Irregular Wave‐Induced Velocities in Shallow Water

Abstract

Irregular water waves were generated in a flat‐bottomed, two‐dimensional wave tank with a partially reflecting spending beach. The horizontal and vertical velocity of the fluid particles was measured with a laser Doppler velocimeter at middepth and near bottom in the water column. The results show that a linear theory equation predicts the root‐mean‐square (rms) water particle velocity to within 10% given the measured incident wave height spectrum, reflection coefficients, and water depth. An extension of the Gaussian probability distribution based on the Gram‐Charlier series was applied to the velocity time series. This extended distribution did not fit the measured data better than the ordinary Gaussian distribution. The Beta‐Rayleigh probability distribution function was applied to peak velocities. A slight improvement is observed over the ordinary Rayleigh distribution. The parameters of the Beta‐Rayleigh distribution are empirically correlated with parameters of the incident wave spectrum.