Hollow vortex in a corner straining flow

A hollow vortex is a solution to the 2D Euler equations with a finite-area region of constant pressure and nonzero circulation. Hollow vortices in straining flow have been previously treated, but the influence of boundaries has not yet been investigated. Equilibrium solutions for a hollow vortex in straining flow in a right-angled corner are found in terms of the Schottky-Klein prime function. Using complex-variable techniques and the prime function, the vortex boundary is constructed as a conformal map from the canonical doubly-connected domain of the concentric annulus to the physical domain of the hollow vortex in a corner. Comparison with the limiting case of a point vortex in a corner is made, and extensions to corners of arbitrary angle and non-equilibrium cases are discussed. Motivation includes regions of high nutrient or pollution density in the ocean, which can be formed in coastal regions from rivers or runoffs; the advection and mixing of the regions depend in part on the local flow and shoreline geometry, and a hollow vortex in straining flow is a possible model for this process.