Calculating crest statistics of shallow water nonlinear waves based on standard spectra and measured data at the Poseidon platform

Abstract

This paper introduces a new approach for the calculation of the wave crest distribution of shallow water nonlinear waves by utilizing a Transformed Rayleigh method where the second order nonlinear wave model is incorporated. The proposed Transformed Rayleigh method is based on a deterministic and time instantaneous functional transformation. It is very efficient and accurate and can be used for engineering purposes. Meanwhile, the correction for the effect of bottom on the wave spectrum, a procedure that is frequently overlooked by some researchers, has been integrated into the Transformed Rayleigh method. The proposed new approach has been first applied for calculating the wave crest height exceedance probabilities of sea states with standard JONSWAP spectra corresponding to different water depths, and the calculation results have been favorably validated against Monte Carlo simulation results. Meanwhile, the wave crest height exceedance probabilities of these sea states obtained from using the Jahns and Wheeler finite depth wave crest height distribution model have also been included for comparison purpose. It is found that in all cases the Transformed Rayleigh method can offer better predictions than the Jahns and Wheeler model. The Transformed Rayleigh method is then applied to calculate the wave crest height exceedance probabilities of a combined sea state with a bimodal Torsethaugen spectrum corresponding to a water depth of 25m, and its accuracy and efficiency are again favorably validated by using Monte Carlo simulations. Finally, the Transformed Rayleigh method is applied to predict the wave crest height exceedance probabilities of a sea state with the surface elevation data measured at the Poseidon platform in the Japan Sea, and its accuracy and efficiency have been once again convincingly substantiated.