Observed Vorticity Structure in Hurricane

Rita (2005)

Methodology Improvements Michael M. Bell

National Center for Atmospheric Research/ Earth Observing Laboratory

Colorado State University

Wen-Chau LeeNational Center for Atmospheric Research/ Earth Observing Laboratory

Vortex Rossby Waves• Waves retrograde and

propagate outward when the radial gradient of mean vorticity is negative, similar to observed spiral bands in hurricanes (Montgomery & Kallenbach 1997)

• Vorticity perturbations can change mean intensity via wave-mean flow interaction at a critical radius r*

• Mesovortices can mix eye-eyewall air and provide a ‘turboboost’ to the hurricane engine (Persing & Montgomery, 2003; Bell & Montgomery, 2006)

€

ω =nΩ 0 +dζ 0

dr

n

r(k 2 + n2 /R2) ⎛ ⎝ ⎜

⎞ ⎠ ⎟

∂v

∂t∝ − ′u ′ζ

€

Cgr =∂ω

∂k=

dζ 0dr

−2kn

R(k 2 + n2 /R2)2

⎛ ⎝ ⎜

⎞ ⎠ ⎟

Radial Mean Vorticity Profiles

• ELDORA’s 300 - 500 m spatial resolution can yield new insights into the 2D mean and 3D perturbation vorticity

Reasor et al (2000); Mallen et al (2005)

Methodology1. Obtain u, v, w & Z in

Cartesian space from dual-Doppler analysis using variational synthesis (Gamache, 1997)

2. Determine vortex center and mean wind at each altitude (Marks et al, 1992)

3. Convert to cylindrical coordinates

4. Determine azimuthal mean and perturbation quantities Hildebrandt et al. 1986

Methodology Improvements1. Do a first pass through

the data and set the time of closest approach (TCA) to each gridpoint.

2. Restrict the closest approach of the beginning and ending of the track to either side of an azimuthal line

3. Define a 4-minute window from which data can be added to a gridpoint based on the time of closest approach.

4. Remove a small wedge (1-5 degrees) of data near the track overlap.

Methodology Improvements

Key Science Questions• Can we find observational evidence of VRWs

and their contributions to intensity change in a moist-baroclinic-nonlinear-forced-dissipative vortex? – Empirical Normal Modes (Brunet, 1994; Chen et al, 2003)

• Where is the critical radius for wave-mean flow interaction?

• Is this radius a dynamically preferred region for secondary eyewall formation/growth?

• Which spatial scales are the most important? (low azimuthal wavenumber vs. convective, 3D structure of filaments)

Empirical Normal Modes• Pseudomomentum and

Pseudoenergy modes are orthogonal

• ENM analysis allows for separation of vortical wave modes (VRWs) and their contribution to E-P flux

Chen et al (2003)

cn =J n

An

Rita 09/22/06 Flight LegsAircraft Leg Start End Midpoint Leg 2 Leg Length Comment

NRL 1 16:04 16:28 16:16 0:24 SE RainbandNRL 2 16:28 16:48 16:38 0:22 0:20 E RainbandNRL 3 16:48 17:04 16:56 0:18 0:16 NE DoglegNRL 4 17:05 17:42 17:23 0:27 0:37 Outer Circle from NENRL 5 17:24 18:01 17:42 0:19 0:37 Outer Circle from WNRL 6 18:01 18:20 18:10 0:28 0:19 Inner Circle from SWNRL 7 18:16 18:35 18:25 0:15 0:19 Inner Circle from NWNRL 8 18:38 19:14 18:56 0:30 0:36 Outer Circle from SWNRL 9 19:14 19:50 19:32 0:36 0:36 Outer Circle from SWNRL 10 19:38 20:16 19:57 0:25 0:38 Outer Circle from NNRL 11 20:17 20:28 20:22 0:25 0:11 Exit leg to NW