Vortex interaction with a zonal Rossby wave in a quasi-geostrophic model

An analytical theory is presented for the motion of a localized vortex in the presence of a zonal Rossby wave on the ββ-plane. In the framework of the equivalent-barotropic quasi-geostrophic model, the analytical method developed by Sutyrin and Flierl [Sutyrin G.G., Flierl G.R., 1994. Intense vortex motion on the ββ-plane: development of the beta gyres. J. Atmos. Sci. 51, 773–790] for intense vortices with piecewise-constant potential vorticity is generalized to take into account a slowly propagating Rossby wave which modifies the background potential vorticity. The predictions of these asymptotic expansions are compared with the results of numerical simulations.The theory describes the vortex advection by the wave and the vortex drift due to the background potential vorticity gradient. The net vortex drift speed due to the wave is found to be smaller than the maximum wave velocity; this is due to the baroclinic β-effect and to the periodic structure of the background potential vorticity gradient. Besides known elliptical core deformations, triangular deformations are generated by the wave on the core boundary. Additionally, the planetary β-effect provides a predominantly westward vortex drift with nearly the same speed as the wave propagation speed.The asymptotic theory is shown to agree well the results of a numerical pseudo-spectral, high-resolution biperiodic model when the vortex velocity is much larger than the wave velocity. Both meridional and zonal vortex drifts are slightly overestimated when the wave velocity is comparable with the vortex velocity. Vortex size is shown to be more influential on vortex trajectory than the Rossby wave length. In particular, smaller vortices drift westward farther and faster than large ones. Vortex core deformations typically contain modes 2 and 3 with a stronger mode 3 component for more intense Rossby waves as predicted by theory.