A two-layer model for a non-Newtonian gravity current subjected to wind shear

Abstract

A theoretical model is developed for the gravity current resulting from the sudden release of a fixed volume of fluid of non-Newtonian power law rheology on top of a slightly denser Newtonian fluid layer in the presence of wind stress. The model incorporates the flow of both layers and accounts for the effects of inertial and viscous forces, and is suited for moderate Reynolds number flows. The governing equations are obtained by depth-averaging the unsteady equations of motion in accordance with the von Karman's momentum integral method, and constitute a hyperbolic system of four equations for the flow rates and thicknesses of the fluid layers. Results are obtained by a well established numerical scheme for systems of nonlinear hyperbolic equations. For a particular case analytical results are obtained by employing an asymptotic matching approach. Good agreement is obtained between the numerical and analytical results. The effects of the thickness of the ambient layer, wind stress, Reynolds numbers, and rheology on the gravity current are discussed.