Modelling Transient Sea States with the Generalised Kinetic Equation
For historical and technical reasons evolution of random weakly nonlinear wave fields so far has been studied primarily in a quasi-stationary environment, where the main modelling tool is the kinetic equation. In the context of oceanic waves sharp changes of wind do occur quite often and can generate transient sea states with characteristic timescales of up to hundreds of wave periods. It is of great fundamental and practical interest to understand wave field behaviour during short-lived and transient events. At present nothing is known about such ephemeral sea states. One, but not the only, reason was that there were no adequate modelling tools. The generalised kinetic equation (gKE) derived without assumptions of quasi-stationarity seems to fill this gap. Here we study transient events with the gKE aiming to understand what is going during such events and capabilities of the gKE in capturing them. We find how wave spectra evolve being subjected to sharp changes of wind, while tracing in parallel the concomitant evolution of higher moments characterizing the field departure from gaussianity. We demonstrated the capability of the gKE to capture short-lived events, in particular, we found sharp brief increase of kurtosis during squalls, which suggests significant increase of the likelihood of freak waves during such events. Although the study was focussed upon wind wave context the approach is generic and is transferrable to random weakly nonlinear wave fields of other nature.
The work was made possible thanks to the UK NERC grant NE/M016269/1. It was also supported by EU FP7 612610. The access to the ECMWF supercomputing facility (special project SPGBVSSA) is gratefully acknowledged. We are grateful to G. van Vledder for providing his code for the Hasselmann equation.
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