Unsteady free surface flow induced by a line sink in a fluid of finite depth

Abstract

The unsteady withdrawal of fluid from a reservoir of finite depth with a free surface through a line sink is considered. A numerical method is used to investigate the evolution of a free surface in several different geometric and initial configurations, and it is shown that there are some critical flow parameters at which the flow changes its nature. The existence of steady states is also considered. Results both with and without surface tension are included and placed in context with previous work. Inclusion of surface tension reveals that solutions either evolve to a steady state or drawdown. As the sink is moved off the base, the behaviour becomes consistent with flows in a fluid of infinite depth, and consequently flows can be classified as either “shallow” or “deep” depending on their drawdown behaviour.