Freak Waves: Rare Realizations of a Typical Population Or Typical Realizations of a Rare Population?

The possible existence of freak waves is discussed. Our aim is not to present a final answer to the question raised in the paper rifle, but rather present some few evidences which, although not scientifically documented, seem to support the idea of a separate freak wave population. Extremes to be expected within a second order model for the surface elevation will be presented. Based on this, a possible definition of freak waves is suggested. A number of references discussing observations of giant waves are briefly reviewed and commented upon in view of the selected freak wave criterion. As a follow up to the observaflons of giant waves, the paper is briefly discussing some ongoing research on the possible modeling of such events. INTRODUCTION A number of incidents of reported damages to ships and offshore platforms suggest the existence of unexpectedly large waves. Such waves are often referred to as freak waves, abnormal waves, or the "one from nowhere", indicating that observers over the years have considered these events as something beyond the extreme waves typically experienced by marine structures. Are such waves extremely rare realizations of a typical, slightly non-Gaussian population? or Are they typical realizations from a rare strongly non-Gaussian population? If the first question can be answered by "yes", then these waves are in principle accounted for by the present design practice, providing that this practice properly accounts for the typical but slight deviation from the Gaussian assumption regarding the surface process. If, on the other hand, a thorough assessment concludes that the observed giant waves most likely are realizations from a very non-Gaussian surface process, emphasis has to be given to the physical mechanisms that are governing these events. This will include a search for onset mechanisms which over a limited time and space can bring a slightly non-Gaussian surface field into an extremely non-Gaussian surface field possibly involving giant waves. Our expectations are that they will be clearly pronounced only for a rather limited time and space. The closing part of this basic work will be to correlate the possible onset mechanisms to the environmental characteristics adopted for engineering purposes. The kinematics to be associated with a freak wave are needed in order to estimate the structural loading. For a discussion of this, reference is made to e.g. TCrum and Gudmestad (1990). Since we think the phenomenon of freak waves is a rather rare one, a statistical method in combination with available data is not the right way to go. This of course is under the assumption that the physics governing possible freak waves differ from the physics governing the typical pattern. We think that there is some reason to believe that this is the case. In order to establish a proper statistical model for the freak wave characteristics, the model needs to be anchored in the underlying physics. It is therefore recommended that emphasis is given to solving the hydrodynamic equations in time and space allowing the process to behave non-stationary, i.e. realizing that the freak wave phenomenon is of a transient nature. It is important to stress, however, that the existence of such a separate "freak wave population" is far from proved. Robin and Olagnon(199t) have carried out a thorough analysis of wave data from the Frigg field in the North Sea. About 11000 wave records with nearly 2 million individual waves are analyzed. Their conclusion is that the observed extremes, wave heights as well as crest heights, are well within what should be expected when accounting properly for the inherent randomness of the extremes. PROBABILISTIC DESCRIPTION OF SURFACE WAVES Gaussian Model A linear stochastic model for the ocean surface process being in agreement with the linearized hydrodynamic equations is given by, see e.g. Jha(1997): N Re[k~l Bk exp(iogkt)] (1) El (I) =k__~l Ak COS(COk t + Ok) = Re [ ] indicates the real part of a complex number, and Bk = Ak exp(i0k) are the complex Fourier amplitudes. Furthermore, A t and Ok are Rayleigh distributed and uniformly distributed, respectively. The mean square of Ak is related to the underlying wave spectrum, s_=(m), through: