CNOIDAL WAVES IN SHALLOW WATER

Frank D. Masch

Abstract


The propagation of long waves of finite amplitude in water with depth to wavelength ratios less than about one-tenth and greater than about one-fiftieth can be described by cnoidal wave theory. To date little use has been made of the theory because of the difficulties involved in practical application. This paper presents the theory necessary for predicting the transforming characteristics of long waves based on cnoidal theory. Basically the method involves calculating the power transmission for a wave train m shallow water from cnoidal theory and equating this to the deep water power transmission assuming no reflections or loss of energy as the waves move into shoaling water. The equations for wave power have been programmed for the range of cnoidal waves, and the results are plotted in non-dimensional form.

Keywords


cnoidal waves; shallow; power transmission

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