Interaction of a monopole vortex with an isolated topographic feature in a three-layer geophysical flow

In the frame of a three-layer quasi-geostrophic analytical model of a \(f\)-plane geophysical flow, Lagrangian advection being induced by the interaction of a monopole vortex with an isolated topographic feature is addressed. Two different cases when the monopole locates either within the upper or the middle layer are of our interest. In the bottom layer, there is a delta function topographic feature, which generates a closed recirculation region in its vicinity due to the background flow. This recirculation region extends to the middle and upper layers, and it plays the role of a topographic vortex. The interaction between the monopole and the topographic vortex causes complex, including chaotic, advection of fluid particles. We show that the model's parameters, namely, the monopole and topographic vortices' strengths and initial positions, the layers' depths and densities are responsible for the diverse advection patterns. While the patterns are rather complicated, however, one can single out two major processes, which mostly govern fluid particle advection. The first one is the variation in time of the system's phase space structure, so that within the closed region of the topographic vortex, there appear periodically unclosed particle pathways by which the particles leave the topographic vortex. The second one is chaotic advection that arises from the nonstationarity of the monopole-topography interaction.