Nonhydrostatic Formulation of Unsteady Single and Two-Layer Flow over Topography

Abstract

A new, concise theoretical model for simulation of unsteady, nonhydrostatic two-layer flow is presented. The formulation is systematically developed from the equations of motion of an ideal fluid using a perturbation technique with shallowness as the small parameter. The advantage of this model over many models in the field is that the shape of streamlines, or velocity and pressure distributions, are dictated by the model rather than being predetermined. This model also relaxes further assumptions involved in the previous formulations and can be used to simulate different two-layer flow cases. In some situations, simulation is impossible without considering the nonhydrostatic pressure, one of which is a two-layer approach-controlled flow. A laboratory transient two-layer flow experiment is conducted to examine transition to the approach-controlled flow, and the new equations are successfully applied to model this transient flow using a total variation diminishing (TVD) MacCormack scheme. Furthermore, new equations for single layer unsteady nonhydrostatic flow are presented and two-steady flow cases of flow over an obstacle and an undular hydraulic jump are excellently simulated.