The formation of mesoscale fluctuations by
boundary layer convection
Harm Jonker
Multi-Scale Physics
Faculty of Applied Sciences
Cold Air Outbreak
Peter Duynkerke,
IMAU
Utrecht University
Agee,
Atkinson and Zhang
……
Multi-Scale Physics
Faculty of Applied Sciences
log E(k)
Stratocumulus Aircraft Observations
log k
Atmospheric Observations: Sc
Nucciarone & Young 1991
w
q
u
q
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
LES of Stratocumulus
L = 25.6km Dx = Dy = 100m
t = 1...16hr, liquid water path
Multi-Scale Physics
Faculty of Applied Sciences
LES of Sc (ASTEX)
Dx = Dy = 100m
Liquid water path
L = 25.6km (16hr)
L = 12.8km
(12hr)
L = 6.4km
(8hr)
“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
qt
u
lwp
w
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 Zhang
Fiedler, van Delden,
Muller and Chlond,
Randall and Shao,
Dornbrack, ……
Convective Atmospheric Boundary Layer
penetrative convection
entrainment
entrainment
zi
heat flux
tracer
flux
Multi-Scale Physics
q
Faculty of Applied Sciences
LES
w
variance spectra



   c( x )  c 2 d x
  Ec (k ) dk
2
0
c
passive
scalar
passive
c scalar
c
q
w
FFT (2D)
Jonker,Duynkerke,Cuypers, JAS, 1999
Saline convection tank
Laser Induced Fluorescence (LIF)
Han van Dop, IMAU
Mark Hibberd, CSIRO
Jos Verdoold,
Thijs Heus,
Esther Hagen
digital camera
fresh water
Laser
salt water (2%)
r(z)
buoyancy flux & tracer flux
fresh water + fluorescent
dye
Dp
Laser Induced Fluorescence
Laser Induced Fluorescence (LIF)
“bottom-up” tracer
boundary layer depth structure
(see also van Dop, et al. BLM 2005)
(Verdoold, Delft, 2001)
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
Inverse Cascade?
E(k)
E(k)
P
D
P
k
k
2-D or not 2-D: that’s the question
Multi-Scale Physics
P
Faculty of Applied Sciences
D
Spectral variance budget
spectral
interaction
C 
log( k )
production
c  c  c1  c2  .....  cn
P
D dissipation
d 2
c  P
dt
 D 
 C
scale by scale variance budget
Scale Interaction Matrix C
16 sections
source
sink


passive scalar
Scale Interaction Matrix C
16 sections
source
sink


dynamics
pdf of spectral flow 
P ( )
or

E(k)
k
P ( )
upscale
transfer
downscale
transfer

Intermediate Conclusions
1) the formation of dominating mesoscale
fluctuations is an integral part of PBL dynamics!
2) latent heat and radiation are not essential
3) budgets show: no inverse cascade
(significant backscatter on all scales)
-
latent heat release
radiative cooling
entrainment
inverse cascade
Mechanism…
E(k)
E(k)
P
D
P
k
Multi-Scale Physics
P
k
Faculty of Applied Sciences
D
weak production, weak transfer
E(k)
P
P
k
Multi-Scale Physics
Faculty of Applied Sciences
D
mechanism (CBL)
transport
spectral

C
c   w
t
z
 C
 
cˆ(k )   wˆ (k )
t
z

C
cl   wl
t
z
c
 uj
 ...
x j
(Leith, 1967)
 transfer  .....
ul cl
 
 ....
l
(Corrsin, ‘68)
large scales
ul cl
C
wl
~
z
l
 wl  2
c ~   l
 ul 
2
l
(Jonker, Vila, Duynkerke, JAS, 2004)
Ec (k ) ~ k 3
t (k ) ~
1
k 3W (k )
weak production, weak transfer.
w crucial!
qt
u
lwp
w
Spectral budget w
 2
w 
t

g
q0
wq
buoyancy
production

Ew ( k )
t

 B (k )
p
 w
z
pressure
correlation
 Pw (k )
w
subgrid
dissipation
 Dw (k )
T
Ew (k ) dk  w2
Multi-Scale Physics
w
Faculty of Applied Sciences
spectral
transfer
 Tw (k )
(k ) dk  0
spectrum
Ew (k )
budget

Ew (k )
t
Spectral budget u
 2
u 
t
u
 uw
z
shear
production

Eu (k )
t
 Su (k )
p
 u
x
pressure
correlation
 Pu (k )
u
subgrid
dissipation
 Du (k )
spectral
transfer
 Tu (k )
 T (k ) dk  0
u
Multi-Scale Physics
Faculty of Applied Sciences
spectrum
Eu (k )
budget

Eu (k )
t
spectrum
Ev (k )
budget

Ev (k )
t
Spectral budget scalar
variance
budget
 2
qt 
t
qt
 wqt
z
gradient
production
spectral
budget

Eq ( k )
t
 Pq (k )
q
subgrid
dissipation
 Dq (k )
spectral
transfer
 Tq (k )
 T (k ) dk  0
q
Multi-Scale Physics
Faculty of Applied Sciences
spectrum
Eq (k )
budget

Eq (k )
t
buoyancy production
production
w
LS
t
q
LS
q
q
LS
l
LS
v
pressure
break the chain …
u
LS
1) w  0
LS
or 2) q , q
LS
t
LS
l
0
test 1:
w
reference
w
filtered
wLS  0
lwp
u
reference
41
Multi-Scale Physics
Faculty of Applied Sciences
test 1:
wLS  0
42
Multi-Scale Physics
Faculty of Applied Sciences
buoyancy production
production
w
LS
t
q
LS
q
q
LS
l
LS
v
pressure
break the chain …
u
LS
1) w  0
LS
or 2) q , q
LS
t
LS
l
0
test 2: qtLS  0, q lLS  0
w
reference
q,q
filtered
lwp
u
reference
45
Multi-Scale Physics
Faculty of Applied Sciences
test 2: qtLS  0, q lLS  0
Multi-Scale Physics
Faculty of Applied Sciences
Concluding: The spectral gap …
(Stull)
Multi-Scale Physics
Faculty of Applied Sciences
Cold Air Outbreak
Multi-Scale Physics
Faculty of Applied Sciences
Conclusions
1) 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
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
Spectral Model
d
c
Ec (k )   Ewc (k )
 Dc k 2 Ec (k )  j Ec (k )  S (k )
dt
z
production
Leith (1967)
dissipation
chemistry

spectral
transfer

d  13/ 2 d 3

S (k )   k
k W ( k ) Ec ( k ) 
dk 
dk

Multi-Scale Physics
Faculty of Applied Sciences
(Jonker, Vila, Duynkerke,
JAS 2004)
Spectral Model: scale analysis …at large scales
d
c
Ec (k )   Ewc (k )
 Dc k 2 Ec (k )  j Ec (k )  S (k )
dt
z
production
dissipation
c*
P ( k ) ~ W ( k ) Ec ( k )
zi

Ec (k ) ~ k
Multi-Scale Physics

3
chemistry
spectral
transfer
kEc (k ) kW (k ) ~ S (k )

3
t (k ) ~ k W (k )
Faculty of Applied Sciences

1/ 2
P ( )