Conformally mapped viscous gravity current

Abstract

We show how the conformal mapping technique can be applied to analyse specific problems in the context of viscous gravity current theory. We examine the edge of steady thin planar viscous gravity currents in the presence of complex external low Reynolds flows. In addition to the uniform ambient flow we look at the case of viscous gravity currents spreading in positively strained flows and around cylindrical bodies. These external flows exert shear stress on the gravity current, which drives it in the streamwise direction. The idealised conditions are re-created in the laboratory using a Hele–Shaw cell with a point source on the bottom plate where the saline is introduced into the flow. The mapped laboratory results are compared to a known similarity solution and the agreement is good. We conclude by identifying a broad class of viscous gravity current problems where this technique may be applied.