The shape of large surface waves on the open sea and the Draupner New Year wave

Abstract

Ocean surface waves are both random in time and nonlinear. For a linear random model of the sea surface, the average shape of a large crest is found to be the scaled auto-correlation function, as is shown mathematically by Lindgren [Lindgren G. Some properties of a normal process near a local maximum. Ann Math Stat 1970;41:1870–83] and Boccotti [Boccotti P. Some new results on statistical properties of wind waves. Appl Ocean Res 1983;5:134–40]. Using field data from the North Sea, the applicability of this simple result is discussed. Stokes-type corrections up to fifth order are incorporated in an approximate but robust manner, valid at least locally in space and time. Exact second-order wave theory is used to check the accuracy of the approximate Stokes treatment and to clarify the magnitude and character of the second-order contributions. A giant wave, called the New Year wave, recorded at the Draupner platform in the North Sea at 15:20 on 1st January 1995, is examined. In a sea-state with a significant wave height of approximately 12m, this freak wave, which has a peak elevation of 18.5m above still water level, was unambiguously recorded. The local asymmetries of this wave are removed using the Stokes model, allowing the probability of occurrence of this remarkable event to be estimated, based on the standard Rayleigh distribution for linear crest amplitude. It is concluded that new physics, not incorporated in standard approaches to offshore engineering design, may have played an important role in the generation of this freak wave.