New equations for Two-layer nonhydrostatic shallow flow

In simulation of layered flows (each layer having constant density), it is usually assumed that the pressure distribution is hydrostatic in each layer. However, in some cases modeling is not possible without considering the nonhydrostatic pressure. One of these cases is two-layer approach-controlled flow. In this study in order to simulate nonhydrostatic unsteady two-layer flow, new equations are derived from the Euler equations via a perturbation technique using shallowness as the small parameter and assuming irrotational flow. To investigate the formation of the approach-controlled flow, a laboratory transient two-layer flow experiment is conducted to monitor a two-layer flow while it changes type to the approach-controlled flow. The experiment is also simulated numerically by solving the new equations making use of a TVD (Total Variation Diminishing) MacCormack scheme. Good agreement has been achieved along with an explanation for the formation of the approach-controlled flow.