Selective withdrawal of a three-layer viscous fluid

Abstract Two dimensional, selective withdrawal of a three-layer fluid in rectangular tank is considered. Each viscous, weakly compressible and miscible. The lowermost, heaviest flows with constant speed out through line sinks located on the base lower side walls tank. uppermost lightest recharges via sources along top upper at rate that matches outward flux. If are turned suddenly, interfaces between fluids drawn downward different rates; this disparity arises due to fact wave configurations propagate two not same. Density vorticity contours presented used determine time which middle transition layer begins be withdrawn from tank; point extraction most dense its greatest. Inviscid linearised calculated serve as checks early stage evolution full nonlinear model.