A Theory for the Vertical Alignment of a Quasigeostrophic Vortex

This article presents a new theory for the rate at which a quasigeostrophic vortex realigns, under conservative dynamics, after being tilted by an episode of external vertical shear. The initial tilt is viewed as the excitation of a three-dimensional ''vortex Rossby mode.'' This mode, that is, the tilt, decays exponentially with time during its early evolution. The decay rate is proportional to the potential vorticity gradient at a critical radius, where the fluid rotation is resonant with the mode. The decay rate also depends on the internal Rossby deformation radius l R , which is proportional to the stratification strength of the atmospheric or oceanic layer containing the vortex. The change of with l R is sensitive to the form of the vortex. For the case of a ''Rankine-with-skirt'' vortex, the magnitude of increases (initially) with increasing l R . On the other hand, for the case of a ''Gaussian'' vortex, the magnitude of decreases with increasing l R . The relevance of this theory to tropical cyclogenesis is discussed.