Monopoles in a zonal flow with constant shear on a quasi-geostrophic f-plane: Effects of Galilean non-invariance

Abstract

Building on the work of Kravtsov and Reznik [J. Fluid Mech. 909, A23 (2021); hereafter KR21], we studied the interactions of a localized monopole with a rectilinear, constant-shear flow in a 1½-layer, f-plane, quasi-geostrophic model. The non-invariance of this model with respect to Galilean transformations plays a crucial role in the dynamics of such interactions. Of particular importance here are two configurations in which the center of the vortex is located on the line of zero zonal current and remains motionless in the background of a nonstationary flow field generated via interactions of the vortex with the zonal flow. In configuration I (II), the vortex is prograde (retrograde), that is, its vorticity is of the same (opposite) sign with the vorticity of the background flow. Configuration I is stable, whereas configuration II eventually breaks down: a retrograde vortex drifts off of the zero-current line, rapidly accelerates and radiates intense Rossby waves, which results in a gradual weakening of the vortex. Naturally, the same scenario plays out if a retrograde vortex is initially off of the zero-current line. On the other hand, a prograde vortex initially located at some distance from the zero-current line drifts toward this line, albeit at a rate that decreases with time, so the solution always tends to configuration I. Therefore, the line of zero zonal current “attracts” prograde vortices and “repels” retrograde vortices. The present numerical experiments with singular vortices, using the scheme developed in KR21, confirm the above scenarios and clarify their dynamics.