INTERFACIAL FLOW OVER A STEP

Steady, supercritical flow of a two fluid system, over a semiinfinite step at the bottom of a channel that is bounded above by a rigid horiz ontal plane, is considered. Both fluids are assumed to be inviscid and incompressible and to flow irrotationally, but to have different dens ities. A transformation technique is used to reformulate the problem a s a system of nonlinear integrodifferential equations, for the interfa cial angle theta, and a connection equation for the jump of the potent ial across the interface. A linearized theory, based upon a small-step height, is presented and indicates that the nature of the interface f ormed depends on whether the upstream flow is subcritical or supercrit ical. Numerical solutions for the system are presented showing their d ependence on the step height, density, speed, and depth ratios, respec tively, and also on the Froude number of the lower fluid.