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

TLDR

Energy loss of travelling water waves caused by sand ripple and vortex formation on sandy beds is important for foreshore movement predictions. The study examined harmonic bottom‑water oscillations by oscillating a bed section, measured drag coefficients for artificial ripples, compared the results with steady flow, and determined critical speeds and amplitudes for grain disturbance across various grain sizes and densities. Pitch of sand ripples scales with the square root of grain diameter and shortens at low amplitudes; the drag coefficient remains constant when R/p<1 but decreases as (R/p)^-0.75 when R/p>1, and the overall results fit a simple empirical expression.

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.