New kinetic equations and their modelling for wind wave forecasting.

Wind waves are a key link in the feedback loop of ocean/atmosphere interaction. The quality of wind wave modelling directly affects the quality of weather forecasting and the accuracy of description of all processes at the air/water interface, since waves control fluxes of momentum, gas and heat exchange. Better wind wave modelling, especially of 'rogue' waves, is literally vital for reliability of growing shipping and offshore activities. At present all wave forecasting and modelling is based on numerical integration of the kinetic equation (KE), which is also referred to as the Hasselmann equation. The equation takes into account wind input, dissipation and interaction between waves of different scales and directions and describes the slow evolution of wind wave spectra in time and space. The interaction term, usually denoted as Snl, is dominant for energy carrying waves. The expression for Snl has not changed for half a century. Now the improved quality of observations and data input for wave modelling made it impossible to ignore the situations where the discrepancy between the KE based models and observations could not be bridged by any means. The following fundamental shortcomings of the modelling based upon the existing kinetic equation became apparent: (i) By construction, the KE cannot describe reaction of wave fields to rapid perturbations (e.g. abrupt changes of wind, wind gusts, sharp boundaries, etc). (ii) The KE based models can predict evolution of wave spectra only, while it is highly desirable to model the evolution of the wave height probability density function, or, more precisely, its departure from the Gaussian distribution. This, in particular, is badly needed for forecasting rogue waves, but also for assessing the validity of the KE based models. The KE itself 'does not know' when it ceases to be applicable. To address these shortcomings, the following radical ideas have been put forward very recently by the authors. New generalised kinetic equations have been derived from first principles by lifting two most restrictive assumptions: proximity of the wave field to equilibrium, and the oversimplification in taking into account the wave field departure from Gaussianity. Crucially, it was also discovered by the authors that for a typical wind waves it is possible to reconstruct evolution of probability density function once the spectrum is found. The proposal aims at creating a new numerical and conceptual framework for the study of wind wave evolution, by elaborating the above ideas and developing a new way of wind wave modelling based on the novel expression for Snl, derived from first principles. The purpose of this proposal is to create a numerical tool (robust parallel code) for solving the new kinetic equations and then to use this tool to address outstanding questions of wave field evolution. In developing the code, we will be greatly helped by the direct numerical simulation (DNS) algorithm developed by the authors for the simulation of long time evolution of wave field. The algorithm will be used for the validation of the new code. With the help of the new tool, we will delineate the situations where the standard KE is indeed valid and where it ceases to be applicable, and will investigate the regimes of wave evolution well beyond the limits of its applicability (e.g. gusty wind). We will model the evolution of wave field departure from Gaussianity, which, in particular, will make possible to assess probability of freak waves. We will formulate 'practical' parameterisations and recommendations for wave forecasting. This project aims to revolutionise wind wave modelling and forecasting. The new approach we propose is better suited to parallelisation of simulations and increase of power of computers, eventually it will replace the existing algorithms of calculating Snl. It will produce not only a more accurate description of reality, it has the potential to do it faster.