Secondary eyewall formation and sheared convection in mature hurricanes

Abstract

The problem regarding the formation of the secondary eyewall of the major tropical cyclone vortex is set up and examined. As an introductory step, the evolution of and structure of the mean flow changes by free convection in a horizontally and vertically sheared environment is studied using a suite of three-dimensional, high-resolution, full-physics model experiments. It is shown that horizontal shearing may be a strong influence on the lifetimes and structure of convective cells. Additionally, the mean flow changes by these shearing profiles show the importance of shear in determining the projection of the convection onto the mean vortex. Vertical shearing forces an antisymmetry in the mean potential vorticity change, while horizontal shear tends to symmetrize these changes. A combination shear appears to force an antisymmetric structure in the mean potential vorticity change that tilts with height. After exploring this introductory work, prevailing hypotheses for secondary eyewall formation are examined using datasets from two high-resolution mesoscale numerical model simulations of the long-time evolution of an idealized hurricane vortex in a quiescent tropical environment with constant background rotation. The modeled hurricanes each undergo a secondary eyewall cycle, casting doubt on a number of these hypotheses for secondary eyewall formation due to the idealizations present in the model formulation. A new hypothesis for secondary eyewall formation is proposed here and shown to be supported by these high-resolution numerical simulations. The hypothesis requires the existence of a region with moderate horizontal strain deformation and a sufficient low-level radial potential vorticity gradient associated with the primary swirling flow, moist convective potential, and a wind-moisture feedback process at the air-sea interface to form the secondary eyewall. The crux of the formation process is the generation of a finite-amplitude lower-tropospheric cyclonic jet outside the primary eyewall with a jet width on the order of a local effective beta scale determined by the mean low-level radial potential vorticity gradient and the root-mean-square eddy velocity. This jet is generated by the anisotropic upscale cascade and axisymmetrization of convectively generated vorticity and kinetic energy anomalies through horizontal shear turbulence and sheared vortex Rossby waves as well as by the convergence of momentum by the induced low-level radial inflow associated with the increased convection. Possible application to the problem of forecasting secondary eyewall events is briefly considered.