Reservoir Flow Prediction by Contravariant Shallow Water Equations

Abstract

Jet-induced mixing is often used to prevent stagnation in shallow service reservoirs. This paper describes a nonorthogonal boundary-fitted model for simulating flows in reservoirs of arbitrary shape. The numerical model solves the curvilinear shallow water equations that are expressed in terms of the depth-averaged contravariant velocity components and free surface elevation. Results are presented for the case of jet-forced flow in a circular reservoir where the inlet and outlet stems are diametrically opposite. Excellent agreement is obtained with alternative analytical and numerical schemes, at inlet Reynolds numbers equal to 10 and 25. A further comparison is given between numerical simulations and experimental measurements of the steady-state velocities in a circular reservoir where the inlet and outlet stems are diametrically asymmetric. Although the present application concerns steady jet-forced circulation, the contravariant shallow water equations should be suitable for modeling wind-driven circulation or tidal flows.