NUMERICAL-STUDIES OF THE BETA-EFFECT IN TROPICAL CYCLONE MOTION .2. ZONAL MEAN FLOW EFFECTS

The motion of tropical vortices in east-west mean flows is studied wit h the barotropic vorticity equation on the beta plane. The vorticity e quation is integrated numerically from an initially symmetric vortex e mbedded in (i) a linear shear flow or (ii) a parabolic jet. The first experiment with flow (i) has beta = 0 and it is linearized about the m ean flow. The vortex is distorted by the mean flow so that the even Fo urier components around the vortex grow, but the vortex does not move. When nonlinear effects are included the distortion is damped in the i nner part of the vortex, but wavenumber two grows in the outer region. The addition of the beta effect causes the vortex to move in the same direction as the no mean flow solution provided the mean flow advecti on is removed from the trajectories. The trajectory for the anticyclon ic mean flow is significantly longer than the cyclonic and no mean flo w trajectories, which are about equal. For mean flow (ii), with the sa me absolute vorticity gradient as beta but on an f plane, the vortex h as a much shorter trajectory and a more westerly direction of movement than the no mean flow solution with beta. This effect comes from the advective distortion of the vortex, which projects onto wavenumber one in the disturbance vorticity equation. It is shown with other experim ents that beta has a stronger effect on vortex motion than the relativ e vorticity gradient.