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

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

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

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

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

Wavenumber m The maximum growth rate of 0.028 occurs at wavenumber 0.5 and oriented 18o to the left of the geostrophic wind.(Brown 1972 JAS)

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

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

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.

Doppler Radar Observations IHRC Tower Observations

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

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

WRF large-eddy simulation (WRF-LES)

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

Simulated hurricane boundary layer roll vortices

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.

Turbulence fields decompose into chaotic turbulence and large eddies

Parameterized turbulent fluxes and the fluxes from resolved eddies

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?

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

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

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

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

MJY YSU 2.5 TKE 3.0 TKE

Eyewall replacement cycle

ERC simulated by WRF-ARW

ERC simulated by WRF-ARW

Radial inflow during ERC

Radius (km) Radius (km) Radius (km)

YSU Scheme

MYNN Scheme