Groups of Ocean Waves: Linear Theory, Approximations to Linear Theory, and Observations

Abstract
Statistics of wave groups observed for a wide range of wave heights, power‐spectral shapes, and water depths are compared to the statistics predicted by both direct numerical simulation and analytic approximation of linear wave theory. Comparisons to numerical simulations show that the observed groups are not inconsistent with linear, Gaussian wave fields with the same spectra as the observations. Differences between ocean observations and linear theory are owing to statistical fluctuations in group statistics estimated with the 2.3‐h‐long data records. One linear analytic model accounts for correlations between two successive waves, and slightly underpredicts the average number of sequential large waves for wave fields with very narrow power spectra. A newly developed extension to Rice better accounts for multiwave correlations, but has only marginally improved accuracy for these data because wave fields with very narrow power spectra rarely occurred. Both approximations overpredict the group lengths for very broad and/ or multipeaked power spectra, but are still useful because the errors are small with commonly occurring spectral shapes. Direct numerical simulations, with computational expense between that of the spectral‐Kimura and extended‐Rice approximations, yield the best predictions of the observed wave group statistics given a power spectrum, and also provide estimates of the statistical fluctuations of group properties about predicted mean values.

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