Multi-Scale Physics Faculty of Applied Sciences

The formation of mesoscale fluctuations by boundary layer

convection

Harm Jonker

Multi-Scale Physics Faculty of Applied Sciences

Cold Air Outbreak

Peter Duynkerke, IMAUUtrecht University

Agee,Atkinson and Zhang……

Stratocumulus Aircraft Observationslo

g E

(k)

log k

Multi-Scale Physics Faculty of Applied Sciences

Sun and Lenschow, 2006

Multi-Scale Physics Faculty of Applied Sciences

Sun and Lenschow, 2006

Multi-Scale Physics Faculty of Applied Sciences

Sun and Lenschow, 2006

Multi-Scale Physics Faculty of Applied Sciences

L = 25.6km Dx = Dy = 100m

t = 1...16hr, liquid water path

LES of Stratocumulus

L = 6.4km(8hr)

Dx = Dy = 100m

L = 12.8km

(12hr)

L = 25.6km (16hr)

LES of Sc (ASTEX) Liquid water path

“Large Eddy Simulations: How large is large enough?”, de Roode, Duynkerke, Jonker, JAS 2004

“How long is long enough when measuring fluxes and other turbulence statistics?”, Lenschow, et al. J. Atmos. Oceanic Technol., 1994

Multi-Scale Physics Faculty of Applied Sciences

w

qt u

lwp

Intermediate Conclusions

1) the formation of dominating mesoscale fluctuations is an integral part of PBL dynamics!- no mesoscale forcings

- what is the origin (mechanism) ?

- latent heat release- radiative cooling- entrainment- inverse cascade

Atkinson and ZhangFiedler, van Delden, Muller and Chlond, Randall and Shao,Dornbrack, ……

Multi-Scale Physics Faculty of Applied Sciences

Convective Atmospheric Boundary Layer

penetrative convection

zi

heat flux

entrainment

entrainment

tracer flux

wpassive scalar c

variance spectra

dkkExdcxc c

0

22 )()(

LES

FFT (2D)

w

c

w

passive scalar c

Jonker,Duynkerke,Cuypers, JAS, 1999

Saline convection tank

Laser Induced Fluorescence (LIF)

fresh water

salt water (2%)

fresh water + fluorescent dye

buoyancy flux & tracer flux

Laser

(z)

digital camera

p

Han van Dop, IMAUMark Hibberd, CSIROJos Verdoold, Thijs Heus, Esther Hagen

Laser Induced Fluorescence

Laser Induced Fluorescence (LIF)“bottom-up” tracer

boundary layer depth structure

(Verdoold, Delft, 2001)(see also van Dop, et al. BLM 2005)

Intermediate Conclusions

1) the formation of dominating mesoscale fluctuations is an integral part of PBL dynamics!2) latent heat and radiation are not essential

- latent heat release- radiative cooling- entrainment- inverse cascade-

Multi-Scale Physics Faculty of Applied Sciences

Inverse Cascade?

P D

k

E(k)

P D

k

E(k)

P

2-D or not 2-D: that’s the question

nccccc .....21

Spectral variance budget

scale by scale variance budget

CDPcdt

d 2

Pproduction D dissipation

C

spectralinteraction

)klog(

sink

source

16 sections

Scale Interaction Matrix C

passive scalar

sink

source

16 sections

Scale Interaction Matrix C

dynamics

k

E(k)

)(P

or

pdf of spectral flow

upscale transfer

downscale transfer

)(P

Intermediate Conclusions

1) the formation of dominating mesoscale fluctuations is an integral part of PBL dynamics!2) latent heat and radiation are not essential

- latent heat release- radiative cooling- entrainment- inverse cascade

3) budgets show: no inverse cascade (significant backscatter on all scales)

Multi-Scale Physics Faculty of Applied Sciences

Mechanism…

P D

k

E(k)

PP D

k

E(k)

Multi-Scale Physics Faculty of Applied Sciences

P D

k

E(k)

P

weak production, weak transfer

mechanism (CBL)

...

jj x

cu

z

Cwc

t

spectral

l

cu

z

Cw lll ~

22 ~ l

u

wc

l

ll

large scales

3~)( kkEc

)(

1~)(

3 kWkkt

..... transfer )(ˆ)(ˆ

z

Ckwkc

t

transport

(Jonker, Vila, Duynkerke, JAS, 2004)weak production, weak transfer.w crucial!

....

l

cu

z

Cwc

tll

ll

(Leith, 1967)

(Corrsin, ‘68)

w

qt u

lwp

Multi-Scale Physics Faculty of Applied Sciences

Spectral budget w

wz

pww

gw

t

0

2

buoyancyproduction

subgriddissipation

pressurecorrelation

)()()()()( kTkDkPkBkEt wwww

0)( dkkTw

spectraltransfer

2)( wdkkEw

)(kEw

budget

)(kEt w

spectrum

Multi-Scale Physics Faculty of Applied Sciences

Spectral budget u

ux

pu

z

uuwu

t

2

)()()()()( kTkDkPkSkEt uuuuu

shearproduction

subgriddissipation

0)( dkkTu

pressurecorrelation

spectraltransfer

)(kEu

budget

)(kEt u

spectrum

)(kEv

budget

)(kEt v

spectrum

Multi-Scale Physics Faculty of Applied Sciences

Spectral budget scalar

qt

tt z

qwqq

t

2

spectral budget )()()()( kTkDkPkE

t qqqq

gradient production

subgriddissipation

spectraltransfer

variancebudget

0)( dkkTq

)(kEq

budget

)(kEt q

spectrum

LSw

LStqproduction

LSl

LSv

buoyancy production

pressure

LSu 0)1 LSwbreak the chain …

0,)2 LSl

LStqor

w lwp u

reference

w filtered

0LSwtest 1:

Multi-Scale Physics Faculty of Applied Sciences

40

reference

Multi-Scale Physics Faculty of Applied Sciences

41

0LSwtest 1:

LSw

LStqproduction

LSl

LSv

buoyancy production

pressure

LSu 0)1 LSwbreak the chain …

0,)2 LSl

LStqor

w lwp u

reference

q, filtered

0,0 LSl

LStq test 2:

Multi-Scale Physics Faculty of Applied Sciences

44

reference

Multi-Scale Physics Faculty of Applied Sciences

0,0 LSl

LStq test 2:

Multi-Scale Physics Faculty of Applied Sciences

Concluding: The spectral gap …

(Stull)

Multi-Scale Physics Faculty of Applied Sciences

Cold Air Outbreak

time

Multi-Scale Physics Faculty of Applied Sciences

Conclusions1) the formation of dominating mesoscale fluctuations is an integral part of PBL convective dynamics!

2) latent heat and radiation are not essential(but speed up the process considerably)

3) budgets: no inverse cascade on average. significant backscatter (on all scales)

4) production: ineffective (slow), but spectral transfer is just as ineffective

5) the spectral behaviour of w at large scales is crucial

Multi-Scale Physics Faculty of Applied Sciences

Jonker,Duynkerke,Cuypers, JAS, 1999

Length scales of conserved quantities in the CBL at t=8h

r w' ' T

w' ' 0

Multi-Scale Physics Faculty of Applied Sciences

)()()()()( 2 kSkEjkEkDz

ckEkE

dt

dcccwcc

dissipationproduction chemistry spectraltransfer

)()()( 32/13 kEkWk

dk

dk

dk

dkS c

Spectral Model

Leith (1967)

(Jonker, Vila, Duynkerke, JAS 2004)

Multi-Scale Physics Faculty of Applied Sciences

)()()()()( 2 kSkEjkEkDz

ckEkE

dt

dcccwcc

dissipationproduction chemistry spectraltransfer

)(~)()( kSkkWkkEc

Spectral Model: scale analysis …at large scales

ic z

ckEkWkP *)()(~)(

3~)( kkEc

2/13 )(~)(

kWkkt

)(P