Relative Validities of Water Wave Theories

by Robert G. Dean, (A.M.ASCE), Chmn.; Dept. of Coastal and Oceanographic Engrg., Univ. of Florida, Gainesville, FL,

Serial Information: Journal of the Waterways, Harbors and Coastal Engineering Division, 1970, Vol. 96, Issue 1, Pg. 105-119

Document Type: Journal Paper


The engineer confronted with an offshore design problem can select one of a rather large number of wave theories; at present, there is an insufficient basis to indicate which of the available theories is best for a particular set of wave conditions. This paper presents the results of an evaluation of the relative validity of eight wave theories, including seven analytical theories and the fifth-order stream function (numerical) wave theory. Relative validity is based on the fit provided, by the various theories, to the governing equations in the boundary value problem formulation. The wave conditions included in the evaluation encompass a wide range of relative water depths, and wave steepnesses from one-quarter of breaking up to the conventional breaking limit. It is found that, of the theories tested, the best fit in deep water is provided by the fifth-order stream function wave theory; in intermediate and shallow water depths, the Airy and first-order Cnoidal wave theories provide the best fits to the governing equations.

Subject Headings: Water waves | Two-dimensional flow | Breaking waves | Wave equations | Numerical analysis | Boundary value problem | Shallow water | Hydraulic design

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