Statistical distribution of nonlinear random wave height in shallow water

Abstract

Here we present a statistical model of random wave, using Stokes wave theory of water wave dynamics, as well as a new nonlinear probability distribution function of wave height in shallow water. It is more physically logical to use the wave steepness of shallow water and the factor of shallow water as the parameters in the wave height distribution. The results indicate that the two parameters not only could be parameters of the distribution function of wave height but also could reflect the degree of wave height distribution deviation from the Rayleigh distribution. The new wave height distribution overcomes the problem of Rayleigh distribution that the prediction of big wave is overestimated and the general wave is underestimated. The prediction of small probability wave height value of new distribution is also smaller than that of Rayleigh distribution. The effect of wave steepness in shallow water is similar to that in deep water; but the factor of shallow water lowers the wave height distribution of the general wave with the reduced factor of wave steepness. It also makes the wave height distribution of shallow water more centralized. The results indicate that the new distribution fits the in situ measurements much better than other distributions.