Wave Statistics for Intermediate Depth Water—NewWaves and Symmetry

Abstract

A study has been made into the average shape of large crests and troughs during several storms using wave elevation data from the WACSIS measurement program. The analysis techniques adopted were data-driven at all times, in order to test whether second-order wave theory could reproduce important features in the field data. The sea surface displayed obvious nonlinear behavior, reflected in the fact that the shapes of crests were always sharper and larger than their trough equivalents. Assuming that the dominant nonlinear correction is second order in the wave steepness (but without a knowledge of the detailed form of second-order theory), the average shapes of maxima in the underlying linear wave components were shown to match NewWave. This NewWave is the scaled auto-correlation function for a linear random process with the same power spectrum as the measured waves. Thus, NewWave was shown to be an acceptable model for the linear part of large waves on intermediate water depth (here ∼17 m). Assuming that NewWave is a good model for the linear part of large crests and troughs, a value for the second-order coefficient required to estimate crest elevation statistics was derived from the measured data for several storms. This coefficient was in good agreement with the results of the second-order random simulations of Forristall and Prevosto [1]. As well as studying vertical asymmetry, required for crest and trough statistics, horizontal asymmetry was examined using the Hilbert transform. Compared to a large amount of vertical asymmetry, the analysis showed that there was virtually no horizontal asymmetry for the bulk of the waves in the records. However, there is a very small degree of horizontal asymmetry exhibited in the largest waves in the records. Thus, given a surface elevation record, it is difficult to distinguish the direction of the time axis, again consistent with most of the nonlinearity being due to simple second-order bound waves.