Interaction of an along-shore propagating vortex with a vortex enclosed in a circular bay

A simple dynamical model of vortex interactions taking place near a curved boundary mimicking a circular bay is formulated and examined. An initial configuration consisting of a point vortex in the bay and of an incident point vortex moving toward the bay along the straight part of the boundary is considered. Both vortices are of equal strengths. Typical stationary regimes of the bay-bound vortex when the incident vortex is far from the bay are obtained. When the incident vortex comes near the bay, its interaction with the bay-bound one may result in irregular motion of both vortices. Typical outcomes of the interaction are established to be (i) the incident vortex passes over the bay without forcing the bay-bound vortex to leave the bay; (ii) the incident vortex becomes entrapped within the bay, whereas the bay-bound vortex leaves it; (iii) both vortices leave the bay shortly after the interaction as separate vortices or as a bound leap-frogging pair; (iv) both vortices exhibit convoluted dynamics being entrapped for a considerable time within the bay, but in the end either one or both of the vortices leave the bay. The model might be useful in getting some insight into typical regimes of eddy dynamics near curved boundaries in the context of ocean studies provided the eddies remain coherent during the interaction