Barotropic Vortex Evolution on a Beta Plane

Abstract

A barotropic, primitive equation (shallow water) model is used on the beta plane to investigate the influence of divergence, total relative angular momentum (RAM) and advective nonlinearities on the evolution of a hurricane-like vortex. The multinested numerical model is based on the spectral application of a finite element representation. The undisturbed fluid depth is taken to be 1 km. Scaling of the vorticity equation, in conjunction with a Bessel function spectral decomposition, indicates that divergence should have a very small effect on the hurricane motion. Simulations with an initially symmetric cyclonic vortex in a resting environment confirm this analysis, and contradict previous published studies on the effect of divergence in a barotropic model. During a 120 h simulation the cyclonic vortex develops asymmetries that have an influence far from the initial circulation. The total RAM within a large circle centered on the vortex decreases with time, and then oscillates about zero. For circles with radii ? 1000 km, the total RAM approaches, but does not reach, zero. An angular momentum budget indicates that the horizontal angular momentum flux tends to counteract the net Coriolis torque on the vortex. If the total RAM of the initial symmetric vortex is zero, the weak far-field asymmetries are essentially eliminated. The motion of the vortex is not, however, related to the RAM in any simple way. Within a few days the near-vortex asymmetries reach a near-steady state. The Asymmetric Absolute vorticity (AAV) is nearly uniform within ?350 km of the vortex center. The homogenization of AAV, which occurs within the closed vortex gyre, is likely due to shearing by the symmetric wind, combined with removal of energy at the smallest scales. The homogenization effectively neutralizes the planetary beta effect, as well as the vorticity associated with an environmental wind.