Axisymmetric withdrawal and inflow in a density-stratified container

Abstract

The axisymmetric withdrawal of fluid from a linearly stratified container is studied over the full parameter range. When only buoyancy and inertia are important the flow in the withdrawal layer is influenced by a virtual control point and is not analogous to that observed in the two-dimensional withdrawal problem. Two further flow regimes are shown to exist in which viscous forces are important : one in which convection of species is important, and a second in which diffusion of species is important. Theoretical arguments and laboratory experiments are used to show that S = (Q2N/v3)~ is the appropriate flow parameter to differentiate between these possibilities. It is also argued that these results may be generalized to describe the features of several related flows : axisymmetric drawdown (or drawup) in withdrawal from a layered density structure, axisymmetric inflow into a linearly stratified environment and the axisymmetric spreading of density currents.