Abstract
Abstract. This paper concerns the description and the predictability of a freak event when at a certain position information in the form of a time signal is given. The prediction will use the phase information for an estimate of the position and time of the occurrence of a large wave, and to predict the measure of phase coherence at the estimated focussing position. The coherence and the spectrum will determine an estimate for the amplitude. After adjusting for second order nonlinear effects, together this then provides an estimate of the form of a possible freak wave in the time signal, which will be described by a pseudo-maximal signal. In the exceptional case of a fully coherent signal, it can be described well by a so-called maximal signal. We give four cases of freak waves for which we compare results of predictions with available measured (and simulated) results by nonlinear AB-equation (van Groesen and Andonowati, 2007; van Groesen et al., 2010). The first case deals with dispersive focussing, for which all phases are (designed to be) very coherent at position and time of focussing; this wave is nearly a maximal wave. The second case is the Draupner wave, for which the signal turns out to be recorded very close to its maximal wave height. It is less coherent but can be described in a good approximation as a pseudo-maximal wave. The last two cases are irregular waves which were measured at MARIN (Maritime Research Institute Netherlands); in a time trace of more than 1000 waves freak-like waves appeared "accidentally". Although the highest wave is less coherent than the other two cases, this maximal crest can still be approximated by a pseudo-maximal wave.
Highlights
In this paper we consider extreme waves that can “accidentally” appear in irregular, uni-directional wave fields with very broad spectrum and relatively low value of the Benjamin-Feir index (BFI)
The four study cases, for which measurements are available to test our descriptions and predictions of appearance of freak waves, are a dispersive focussing wave in a wave tank, MARIN experiment 202002, the Draupner wave with elevation measurement obtained from Sverre Haver of Statoil, and two irregular waves of Jonswap type, which were measured at MARIN but scaled (1 : 50 in space) to geophysical dimensions
For the Draupner wave and the irregular waves we provide the significant wave height and the Benjamin Feir index BFI as calculated at Xfoc
Summary
In this paper we consider extreme waves that can “accidentally” appear in irregular, uni-directional wave fields with very broad spectrum and relatively low value of the Benjamin-Feir index (BFI). Instead of nonlinearly dominated waves, the extreme waves here will appear at position and time of a high degree of coherence, in the sense that many wave components contribute to a linearly dominated constructive interference phenomenon. In this paper we will characterize and discuss in various ways the appearance of extreme events and the role played by coherence as a constructive interference property By this is meant that the phase nearly vanishes for waves in a considerable interval around the peak frequency. The nonlinear effects on the maximal wave are small, and just as well for the irregular wave, except for some different propagation speed In line with these observations, we formulate in Sect.
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