Motion of waves in shallow water. Interaction between waves and sand bottoms

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Abstract
The loss of energy of a travelling water wave, due to the mechanism of the formation of sand ripples and water vortices on a sandy bed, becomes of practical importance when models are used to predict full-scale foreshore movements. On the assumption that the bottom-water oscillation is nearly simply harmonic, the mechanism was studied by oscillating a section of bed through still water. The pitch, p , of the sand ripple formed was found to vary as the square root of the grain diameter, independently of the speed and of the grain density, for amplitudes, R , of water motion exceeding this pitch. But for smaller amplitudes the pitch shortens with decreasing amplitude of movement. The mean drag coefficient, k , in the case of artificial rigid ripples, was measured directly. For R / p less than unity, k remains constant. For R / p greater than unity, k was found to vary as ( R / p ) -0.75 . These results are compared with the case of steady flow. The critical water speeds and amplitudes for first disturbance of grains on a smoothed surface was also measured, over a wide range of grain diameters and densities. The results conform closely to a simple empirical expression.

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