Monopoles In A Uniform Zonal Flow On A Quasi-Geostrophic Beta-Plane: Effects Of The Galilean Non-Invariance Of The Rotating Shallow-Water Equations

Galilean non-invariance of the shallow-water equations describing the motion of a rotating fluid implies that a homogeneous background flow modifies the dynamics of localized vortices even without the beta-effect. In particular, in a divergent quasi-geostrophic model on a beta-plane, which originates from the shallow-water model, the equation of motion in the reference frame attached to a uniform zonal background flow has the same form as in the absence of this flow, but with a modified beta-parameter depending linearly on the flow velocity (U) over bar. The evolution of a singular vortex (SV) embedded in such a flow consists of two stages. In the first, quasi-linear stage, the SV motion is induced by the secondary dipole (beta-gyres) generated in the neighbourhood of the SV. During the next, nonlinear stage, the SV merges with the beta-gyre of opposite sign to form a compact vortex pair interacting with far-field Rossby waves radiated previously by the SV, while the other beta-gyre loses connection with the SV and disappears. In the absolute reference frame and with beta = 0, the SV drifts downstream and at an angle to the background flow. The SV always lags behind the background flow, with the strongest resistance during the quasi-linear stage and weakening resistance at the nonlinear stage of SV evolution. In the general case where beta > 0, the SV can move both upstream (for small-to-moderate (U) over bar > 0) and downstream (for (U) over bar < 0 or sufficiently large <(U)over bar>> 0). Under weak-to-moderate westward and all eastward flows the SV cyclone (anticyclone) also moves northward (southward), its meridional drift increasing with (U) over bar.