Eddy kinetic-energy redistribution within real and idealized extratropical storms
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Transcript of Eddy kinetic-energy redistribution within real and idealized extratropical storms
Eddy kinetic-energy redistribution within real and idealized extratropical storms
1 LMD-ENS, IPSL/CNRS, Paris
2 CNRM-GAME, Météo-France & CNRS, Toulouse
Gwendal Rivière12
Collaboration: Philippe Arbogast, Alain Joly
A 3D easterly view of the storm Christian (Oct 2013)
Forecast from Arpege, 00 UTC 28 October, step 9h
w 0w 0w
Max u (900 mb): poisonous tail of the bent-back warm front
L Warm
front
Cold frontSouth
North
Another example: the storm Klaus (24/01/09)
12 UTC 23 Jan
Lθe (900hPa)
Max wind speed (650-850 mb)
Warm front
Cold front
Warm front
Col
d fr
ont
L00 UTC 24 Jan
EKE=u’2/2 (650-850 mb)
Approach: separation into a background flow and a perturbation by time filtering
L LPerturbation wind u'
Mean westerlies u
Early stage: strongest wind speeds are reached along the WCB
Later stage: strongest wind speeds are reached in the frontal fracture zone
(e.g. Gronas, 1995)
Data: ERAinterim (0.75° grid spacing)
Idealized study: use of the two-layer quasi-geostrophic model
lull
luuu
fq
fq
2
2
0 kkt qq .uk
Rossby radius of deformation
0' u
0' l
ζ’ (300mb) >0
ζ’ (900mb) >0
uu
luUpper layer
Lower layer
Isolated cyclonic anomaliesBasic state
Klaus case
u 300mb
The eddy kinetic energy (EKE) equation
')(2
2
au''uuu'u'
t
'')'('
''
pp aa u'u'
Horizontal ageostrophic geopotential fluxes
Vertical ageostrophic geopotential fluxes
Baroclinic conversion
Pressure work
u geostrophic windΦ geopotential
ua ageostrophic wind
af kua
0
1
p
p
vf
pfs
f
yvuJa
2
02
220
22
0
2
2
),(2
Q Omega equation
Q-vector
Diagnostic equation forageostrophic scalar
a
EKE redistribution at the lower layer in presence of the vertical shear
t=12H
2
2u'
dt
d
2
2u'
t=0H
f-plane, linear
'au'
X (1000km)
t=0H
β-plane, linear
t=12H EKE accumulation east of the low
X (1000km)
y (1
000k
m)
y (1
000k
m)
EKE accumulation west of the low
South
North
)'( au'
EastWest
Role of β and the vertical shear in EKE redistribution
'au'
k''
No βWith β
)''()'')(()2(
'
'')()''()()2(
'
200221
22
2222
20022
0
2
lululu
ullulual
vvK
vvuuKs
K
KK
uuKf
mu
Wavelike disturbance assumption (wavenumbers m, K)
β increases the upward transfer and decreases the downward transfer, so a sink of energy for the lower layer !!!
Role of nonlinearities in EKE redistribution
t=12H
2
2u'
dt
d
2
2u'
t=0H
Linear
'au'
f-plane
X (1000km)
t=0H
Nonlinear
t=12H EKE accumulation southwest of the low
X (1000km)
y (1
000k
m)
y (1
000k
m)
)'( au'
Role of background lateral shear in EKE redistribution
Linear
Cyclonic shear
Anticyclonic shear
2
2u'
dt
d
f-planet=12H
X (1000km)
y (1
000k
m)
y (1
000k
m)
Nonlinear
Cyclonic EKE redistribution
EKE accumulation
2
2u'
X (1000km)
Combined effects of anticyclonic shear / PV gradient in EKE redistribution
t=12h
X (1000km)
y (1
000k
m)
2
2u'
X (1000km)
f-plane, nonlinear
Anticyclonic shear
EKE accumulation to the east
β-plane, nonlinear EKE accumulation to the west
2
2u'
dt
d
The stronger the vertical average of the PV gradient, the more important the EKE accumulation to the east
Isolated cyclonic anomalies initiated south of a westerly jet
uu
lu
Upper layer
Lower layer
Isolated cyclonic anomalies
Basic state
Isolated cyclonic anomalies initialized south of a meridionally confined zonal jet
ζ’ (300mb) >0
ζ’ (900mb) >0
0' u
0' l
u 300mb
Evolution of the idealized jet-crossing cyclone
The key finding: once the cyclone has crossed the large-scale jet, EKE is cyclonically redistributed by ageostrophic geopotential fluxes in regions where the eddy and mean winds align with each other !
Jet axis u'u
u
t=12H
Jet axis
t=24H
Jet axis
t=36H
Jet axis
t=48H
)''()(
)'')(()2(
'
'2
'')()(
)''()(
)2('
2
2
221
22
222
22
2222
2
2
220
2
luluy
lulu
llyuy
ulluy
lulu
al
vvK
uuvvuu
Ks
K
uuK
K
KK
uu
uu
Kf
mu
'au'
)'( au'
Data: ERAinterim (0.75° grid spacing)
00 UTC 23 Jan 2009
Interpreting EKE distribution during for the storm Klaus
06 UTC 23 Jan 200912 UTC 23 Jan 200918 UTC 23 Jan 200900 UTC 24 Jan 2009
environment 2/EKE 2u' u'
'au'
)'( au'
L
u
A 3D view of Klaus at the later stage
Mid-tropospheric baroclinic conversion
Downward EKE transfer –ω’Φ’k
Lower-tropospheric cyclonic EKE redistribution u’aΦ’
Spain
Atlantic Ocean
EKE
p '
'
Confirmation of dry simulations of NWP model (Papritz and Schemm, 2013)
Conclusions
• Before jet crossing: both the background anticyclonic shear and PV gradient explain EKE accumulation to the southeast
• After jet crossing: rapid cyclonic EKE redistribution to the southwest by ageostrophic geopotential fluxes (also nonlinear advection) due to the action of the cyclonic shear
EKE
Schematic of EKE redistribution processes for jet-crossing cyclones following the Shapiro-Keyser conceptual model
Max |u|
Rivière et al (2014a,b; QJRMS)
Outlook
• What is the role played by the synoptic-scale EKE redistribution in the formation of mesoscale jets (sting jets, cold-conveyor-belt jets)
(Browning, 2004; Gray et al. 2011; Martinez-Alvarado, 2014) ?
• Relation with jet-crossing cyclones.
Friedhelm at 12 UTC 8 Dec 2011
From Baker et al (2013)
L
Other slides
EKE budget for the idealized cyclone at the lower layer EKE ct
'- au' EKE
'-
c
uuu'
EKE budget in the cyclone frame of refrence (c phase speed of the cyclone)
'' p
)''( p )'( au'
uuu' '-
EKE'- u EKE)-(c u
EKE budget for the storm Klaus (650-850 hPa) EKE ct
'- u' EKE
'- 33
c
uuu'
EKE budget in primitive equations in the cyclone frame of refrence (c phase speed of the cyclone)
'' p
)''( p )'( au'
33 '- uuu'
EKE'- 33u EKE)-(c 33 u
EKE)'('- cuuu'u' 33
Data: ERAinterim (0.75° grid spacing, 3 hour time steps)
EKE budget for the storm Friedhelm (650-850 hPa) EKE ct
'- u' EKE
'- 33
c
uuu'
EKE budget in primitive equations in the cyclone frame of refrence (c phase speed of the cyclone)
'' p
)''( p )'( au'
33 '- uuu'
EKE'- 33u EKE)-(c 33 u
EKE)'('- cuuu'u' 33
Data: ERAinterim (0.75° grid spacing, 3 hour time steps)
3D view of Klaus
(u’a,ω’ k)Φ’
u’aΦ’
EKE
p '
'