A Theory for the Vertical Alignment of a Quasigeostrophic Vortex

Abstract

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 lR, which is proportional to the stratification strength of the atmospheric or oceanic layer containing the vortex. The change of ? with lR is sensitive to the form of the vortex. For the case of a ?Rankine-with-skirt? vortex, the magnitude of ? increases (initially) with increasing lR. On the other hand, for the case of a ?Gaussian? vortex, the magnitude of ? decreases with increasing lR. The relevance of this theory to tropical cyclogenesis is discussed.