Point sink flow in a linearly stratified fluid of finite depth

Abstract

The evolution of selective withdrawal through a point sink of horizontally unbounded, linearly stratified fluid of finite depth is studied as an initial-value problem. Following the initiation of discharge from the sink, internal gravity wave modes propagate radially upstream to change the flow pattern. These modes are called cylindrical modes. We first consider the case of F→0 (where F is the Froude number) to get linearized governing equations, and seek a linear asymptotic solution for large times t* after starting the discharge, of the cylindrical modes in a stratified fluid where viscous and diffusive effects are negligible. The obtained solution shows that the strength of the modal front grows like t*1/3, unlike the case of two-dimensional modes whose strength at the front is kept constant. Numerical calculations are also performed to study the case of F>0. The results then indicate that all the cylindrical modes can propagate upstream for any F except infinity. The steady-state withdrawal-layer thickness and time to steady state are also investigated over the full parameter range considering the viscous and diffusive effects. The obtained results are then compared with both the analytical and experimental results of prior works.