The motion of tropical vortices in east–west mean flows is studied with the barotropic vorticity equation on the beta plane. The vorticity equation is integrated numerically from an initially symmetric vortex embedded in (i) a linear shear flow or (ii) a parabolic jet. The first experiment with flow (i) has β = 0 and it is linearized about the mean flow. The vortex is distorted by the mean flow so that the even Fourier components around the vortex grow, but the vortex does not move. When nonlinear effects are included the distortion is damped in the inner 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 advection is removed from the trajectories. The trajectory for the anticyclonic mean flow is significantly longer than the cyclonic and no mean flow trajectories, which are about equal. For mean flow (ii), with the same absolute vorticity gradient as β but on an f plane, the vortex has 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 experiments that beta has a stronger effect on vortex motion than the relative vorticity gradient.
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Williams et al. (1994) studied this question.