STEADY FLOW BETWEEN 2 RESERVOIRS OF FLUID WITH DIFFERENT DENSITIES AND LEVELS THROUGH A RECTANGULAR CHANNEL SECTION OF VARYING DEPTH AND WIDTH

The steady hydrostatic flow through a channel of rectangular cross sec tion connecting reservoirs of infinite width and depth and containing inviscid fluids of different densities and levels is studied. The main goal is the determination of the discharges of the lighter and denser fluids in terms of the external conditions (reservoir levels, fluid d ensities and Variation of width and depth along a channel). It is show n that the key parameter is delta, which is the ratio of relative rese rvoir level difference, gamma, to relative density difference, epsilon . If delta < 0 then the denser fluid plunges under the stationary ligh ter layer. If delta > delta, (1 < delta, < 1.5) then the lighter fluid runs up on a wedge of stationary heavier fluid. Here delta, depends on the geometry of the constriction. The solutions describing these re gimes are stated. If 0 < delta < delta then both layers are in motion . A qualitative analysis of the solution for arbitrary bottom shape an d channel width and arbitrary epsilon is presented and the problem is reduced to a system of two equations which can be easily solved numeri cally for any particular channel profile. We give detailed analyses fo r the following two cases: 1) the narrowest width of the channel is on the side of the heavier fluid and the top of the sill is on the side of lighter fluid; 2) the minima in channel depth and width coincide. I n the second case the discharges for one class of geometries in the Bo ussinesq approximation are calculated and discussed. (C) 1998 Elsevier Science B.V. All rights reserved.