Simulations of shallow water surface waves and comparison with water table experiments

Abstract

The hyperbolic systems of equations describing the shallow water surface waves are solved numerically using finite difference schemes and an explicit time integration procedure. The equations are similar to isentropic Euler equations (with γ = 2) and can be simplified using a potential flow model. The results of isentropic Euler, potential model, transonic small disturbance, and full Euler equations are compared for typical flows around pointed and blunt bodies for several Mach numbers. On the other hand, water table experiments are described and the flow over obstacles is studied. Using the theory of hydraulic analogy, the relations between compressible flows and shallow water surface waves are discussed. Flow patterns, including formation of shock waves and expansion fans are presented. It is demonstrated that the water table can be an inexpensive educational tool for demonstration of transonic and supersonic flow phenomena.