3D alignment and co-rotation of TC-like vortices via linear vortex Rossby waves

The vertical alignment of an initially-tilted geostrophic vortex is shown here to be captured by linear vortex Rossby wave dynamics when the vortex cores at upper and lower levels overlap. The vortex beta Rossby number, defined as the ratio of nonlinear advection in the vorticity equation to linear radial advection, is less than unity in this case. A useful means of characterizing a tilted vortex flow in this parameter regime is through a wave, mean-flow decomposition. From this perspective the alignment mechanism is elucidated using a quasi-geostrophic model in both its complete and linear, equivalent-barotropic forms. Attention is focused on basic state vortices with continuous and monotonically-decreasing potential vorticity profiles.

For internal Rossby deformation radii larger than the horizontal scale of the tilted vortex an azimuthal wavenumber one quasi-mode exists. The quasi-mode is characterized by its steady cyclonic propagation, long lifetime, and resistance to differential rotation, behaving much like a discrete vortex Rossby wave. The quasi-mode traps disturbance energy causing the vortex to precess, or co-rotate, and thus prevents alignment. For internal deformation radii smaller than the horizontal vortex scale, the quasi-mode disappears into the continuous spectrum of vortex Rossby waves. Alignment then proceeds through the irreversible redistribution of potential vorticity by the sheared vortex Rossby waves. Further decreases in the internal deformation radius result in a decreased dependence of vortex evolution on initial tilt magnitude, consistent with a reduction of the vortex beta Rossby number.

These results are believed to have relevance to the problem of tropical cyclone (TC) genesis. Cyclogenesis initiated through the merger and alignment of low-level convectively-generated positive potential vorticity within a weak incipient vortex is captured by quasi-linear dynamics. A potential dynamical barrier to TC development in which the quasi-mode frustrates vertical alignment can be identified using the linear alignment theory in this case.