine'generated curve is less than for any other

regular gcouretric curve. 'fhis nreans that whðn the changes in direction are tabulated

for small ¿istances "tong

;o."1 ¡ypothetical nrean¿crs, the sunrs of the squares of the

changes in direction wilibe less for a si rve' The

changcs in dircction wcre rneast¡rcd in for each

of the four curves depictcrl here' Whe med' the

following valucs were olltainerl: parabolic ar curvet

4,8,10; sine-gencrate<l c,,,*, 3,9'l'0' 'l'he f( ngth and

sirrrtosity."

'|

I

I

I

Plan

Feet

050 lm

N{iles

30

It{ean rlown-valley

20 directior'

l,400

I,000

FeetÊ:l-l

t0

l5a

0

D0

III,,t

III

I I,I

III

V

26

b

0

c50

7526

0

Shoals

50

- Thalweg

100

ILEOPOLD and LÀNGRlllN' 19661

Flgure 24. Above are shown "segments of two typical meanderìng streams! the Mississippi R'iver

nerr Gr.enville, N{iss. (a), and Rlackrock Creek in Wyoming (b), as well as a segment of an

experimental mean¿er foimed in a homogenous medium in the laboratory (c)." Dashed lines tr¿ce

the correspondent sine-ge¡rerat'ed curves.

Plan

sine-generated curve bend

ú

sìnusoidal bend

semi-circular bend

/ÍT

út_TJ

I

parabolic bend

/ tperpendicular bend

Flgure ?6. Asymmebry of turnïng flow and the assoclated turbulence are minimalized in

n .i"nn.l bend conformìng bo a sine-generated curve'

AA

É-B

Plan

C

É-

D

II,EOPOLD ancl LÀNGREIN, 19661

Plan

IB^GNOLD, l960l

Figure TI . ,l¿e.alize{ fliagram of shearing motion tretrveen wator fìlanrents in a pipe bend

if transverse llow were prevented."

B

E

ê

.?

c

D

E

Figure 76. ,,Idealized flow pattern of a typical meander'" Vertical velocity profìles are

provirled for fìve sections at various points along the first bend (t' B' C, f) and E)' Note

the counterc.lockwise rotation of thã flo* ,ounãing this bend. Flow rotation would l¡e

clockrvise around the subsequent bend.''

ulell¡g e.s quoN

'rorr pðllold Jo u()lltrol s/ìlotls losul ..'tJ 09

Puu gg ,g¡ 1u sq¡rqo$l .rÐJu sTueü llorroN Ðrlì Jo s{uu(ì l)ur:s rtðull,, ¡o du¡1 '3¿ ornt¡¡

x'toJ uo N

lz¿or 'No¡,svclsellu letllneN

r-ffi.oq.¿t

ìt/

q¡.þ¡oq¡l¡H

uol¡alulM

\)\¡0f

\..¡'r.J

PlOúu¡Hq0no¡oqlleH

ltoux¡qltùs

r¡0ptUl¡0[.]{

I3.

trl

,tl¡e9Hq)l

c6p u

t-\,I ouyPusS

.oo¡t ll'

'\_4..:::)

\EB.

-'ooJss

.ot.[t $/ñ

u9uallu.g

lu¡g

¡t

¡9ho

-,0rtS ù¡¡uu

lurS

lu30I t.il^

z-

.ottß N\'

\

u.lo¡g

lu¡8aù ¡¡hs ¿,0t 'tTll

(. ( - - to9- \'- _ t..,-- \r

t/.otSçll

PlanDeep

¡--- :) ------f

Shallow

\\'-

a

Deep----)

[IlIJTIINANCE, 1982a]

Figure 79. Flow and sediment transport cleflcction in the shallow water over I'he linear

sand bank.

A

!¡u

Ìtu

l.t'

H

UI(OIIII-]TIIN ANCJE, l982al

B

'Far' current lluid colrrnln

¡

z

z

Conceptual fluld eolumns ¿re bounded

of iop and bottom bY unit areas.litrear sond bank

Figure so. ^)

Axcs of topography.. B) Nlomentrtnr is conscrved over the sand bank' The

,far,current momentum (pliuitt} must eqtral the fluid column momentttm (p[u) over

tlre sand bank. 1'hat is, HU l(tl = hu'

general ßuid column

fíl-¡lr t-

I

Plan

Þ

ilõÉ.n

\\ts

f{ 1\ù

HUI(r)cosa = lru

Flgure 81. lr{omentum vector and its components'

fluid layer surface

Sectlon

z

u hH

v (+)

Íl .o trro#=o

Flgure 82. The relationshìp between the parameters h antl $| an<l ühe bottom topography,

ô [c(t) cos y + å(t) sin y]

(lateral flow speed voriation)

,(+)

7 h12

2tl2tI

I

I

u(+)

l¡=l*6siny(topography)

¿(+) sand bank crest

r,(+)

polnt on s¿nd bank where

peak lateral flow sPeed occurs

Ftgure E3. The relationship between lateral flow speed variation and topography.

90

60

a

30

æ

IfIUTHNANCE, l982al

Flgure E4. "Contours of growth rate ø(rc,c) as a multiple ol SII2Fnlz(l - p)gll when

f =0, F = l¡ A = O.005 and m =2= î."

roo,c

z(+)

z(+l

(+)

"(+)

,(+)

II

Iril -JPJ6z

(+)

(+)

II

(+) (-)

(-)il#)tu æ¡lIJJ,-l¡t,o

"ft|

(+)N

Figure t6. lnflec.tion point vertical velocity profìle (A) and vertic.al prolìlesof associated

paiamcters (B - D), ,,1" in¿icates the inllcction point, and N =vorticity.

I

T

@@!v

46

ó

U

ó

U

stable

R*, Rcnt

/l \ \\\r:-s-

[scHLICHTING, l960l

¡- u-ó

Figure go. ,,curves of neutral stability for a two-dimensional boundary layer with trvo-

dimensional ¿istur¡anles-l.i ì"..-tiscåus' instability; in the case of velocity profìles of

type with point of inflectiàri PI, the curve of neutral stability is of type a (5) 'viscous'

instability; ¡ ttr" "."" oi u"to.ity prolìles of type l> withot¿t point of inflexion' the curve of

neutral stabilitY is of tYPe b'"

<:::1:>

U

t*',

l!

qS,

D\ t "r' sì

\

/ lMóuNlLr ttì,\\

s

S = solino

[TWIDALII, 19721

I

,t

tf'

¡t'I,I

t'l

It

I

I

I

LÀKE PHILIPPI (SÀTINA)

Figure g7. ,,sketch of the Lake Phillipi area, near the eastern nìargin of the sitlpson

Desert in western C¿u..orfnn¡. Note thl leesicle u.tottncl sorlre 20 klll east'west' stancling

so're 30 'r above th" ;ä;i trre sari.a, ancr the relatc¿ ¿une 'iclges."

Hou ND

/,I

ri

F[TWID^LE, 19721

I¡t'¡

ttl,tr

'I

Ii

i

ì

I

t/

t,

8EÁC;trB

[TWll)^l,tt, 19721

Â

olm

'N{ap of lìlal'gin of Lake Dyre near Warritters -At'tll'

bris mou dune"ridges' (Drarvn fronr air photographs)"

of the iak" G"rtgory shorving deblis mound and

(Drawn Phs)"

[rhì,

fr

\,\

"\

I\I

\ i

f lood

ploin

f lood

ploin N

0 km.

Figure 89. ,,Map drawn frorn air photographs of the Dia¡Dantina flood plain near

Birdsville, south-west Queensland, showing leeside mound and longitudinal sand ridges

extending frorn it."

z(+)

Sectlon i¿(z)

--+Pot

VPo

Poz

u (+)

Flgure gO. The vertical velocity profile for flow, the resultant stagnation pressure varia-tion with height and the pressure gradicnt created over the flowward sunface of an obstacle.

Pol =the stagnation pressure vector at arbitrary level d, and V? :the pressure graclient

vector.

z(+)

vËJ

obstacle r(+)

v(+)

l

0

g

+VP

VP

"(+)

z(+)

v(+)

Flgure 91. Pressure gradient generation of vortical flow around an obstacle. Dashed lines is the flow separation bounclary.

ú

o

I

.4,

B

Figure 92. ^)

Roll vo¡tices generated around a narrow obstacle. D) Vortical currentsgeneratcd arot¡nd the encls of ¿ wicle obstacle and rotors generated to leeward of theobstacle's main body.

z(+) +l¡æ

u(")

insbrinsically unstable

z(+)intrinsically stable

u(")

Figure 93. Görtlcr instability or instability ovcr a concave surfacc. Notc that in gen-eral, llow over a convex surface is intrinsically stable and flow ovcr a concave sr¡rface isintrinsically u nstable.

l¡æ

I

I

'(+)

roll vorticesA

+-{t

/ lrulgt

Sectlon

secondary vortices

/

B _==-¿'7- <-

?-riro$

ò"!:"' '

\iù

a'- -

/r*-,'"Io

Sectlon

7- z/- 2

f--:

/_ --f-

c Sectlon

Flgure 94. Â) Â Ìrulge in a sancl shcet gives rise to roll vortices. B) ^

longit,u<linalrlcr¡ros;it,ion lail is frrrnrcrrl lo lcervarrl of llrc ori¡çin;rl brrlgc. Âs this linear nrounrl grows, thcroll vorticcs it gives rise to intensify. Seconrlary vortices are l)ro(luced, arrrl those inil,iatesrrbsirliar¡'srrrfacc bulges. Cl) A sct of longit,urlirr;rl rnounrls anrl tlreir associiìtc(ì r'orticespairs l>cgins to fornr.

À

¿ /----¿¿t /t'

/./

Figure 9õ . The developntent of longitudinal dunes from a single dcbris mound. A)original dcbris nror¡nd. B) 'flre atn¡rlifìcation of topograplric irregularities anrt t,he initiationof longil,urlinal deposit,ion tails. O) 'l'he <leveloprrrent of longitudinal rlunes.

Plau v

Plan

Plan

deposition tail

ri<lge

PIa¡

ol-rstacle

Plan

depression

[TWID^LE, le72l

\

v

o

PIan

î

Sectlon

Flgure g0. Leeward scconrlary flow anrl the resrrltant ìongituclinal deposit,ion in wincl

tunncl trials using pliusticene obst¿cles. V= vortices.

Sectlo¡

\.--l

Figure 97. \Yinrl rotor betu'tlcn trvo r:tlnvt'l'ging lincar dtln'¡s'

c

MEAN DOWNVALLEY DIRECT

G

100

0

r00

6UJt¡¡É(9¡JeI

l¡¡JJl¡JzozYI(.)l^:z9HFC)l¡JGõ

0 .b .5 .75

DISTANCE ALONG CHANNEL

1.25.25

II,EOPOLD and LANGBBIN, 19661

Flgure g8. "Sine-generated curve (lop/ closely approximates the shape of real river

meàn¿ers. This means that the angular direction of the channel at any point with respect

to tlre r¡ean dorvn-valley direction (lourard the ilght) is a sine function of the distance

mea^sured along the channel (graph at boltont). At the axis of each bend (I), D and F)the channel is directed in the mean down-valley direction and the anglc of dellection iszero, rvhcreas at ear:h poiut of i¡lflc.ction (A, G, E and G) the angle of dc'flection reaches a

maximum value."

c G

F

A E

,? /400TUUU

23 t0m.

I

500

t00

-200

\

À

so m

)

??

20

r8

t6

l4dc)

?. tzoclelos

I

6

4

?.

0

¿¿, m. Per sec.

FAURWITZ, lo'lll

Flgure 99. ,,Vertical variation of the wind distribution (llkman spiral)."

1o

Aú =É!

\ û

\t/(r)

surface

Figure l0O. For flow over a concave surface, florv speecl decreases non-linearly with

disìance away from the center of curvature and approaching the surface. Centrifugal

acceìeration at any point is ec¡ual to the s<¡uare of the florv speecl divided by the distance

from the center ofcurvature. Thcrefore, flow centrifugal acceleration decre;uses non-linearly

fa-ster than {oes flow speed approaching the surface, ancl instability results. In the fìgttre,

o :centcr of curvaturc, r =r.,linl clistancc to any point of interesl' anrl rl"¡ =c-entrifrrgalaccclcration.