Deep convection in elliptical and polygonal eyewalls of tropical cyclones

In observations, tropical cyclones with cyclonically rotating elliptical eyewalls are often characterized by wave number 2 (WN2) deep convection located at the edge of the major axis. A simple modeling framework is used to understand this phenomenon, where a nondivergent barotropic model (NBM) is employed to represent the elliptical vortex in the free atmosphere, and an asymmetric slab boundary layer (SBL) model is used to simulate the frictional boundary layer (BL) underneath the free atmosphere. The interaction is one way in that the overlying cyclonic flow drives the BL, but the BL pumping does not feed back to the overlying flow. The nonlinear-balanced pressure field from the NBM drives the winds in the SBL model, which then causes BL convergence and pumping near the eyewall. The strong updrafts at the edge of the major axis for the elliptic vortex in the BL are induced by the larger convergent radial wind from the asymmetric distribution of the pressure fields of the free atmosphere with noncircular vortex. The large radial inflow maintains the supergradient wind at the edge of the elliptical vortex. The results emphasize the cyclonic rotation of the WN2 feature of strong updrafts at the top of the BL from the local shock-like BL radial wind structure. Similar radial profiles and strong BL top updrafts occur at the edges of higher-order polygonal eyewalls with the magnitude of the peak updraft decreasing as the wave number structure of the vortex increases.