Flow induced by a line sink near a vertical wall in a fluid with a free surface, Part II: finite depth

Abstract

Flow caused by a line sink near a vertical wall in an otherwise stagnant fluid with a free surface is studied. A linear solution for small flow rates is obtained and a numerical method based on fundamental singularities techniques is applied to the full nonlinear problem. The sink is located at an arbitrary location away from all boundaries and the fluid is of finite depth. Steady solutions are presented for various flow rates and sink location. It is shown that the numerical results and linear solutions are in good agreement for small flow rates. The results suggest that steady nonlinear solutions are limited to flow rates below some critical value. Some interesting surface shapes are obtained depending on the location of the sink.

Models of Flow and Diffusion: Selective Withdrawal From a Stratified Fluid and Dispersal of Hydrogen in the Retina

“…Three related problems are studied in the first part and one in the second part. In the first problem, the flow induced by a line sink at an arbitrary location in a fluid of finite depth with a free surface, relevant to flows in reservoirs, lakes and cooling ponds, is examined [4]. A rigid-lid solution for small flow rates is obtained and a numerical method based on fundamental singularities techniques is applied to the full nonlinear problem.…”