University Of Tasmania
154910 - Selective withdrwal.pdf (1.07 MB)
Download file

Selective withdrawal of a three-layer viscous fluid

Download (1.07 MB)
journal contribution
posted on 2023-05-21, 15:45 authored by Lachlan WestLachlan West, Jason CosgroveJason Cosgrove, Andrew BassomAndrew Bassom
Two dimensional, selective withdrawal of a three-layer fluid in a rectangular tank is considered. Each fluid is viscous, weakly compressible and miscible. The lowermost, heaviest fluid flows with constant speed out through line sinks located on the base and lower side walls of the tank. The uppermost and lightest fluid recharges the tank via line sources located along the top and on the upper side walls at a rate that matches the outward flux. If the line sinks are turned on suddenly, the interfaces between the fluids are drawn downward at different rates; this disparity arises due to the fact that the wave configurations that propagate along the two interfaces are not the same. Density and vorticity contours are presented and used to determine the time at which the middle transition layer of fluid begins to be withdrawn from the tank; at this point the rate of extraction of the most dense fluid is its greatest. Inviscid linearised interfaces are calculated which serve as checks on the early stage evolution of the full nonlinear model.


Publication title

Journal of Engineering Mathematics








School of Natural Sciences


Springer Netherlands

Place of publication


Rights statement

© The Author(s) 2022. This article is licensed under a Creative Commons Attribution 4.0 International (CC by 4.0) License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.

Repository Status

  • Open

Socio-economic Objectives

Expanding knowledge in the mathematical sciences

Usage metrics

    University Of Tasmania