Some solutions of simplified open channel flow equations

Abstract

Open channel flows of shallow depth in hydraulics are characteristically turbulent due to disturbances generated by bed friction and other causes. The governing equations of such flows based on Reynolds Averaged Navier – Stokes (RANS) equations have been developed in recent years in collaborative papers by Bose and Dey, and have found useful applications. In as much as the equations are of nonlinear evolution type, several types of solutions can exist. The present paper develops five types of solutions, based on the similarity method, localized solution method, and the method of separation of variables. The last two methods deliver two solutions in each case. The self-similar solution and the two localized solutions, reduce to solution of ODE’s that are numerically presented. The two separation of variables solutions are obtained in explicit form.