Flow induced by a line sink near a vertical wall in a fluid with a free surface Part I: infinite depth

Abstract

AbstractThe two-dimensional, steady flow of an inviscid fluid induced by a line sink located near a vertical wall in a region of infinite depth is computed. The effects of surface tension are investigated. The solution in the limit of small Froude number is obtained analytically, and numerically for the nonlinear problem. The asymptotic solution is found to have a property that if the horizontal location of the sink, $$x_\mathrm{{s}} < 1$$ x s < 1 , there is only one stagnation point on the surface, at the wall. However, if the horizontal location $$x_{\mathrm{s}} > 1$$ x s > 1 , a second stagnation point forms on the free surface. Numerical solution for the nonlinear problem confirms these properties. The effect of moving the sink horizontally has also been considered. The maximum Froude numbers at which steady solutions exist are computed and compared with the previous work.