Narrow Results

A sequence of analytical solutions explore the spectrum of response patterns expected from numerical codes for flood and tide propagation in channels. Complete analytical details of the solutions are provided, together with specific suggestions for an associated set of analytical benchmark tests. Illustrations of predicted response patterns provide the basis for a discussion of many significant physical aspects and their representation in discrete numerical codes.

A hybrid analytical-numerical method for standing waves in water of any depth exactly satisfies the field equation, the bottom boundary condition, the periodic lateral boundary conditions and the mean water level constraint. The wave height and the kinematic and dynamic free surface boundary conditions are imposed numerically, as a problem in nonlinear optimization. The algorithm is confirmed against an existing fifth-order analytical theory. The method extends the available predictive range for standing waves to near-limit waves in deep, transitional, and shallow water. The limitations of the numerical method are clearly identified. The limit wave cannot be predicted but near-limit extreme wave indicators for wave height, wave number, and crest elevation are defined over the complete range of water depths.