Angular momentum dynamics and the intrinsic drift of monopolar vortices on a rotating sphere

Abstract

On the basis of the angular momentum equation for a fluid shell on a rotating planet, we analyze the intrinsic drift of a monopolar vortex in the shell. Central is the development of a general angular momentum equation for Eulerian fluid mechanics based on coordinate-free, general tensorial representations of the underlying fluid dynamics on the one hand, and an appropriate representation of the Lie algebra so͑3͒ of rotations on the other hand. We show that angular momentum fluid dynamics concisely describes the motion of vortices along the sphere and explains why both geostrophic cyclones and anticyclones drift in retrograde direction ͑west-ward͒, why anticyclones do so faster than cyclones, and why this difference is enhanced by a cyclostrophic correction. Technically, the analysis is based on a tensorial representation of the integral angular momentum equation for the fluid shell as a whole, and, derived from this, a coordinate representation with respect to coordinates which may move with the vortex along the surface of the planet. Depicting the angular momentum balance of cyclones and anticyclones in terms of vector diagrams, we present an overview of the results achieved.