1. Hurricane Vortex X L Converging Spin up Diverging Spin down Ekman
Pressure grad.
force
Coriolis
force L
Centrifugal
force
Converging
Spin up
Diverging
Spin down
Buoyancy X
Ekman
Pumping
Boundary
Layer
It is the convective clouds that generate spin up process to overcome the spin down process induced by the Ekman pumping

2. Where do energy and moisture come from to foster
a large amount of convection in a hurricane?
Warm ocean
What process is responsible for bringing the energy and moisture taken from the ocean surface to the atmosphere?
Boundary layer turbulent transport process

3. Instabilities in the boundary layer
a. Kelvin-Helmholtz instability Z U
(not a mechanism for generating large turbulent eddy circulations, particularly, roll vortices)

4. b. Inflection-point instability in rotation-shear flow
Barotropic Ekman flow with constant Km (the simplest PBL flow) y v u Vg x
ξ×1000
Roll axis z
Inflection point
Vorticity maximum ξ ε

6. In the roll-coordinate, the vorticity equation of horizontal
homogeneous Boussinesq flow
Procedure for solving the problem (classic linear method)
1. Using small perturbation method to linearize equation
2. Assuming simple harmonic wave solution
m is the wavenumber; c is the complex eigenvalue with
real part the wave velocity and imaginary part the growth rate.
3. Obtaining Rayleigh necessary condition for instability

7. Wavenumber m
The maximum growth rate of occurs at wavenumber 0.5 and oriented 18o to the left of the geostrophic wind.(Brown 1972 JAS)

8. c. Parallel instability
First found by Lilly (1966) and named as parallel instability
It is associated with the variation of u, which is transmitted to the cross-flow vorticity through the term
The growth rate is quite slow compared with that of
inflection-point instability, and thus, it does not appear
to be important in the atmosphere

9. d. Convective instability
This is an instability mode that is much larger than the inflection-point instability.
Criterion for onset of LTECs based on observations and theoretical analyses
Overland 1984; Brummer 1985; Chlond 1992; Etling & Brown 1993; etc.
3D convective cellular cells
Convection unlikely
Taken over by inflection-point instability
2D roll-like vortices

10. Hurricane boundary layer roll vortices
Rolls
Eye
Typhoon Fengshen
HBL roll vortices are also believed to be caused by the inflection-point instability. Ralph Foster (2005) made a theoretical instability analysis in the hurricane condition.

11. Doppler Radar Observations
IHRC Tower Observations

12. Momentum fluxes induced by rolls can be 2-3 times
larger than those estimated from standard turbulent
mixing parameterizations (Morrison et al. 2005)
How to represent
sub-kilometer rolls
in numerical model
is challenge

13. Large eddy simulation (LES)
Initialized with idealized vertical profiles and forced with uniform surface conditions and horizontal homogeneous large-scale atmospheric forcings.
Hurricane vortex is a moving target.
Swirling hurricane wind changes the speed and direction continuously.
Highly asymmetric structure of a hurricane vortex.
Classic LES is not a good approach to study hurricane boundary layer

14. WRF large-eddy simulation (WRF-LES)

15. IHRC Tower Observations
TKE (m2/s2)
WRF-LES in a hindcasting mode allows a directly comparison
with observations such as, CBLAST and RAINEX, etc.

16. Simulated hurricane boundary layer roll vortices

17. Vorticity front from my simulation of Hurricane Katrina
Largest vorticity > 0.1 s-1, which is greater than the vertical vorticity usually observed in weak tornadoes.

18. Turbulence fields decompose into chaotic turbulence
and large eddies

19. Parameterized turbulent fluxes and the fluxes from resolved eddies

20. Interaction between HBL and other processes in a hurricane
Deep Convection
Boundary Layer
1. To what extent can convection modify the hurricane boundary layer structure and turbulent processes?
2. How does the interaction between convection and boundary layer
turbulent processes affect the vertical transport?
3. Whether the existing turbulent mixing scheme and convection scheme can realistically represent this interaction?

21. Eyewall Mesovortices Hurricane Isabel Hurricane Alberto
Observations show that the hurricane intensification seems to be always accompanied by the occurrence of eyewall mesovortices.

22. PV decrease
PV decrease
Linearized barotropic nondivergent vorticity equation in cylindrical
coordinates :

23. Assuming wave solution and solving eigenvalue problem, we
can obtain Rayleigh necessary condition for instability

24. m: wavenumber
But PV will not conserve if boundary layer effect is considered. How do boundary layer processes affect the formation of mesovortices?

25. MJY
YSU
2.5 TKE
3.0 TKE

30. Eyewall replacement cycle

31. ERC simulated by WRF-ARW

32. ERC simulated by WRF-ARW

35. Radial inflow during ERC

36. Radius (km) Radius (km) Radius (km)

37. YSU Scheme

38. MYNN Scheme