Nonlinear interactions between sea waves and the sea bottom are a major mechanism for energy transfer between the different wave frequencies in the near-shore region. Nevertheless, it is difficult to account for this phenomenon in stochastic wave forecasting models due to its mathematical complexity, which mostly consists of computing either the bispectral evolution or non-local shoaling coefficients. In this work, quasi-two-dimensional stochastic energy evolution equations are derived for dispersive water waves up to quadratic nonlinearity. The bispectral evolution equations are formulated using stochastic closure. They are solved analytically and substituted into the energy evolution equations to construct a stochastic model with non-local shoaling coefficients, which includes nonlinear dissipative effects and slow time evolution. The nonlinear shoaling mechanism is investigated and shown to present two different behaviour types. The first consists of a rapidly oscillating behaviour transferring energy back and forth between wave harmonics in deep water.Owing to the contribution of bottom components for closing the class III Bragg resonance conditions, this behaviour includes mean energy transfer when waves reach intermediate water depths. The second behaviour relates to one-dimensional shoaling effects in shallow water depths. In contrast to the behaviour in intermediate water depths, it is shown that the nonlinear shoaling coefficients refrain from their oscillatory nature while presenting an exponential energy transfer. This is explained through the one-dimensional satisfaction of the Bragg resonance conditions by wave triads due to the non-dispersive propagation in this region even without depth changes. The energy evolution model is localized using a matching approach to account for both these behaviour types. The model is evaluated with respect to deterministic ensembles, field measurements and laboratory experiments while performing well in modelling monochromatic superharmonic self-interactions and infra-gravity wave generation from bichromatic waves and a realistic wave spectrum evolution. This lays physical and mathematical grounds for the validity of unexplained simplifications in former works and the capability to construct a formulation that consistently accounts for nonlinear energy transfers from deep to shallow water.

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Ocean submesoscale currents, with spatial scales on the order of 0.1 to 10 km, are horizontally divergent flows, leading to vertical motions that are crucial for modulating the fluxes of mass, momentum and energy between the ocean and the atmosphere, with important implications for biological and chemical processes. Recently, there has been considerable interest in the role of surface waves in modifying frontal dynamics. However, there is a crucial lack of observations of these processes, which are needed to constrain and guide theoretical and numerical models. To this end, we present novel high resolution airborne remote sensing and in situ observations of wave-current interaction at a submesoscale front near the island of O’ahu, Hawaii. We find strong modulation of the surface wave field across the frontal boundary, including enhanced wave breaking, that leads to significant spatial inhomogeneities in the wave and wave breaking statistics. The non-breaking (i.e. Stokes) and breaking induced drifts are shown to be increased at the boundary by approximately 50% and an order of magnitude, respectively. The momentum flux from the wave field to the water column due to wave breaking is enhanced by an order of magnitude at the front. Using an orthogonal coordinate system that is tangent and normal to the front, we show that these sharp modulations occur over a distance of several meters in the direction normal to the front. Finally, we discuss these observations in the context of improved coupled models of air-sea interaction at a submesoscale front.

Through the analysis of propagation times of infragravity wave packets along ray paths, reanalysis data, and our field measurements in the East Mediterranean, we find evidence of deep water infragravity wave generation by offshore storms. We confirmed the results also using deep water pressure cell measurements in the Pacific. The known nearshore generation mechanism showed large discrepancies with the observed infragravity energy near Aogashima, Japan, during winter. A new model of deep water infragravity wave generation is developed, based on nonlinear interactions of wind wave triads with submesoscale wind oscillations. The observed underprediction of infragravity waves is resolved using this new gustiness‐based model. The new source term is found to be of importance during strong storms in the open ocean and underlines the importance of accounting for submesoscale wind oscillations in wind wave models.