Bottom Withdrawal of Viscous Stratified Fluid

A theoretical investigation was conducted to predict the fundamental behavior of nondiffusive, viscous flow to a sink located at the bottom of a density-stratified reservoir. The governing partial differential equation was transformed into an ordinary differential equation by utilizing a similarity technique. Numerical and series solutions were obtained and predict a flow field characterized by a withdrawal layer near the reservoir bottom moving toward the sink bounded above by a narrower reverse flow with a much smaller volumetric discharge. The theoretical development further indicates that normalized profiles of horizontal velocity, vertical velocity, and horizontal shear are similar, i.e., have shapes that are independent of the fluid and flow parameters. Mathematical expressions were developed for various aspects of the fluid motion such as horizontal and vertical velocity, horizontal shear, withdrawal layer thickness, and the distribution of flow within the withdrawal layer.