Numerical Studies of Line Sink Flow in a Rotating Stratified Fluid.

Abstract

The time development of two-dimensional fluid motion induced by a line sink of a rotating linearly stratified Boussinesq fluid in a finite-depth reservoir is numerically studied. The flow is characterized by a Froude number, Fr and the ratio of the inertial frequency, f, to the buoyancy frequency, N. Following the initiation of the sink, the inertial gravity wave modes are generated to propagate upstream, which results in the narrowing of a withdrawal-layer thickness. Attention is focused on investigating the evolution of the mode propagation and the resultant flow patterns for various Fr and f/N. The numerical results clarify that the nature of the mode propagation has little dependence on the parameter Fr if the distance from the sink is larger than a critical one, Nd/f where d is the reservoir's depth. The withdrawal layer thickness for Fr=0 is linearly proportional to the distance from the sink and the nonlinear effect (Fr〓0) can be easily incorporated only by adding the term representing the thickness under no rigid rotation. Furthermore, profiles of the withdrawal layer thickness show strong time-dependence whose period is about 2π/f.