Spatial Coherence and Crest-Length Statistics of Waves in Deep Water

摘要

The methodology to simulate realizations of a nonlinear sea surface with a specified frequency-directional spectrum and a specified bispectrum have been developed. The simulation algorithm accounts for interactions between waves traveling in different directions. The target wave number spectrum can be obtained from observations, the output of a wave prediction model, or theory. The target bispectrum can be obtained from observations or from second-order nonlinear theory given the wave number spectrum. The bispectrum estimated from the wave number spectrum from LIDAR observations and second-order theory compares well with the bispectrum estimated directly from the images of approximately 1 m high waves in 20-30 m water depth near the North Carolina coast. Third-order statistics of the sea surfaces obtained from numerical simulations using the observed wave number spectrum and either the observed theoretical bispectrum compare well with the statistics of the observed sea surface, verifying both the simulation technique and second-order nonlinear theory.