Interaction between an upper-layer point vortex and a bottom topography in a two-layer system

Abstract

In this paper, the interaction between an upper-layer vortex and a bottom topography is investigated using an $f$ -plane two-layer quasi-geostrophic model with a point vortex and step-like topography. The contour dynamics method is used to formulate the model. A steadily propagating linear solution along the topography, known as the pseudoimage solution, is derived analytically for a weak point vortex, and the nonlinear solution is obtained numerically. Numerical experiments show that the nonlinear pseudoimage solution collapses with time. Saddle-node points in the velocity field are critical in this collapse. Even after the collapse, the point vortex propagates along the topography similarly to in the steadily propagating solution. Numerical experiments with various initial conditions show that the point vortex has two types of motion in this system: motion along the topography and motion away from the topography. In the latter case, the point vortex and lower-layer potential vorticity anomaly form a heton-like dipole structure. The motion classification results show that an anticyclonic (cyclonic) point vortex on the deeper (shallower) side is more likely to form a dipole structure than a cyclonic (anticyclonic) vortex on the deeper (shallower) side when their initial distance from the topography is the same.