Stratified Flows with Vertical Layering of Density:
Experimental and Theoretical Study of the Time Evolution of Flow Configurations and their Stability

Courant Institute

New York University

A vertically moving boundary in a stratified fluid can create and maintain a horizontal density gradient, or vertical layering of density, through the effect of viscous entrainment.  We perform experiments that successfully create axisymmetric flows in which the density is layered vertically, with a layer of dense fluid entrained by a narrow fiber that is towed upwards.  In order to determine the time evolution of the flow observed in the experiments, a lubrication model is developed and is shown to be in excellent agreement with observations.  We perform stability analysis on a family of exact shear solutions in both two dimensions and the axisymmetric geometry of the experiment, using asymptotic and numerical methods.  The stability properties of the flow depend strongly on the size of the layer of dense fluid viscously entrained by the moving boundary.  A critical layer size is found, below which the flow configuration is stable and beyond which the flow configuration is unstable.  This bifurcation is independent of the Reynolds number of the flow and the Reynolds number only affects the magnitude of the amplification or damping of disturbances.  It is found that unstable layer sizes are possible to achieve from the initial value problem of stable stratification.  Layer sizes which are predicted to be unstable are observed in the experiment, however the amplification of disturbances is not observed because the rate of amplification is too small.