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 γ is proportional to the potential vorticity gradient at a critical radius, where the fluid rotation is resonant with the mode. The decay rate γ 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 γ with lR is sensitive to the form of the vortex. For the case of a “Rankine-with-skirt” vortex, the magnitude of γ increases (initially) with increasing lR. On the other hand, for the case of a “Gaussian” vortex, the magnitude of γ decreases with increasing lR. The relevance of this theory to tropical cyclogenesis is discussed.