Depth-integrated models for three-dimensional flow over topography

Abstract

Considered in this investigation is the three-dimensional, gravity-driven flow of a thin viscous fluid layer down an incline, and spreading over topography. Three depth-integrated models are presented and contrasted. These include an integral-boundary-layer model, a weighted-residual model and a hybrid model. A numerical solution procedure suited for solving three-dimensional flows is also proposed. Numerous simulations have been conducted using the models for various steady subcritical, and unsteady supercritical flows over several topographies. Good agreement among the three models was found. In addition, the models were also validated using experimental results, and, again, good agreement between the three models and with experiments was obtained.