3D alignment and co-rotation of Weak, TC-Like Vortices Via Linear Vortex Rossby Waves

The process of vertical alignment of an initially-tilted three-dimensional vortex is shown here to be captured by the linear interaction of vortex Rossby waves with the mean vortex flow for vortex beta Rossby numbers less than unity. Although many of the previous studies of vortex alignment fall within this parameter regime, the linear aspects of the dynamics have been largely overlooked. The essence of the alignment mechanism is elucidated using an f-plane Quasi-Geostrophic (QG) model in both its complete and truncated equivalent barotropic forms. Attention is focused on basic state vortices with continuous and monotonically decreasing PV profiles.

For a vertically tilted PV column we demonstrate the existence of a discrete linear neutral Rossby wave for azimuthal wavenumber one for internal Rossby deformation radii larger than or equal to the scale of the vortex. This Rossby wave propagates cyclonically around the vortex but at a slower speed than the local mean tangential wind. The initial perturbation excites both sheared vortex Rossby waves which disperse on the vortex and the discrete Rossby wave which traps part of the disturbance energy preventing alignment. As the deformation radius is decreased below a cutoff value, alignment does occur. The rate of axisymmetrization and alignment becomes increasingly independent of the initial asymmetry amplitude (i.e., vortex tilt) with decreasing deformation radius, consistent with a decreasing vortex beta Rossby number.

These QG findings have been verified for vortices ranging in strength from a mesoscale convective vortex to a minimal tropical storm using the Asymmetric Balance model developed for local Rossby numbers less than unity (Shapiro and Montgomery, 1993). An amplitude threshold for the mean vortex of dynamical origin, in contrast to a thermodynamically-derived one, is found below which alignment and, hence, further development are greatly inhibited. These results have important implications for the problem of tropical cyclogenesis as they suggest a dynamical barrier to development based on simple linear, wave-mean ideas. The application of these ideas to the tropical cyclogenesis mechanism of Montgomery and Enagonio (1998) is also presented.