Evolution of kurtosis for wind waves

Abstract

Long-term evolution of random wind waves is studied by direct numerical simulation within the framework of the Zakharov equation. The emphasis is on kurtosis as a single characteristics of field departure from Gaussianity. For generic wave fields generated by a steady or changing wind, kurtosis is found to be almost entirely due to bound harmonics. This observation enables one to predict the departure of evolving wave fields from Gaussianity, capitalizing on the already existing capability of wave speptra forecasting. Kurtosis rapidly adjusts to a sharp increase of wind and slowly decreases after a drop of wind. Typically kurtosis is in the range 0.1-0.3, which implies a tangible increase of freak wave probability compared to the Rayleigh distribution. Evolution of narrow-banded fields is qualitatively different from the generic case of wind waves: statistics is essentially non-Gaussian, which confirms that in this special case the standard kinetic equation paradigm is inapplicable. Copyright 2009 by the American Geophysical Union.