Two-layer shallow water computation of mud flow intrusions into quiescent water

Abstract

The present computational study addresses two-layer shallow flows in which the superposed layers differ in velocity, density and rheology. The geomorphological phenomena motivating this model are confluence problems in which mud and debris surges slump into upland lakes and rivers. Specifically, the flows of interest are assumed to be sharply stratified, with a clear water layer flowing over a moving layer of mud modelled as a Herschel–Bulkley fluid.A finite volume computational scheme suitable for the simulation of such flows is presented and applied to various validation cases. The scheme extends to two-layer flows the robust method of Harten, Lax and Van Leer. Special care is devoted to the following numerical issues: the treatment of pressure along interfaces, the ”contact points“ at which the thickness of either layer can vanish, and the finite yield stress characterizing the mud rheology. Results are presented for the intrusion of mud surges into shallow quiescent water.

Keywords:

• Two-layer shallow water equations
• Herschel–Bulkley fluid
• confluence problem