A theory for the Vertical Alignment of a tilted geophysical vortex

In this paper, the alignment of a tilted geophysical vortex is examined analytically and computationally. The alignment is viewed as the damping of a three-dimensional vortex Rossby mode, by a resonant "wave-fluid" interaction. The mode decays exponentially with time. The exponential decay rate \gamma is proportional to the radial vorticity gradient at a critical radius in the vortex, where the fluid rotation is resonant with the mode. The decay rate \gamma is also examined as a function of the internal Rossby deformation radius l_R of the stratified atmosphere or ocean in which the vortex resides. This function is sensitive to the form of the vortex. In the case of a "Rankine-with-skirt" vortex, \gamma increases (initially) with l_R. On the other hand, in the case of a "Gaussian" vortex, \gamma decreases with l_R. Limitations on the theory of resonant damping are discussed.