Selective Withdrawal Through A Point Sink And Pycnocline Formation In A Linearly Stratified Flow

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Abstract
Experiments were carried out on selective withdrawal through a point sink in the endwall of a rectangular tank containing a linearly stratified fluid. The results indicate that the withdrawal layer half thickness d may be expressed as d/(Q/N)1/3 = 1.02 (standard error .02), where Q is discharge through the point sink in the endwall and N is the buoyancy frequency of the fluid. This result is restricted to the inertial regime for which Q/νL>l, where ν is kinematic viscosity and L the tank length. An attempt to account for asymmetry in the withdrawal layer and in the evolving background density profile did not significantly reduce experimental scatter. The development of a sharp pycnocline in the initially linear stratification can be predicted using a kinematic approach. A solution is presented of the equations of conservation of mass and volume for an incompressible, nondiffusive fluid, using steady-state empirical relations between d, Q, N, and the velocity field in lieu of the momentum equations. Predictions based on this solution are compared with experimental results, with generally good agreement.

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