Selective withdrawal from a finite rectangular tank

The time development of two-dimensional fluid motion induced by a line sink in a rectangular, density stratified reservoir with a free surface is given. It is shown that the initiation of such a sink gives birth to a spectrum of internal expanding shear fronts with a progressively decreasing vertical wavelength. These fronts move out from the sink and travel towards the far wall, where they are reflected. This process ceases once the front with a vertical wavelength equal to the steady withdrawal-layer thickness has reached the end wall. The fronts so introduced continue to move back and forth, expanding to standing waves if the viscosity of the fluid is small enough. The evolution and nature of the withdrawal layer are shown to depend critically on the relative magnitude of the convective inertia and viscous forces, the number of reflexions from the rear wall and the Prandtl number.