FREE-SURFACE FLOW OVER CURVED SURFACES - PART-I - PERTURBATION ANALYSIS

The standard two-dimensional shallow water equation formulation assume s a mild bed slope and no curvature effect. These assumptions limit th e applicability of these equations for some important classes of probl ems. In particular, flow over a spillway is affected by the bed curvat ure via a decidedly non-hydrostatic pressure distribution. A detailed derivation of a more general equation set is given here in Part I. The method relies upon perturbation expansion to simplify a bed-fitted co -ordinate configuration of the three-dimensional Euler equations. The resulting equations are essentially the equivalent of the two-dimensio nal shallow water equations but with curvature included and without th e mild slope assumption. A finite element analysis and flume result ar e given in Part II. (C) 1998 John Wiley & Sons, Ltd.