1. Eddy kinetic-energy redistribution within real and idealized extratropical storms
Gwendal Rivière12
Collaboration: Philippe Arbogast, Alain Joly
1 LMD-ENS, IPSL/CNRS, Paris
2 CNRM-GAME, Météo-France & CNRS, Toulouse

2. The case of the storm Klaus (24/01/09)
12 UTC 23 Jan
00 UTC 24 Jan
θe (900hPa) L
Warm front L
Warm front
Cold front
Cold front
Max wind speed ( mb)
Data: ERAinterim (0.75° grid spacing)
EKE=u’2/2 ( mb)
Approach: separation into a background flow and a perturbation by time filtering L
Perturbation wind
Mean westerlies
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)

3. Idealized study: use of the two-layer quasi-geostrophic model
Klaus case
ζ’ (300mb) >0
300mb
Rossby radius of deformation
ζ’ (900mb) >0
Basic state
Isolated cyclonic anomalies
Upper layer
Lower layer

4. The eddy kinetic energy (EKE) equation
Φ geopotential
u geostrophic wind
ua ageostrophic wind
Horizontal ageostrophic geopotential fluxes
Vertical ageostrophic geopotential fluxes
Baroclinic conversion
Pressure work
Omega equation
Q-vector
Diagnostic equation for
ageostrophic scalar

5. f-plane, linear β-plane, linear
EKE redistribution at the lower layer in presence of the vertical shear
f-plane, linear
t=0H
β-plane, linear
t=12H
EKE accumulation east of the low
X (1000km)
North
t=0H
y (1000km)
West
East
South
t=12H
y (1000km)
EKE accumulation west of the low
X (1000km)

6. Role of β and the vertical shear in EKE redistribution
No β
With β
β increases the upward transfer and decreases the downward transfer, so a sink of energy for the lower layer !!!
Wavelike disturbance assumption (wavenumbers m, K)

7. Role of nonlinearities in EKE redistribution
t=0H
Nonlinear
t=12H
EKE accumulation southwest of the low
X (1000km)
f-plane
t=0H
y (1000km)
t=12H
y (1000km)
X (1000km)

8. f-plane Cyclonic shear β-plane Anticyclonic shear
Combined effects of anticyclonic shear / PV gradient in EKE redistribution
f-plane
t=12h
Cyclonic EKE redistribution
Cyclonic shear
y (1000km)
X (1000km)
EKE accumulation to the east
β-plane
EKE accumulation to the west
Anticyclonic shear
y (1000km)
X (1000km)

9. Isolated cyclonic anomalies initiated south of a westerly jet
Isolated cyclonic anomalies initialized south of a meridionally confined zonal jet
ζ’ (300mb) >0
300mb
ζ’ (900mb) >0
Basic state
Isolated cyclonic anomalies
Upper layer
Lower layer

10. Evolution of the idealized jet-crossing cyclone
Jet axis
t=48H
Jet axis
t=36H
Jet axis
t=12H
Jet axis
t=24H
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 !

11. Interpreting EKE distribution during for the storm Klaus
environment
00 UTC 24 Jan 2009
18 UTC 23 Jan 2009
12 UTC 23 Jan 2009
00 UTC 23 Jan 2009
06 UTC 23 Jan 2009 L
Data: ERAinterim (0.75° grid spacing)

12. A 3D view as a summary
Downward EKE transfer –ω’Φ’k
Mid-tropospheric baroclinic conversion
Lower-tropospheric cyclonic EKE redistribution u’aΦ’
EKE
Spain
Atlantic Ocean
The background flow controls the EKE redistribution !

13. Relation with jet-crossing cyclones.
Outlook
Friedhelm at 12 UTC 8 Dec 2011 L
From Baker et al (2013)
What is the role played by the synoptic-scale EKE redistribution in the formation of mesoscale jets (sting jets) (Browning, 2004; Gray et al. 2011; Martinez-Alvarado, 2014) ?
Relation with jet-crossing cyclones.