Modelling wind waves. What lies beyond the significant wave height?

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Modelling random wind waves in the ocean is a fundamental problem with wide ranging applications of great significance. Proper wave modelling is crucial for navigation, fisheries, offshore industries, managing of coastal environments; on the other hand, being integrated into the weather and climate models it is fundamental for air-sea interaction. Crucially, all the ocean remote sensing in various bands of electromagnetic spectrum (including the satellite, airborne, on-shore and ship based devices) relies on knowledge of wind wave field characteristics. Improving this knowledge would increase remote sensing capabilities.Currently, all wave modelling is based on the Hasselmann kinetic equation, aka KE, and its modifications. Wind waves are random, and the KE describes evolution of ensemble averaged quantities caused by energy exchange between waves of different scales and directions owing to nonlinear resonant interactions, as well as energy input from wind and dissipation. The part concerned with the redistribution of energy between spectral components, S_nl, was considered to be firmly established for many decades, since it was derived from first principles in the same way as in other branches of physics.The overall situation in wave modelling cannot be considered satisfactory. Although the KE does capture the behaviour of bulk characteristics (peak frequency, significant wave height) there are unexplained major systematic discrepancies between the KE modelling and the high quality observations: the observed spectra are much wider and the magnitude of the spectral peak could be considerably smaller.The essence and main novelty of the project is in applying original direct numerical simulations algorithm (DNS-ZE) to analyse high quality data: unique observations off the Mexican coast by Romero & Melville (the Tehuantepec experiment) and data from observations by D.Hauser obtained using airborne and satellite scatterometers (KuROS and SWIM of CFOSAT). The DNS-ZE is an algorithm based on integration of a weakly nonlinear reduction of the Euler equations in nonlinear canonical variables. Currently it is the only DNS code able to perform simulations of wave evolution over several hundred kilometers. The simulations with the DNS-ZE showed excellent agreement with the observations and major discrepancies with the KE predictions.The proposal aims to utilise the unique opportunities opened by synergy of the DNS-ZE algorithm and new high quality datasets (revisited Tehuantepec observations and processed KuROS and SWIM data) and to address the following key problems:(i) To show that for various wave evolution scenarios supported by high quality data, the DNS-ZE indeed faithfully captures the evolution.(ii) To retrieve the source functions (wind input and dissipation) for various steady wind conditions.(iii) To quantify how wrong are the KE based predictions, to examine the specific implications sensitive to the shape of the spectra, e.g. for evolution of probability of freak waves, wave induced mixing in the upper ocean.(iv) To advance in finding the cause of the KE failure.The realisation of this project would change radically the present understanding of the accuracy of wave modelling and the serious limitations of the existing models. Advance in finding the cause of the KE failure would be a breakthrough in understanding of not only wind waves, but all kind of random nonlinear waves in fluids and plasmas.