A stable precessing quasi-geostrophic vortex model with distributed potential vorticity

Abstract

The permanent precession of a baroclinic geophysical vortex is reproduced, under the quasi-geostrophic approximation, using three potential vorticity anomaly modes in spherical geometry. The potential vorticity modes involve the spherical Bessel functions of the first kind and the spherical harmonics , where is the degree, is the order, and are the spherical coordinates. The vortex precession is interpreted as the horizontal and circular advection by a large-amplitude background flow associated with the spherical mode of the small-amplitude zonal mode tilted by a small-amplitude mode , where are constant potential vorticity modal amplitudes. An approximate time-dependent, closed-form solution for the potential vorticity anomaly is given. In this solution the motion of the potential vorticity field is periodic but not rigid. The vortex precession frequency depends linearly on the amplitudes and of the modal components of order 0, while the slope of the precessing axis depends on the ratio between the modal amplitude c2;1 and !0.