The bath-plug vortex

Forbes, L.K. and Hocking, G.C. (1995) The bath-plug vortex. Journal of Fluid Mechanics, 284 (1). pp. 43-62.

Abstract

Steady flow with constant circulation into a vertical drain is considered. The precise details of the outflow are simplified by assuming that the drain is equivalent to a distributed volume sink, into which the fluid flows with uniform downward speed. It is shown that a maximum outflow rate exists, corresponding to no fluid circulation and vertical entry into the drain hole. Numerical solutions to the full nonlinear problem are computed, using the method of fundamental solutions. An approximate analysis, based on the use of the shallow-water equations, is presented for flows in which the free surface enters the drain. There is, in addition, a second type of solution, having a stagnation point at the free surface and no fluid circulation. These flows are also computed numerically, and results are presented.