Selective withdrawal through a line sink of non-rotating and rotating stratified fluid in a reservoir of finite depth

Abstract

Selective withdrawal through a line sink of both non-rotating and rotating stratified fluid in a reservoir of finite depth is studied under an assumption that viscosity and diffusivity of the fluid are negligible. This flow is characterized by the two parameters: the Froude number F; and the ratio of the inertial frequency f to the buoyancy frequency N. Following the initiation of discharge from the sink, internal (or inertial) gravity wave modes propagate upstream. We first consider the case of F→0 to get linearized governing equations and seek a linear asymptotic solution for large t ∗ (where t ∗ is time after starting the discharge) which is uniformly valid in space. The obtained solution shows the propagation of the individual modes clearly and it is found that the amplitude of the modal front is kept constant with time t ∗ when f=0, whereas it decreases as t ∗−1/3 when f>0. Next, numerical calculation is conducted to study the case of F>0. Specifically, the validity of both our linear solution and the theory suggested by Clarke and Imberger in describing the mode propagation for F>0 is explored. Investigations are also made of the flow patterns constructed by the passage of these modes. It is then found that the withdrawal-layer thickness shows strong time dependence whose period is about 6/ f.