Bulges at vortical outflows

Abstract

This paper constructs steady solutions of the two-dimensional Euler equations corresponding to a line source of vortical fluid on the impermeable boundary of a quiescent flow. The nonlinear, free-boundary problem is solved by mapping the flow domain to the hodograph plane. A vortex dipole or, equivalently, a source–sink doublet is superposed on the source leading to flow patterns that model the ballooning outflows observed where rivers and straits discharge into the open ocean and in the rotating flow experiments and numerical simulations designed to reflect these observations.