the formation of mesoscale fluctuations by boundary layer convection

Multi-Scale Physics Faculty of Applied Sciences

The formation of mesoscale fluctuations by boundary layer

convection

Harm Jonker


Cold Air Outbreak

Peter Duynkerke, IMAUUtrecht University

Agee,Atkinson and Zhang……

Stratocumulus Aircraft Observationslo

g E

(k)

log k


Sun and Lenschow, 2006


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

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, ……


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)


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-


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


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)


Mechanism…

P D

k

E(k)

PP D

k

E(k)


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


Spectral budget w

wz

pww

gw

t

0

2

buoyancyproduction

subgriddissipation

pressurecorrelation

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

0)( dkkTw

spectraltransfer

2)( wdkkEw

)(kEw

budget

)(kEt w

spectrum


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


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:


40

reference


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:


44

reference


0,0 LSl

LStq test 2:


Concluding: The spectral gap …

(Stull)


Cold Air Outbreak

time


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

Jonker,Duynkerke,Cuypers, JAS, 1999

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

r w' ' T

w' ' 0


)()()()()( 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)


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

ckEkE

dt

dcccwcc

dissipationproduction chemistry spectraltransfer

)(~)()( kSkkWkkEc

Spectral Model: scale analysis …at large scales

ic z

ckEkWkP *)()(~)(

3~)( kkEc

2/13 )(~)(

kWkkt

the formation of mesoscale fluctuations by boundary layer convection

Documents

scale analysis

spectral transfer

scales4 production

inverse cascade3 budgets

spectral behaviour of

pbl dynamics

mesoscale fluctuations

pbl convective dynamics