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In order to improve the predictive abilities of weather and climate models, it is essential to understand the behaviour of wind stress at the ocean surface. Wind stress is contingent on small-scale interfacial dynamics typically not directly resolved in numerical models. Although skin friction contributes considerably to the total stress up to moderate wind speeds, it is notoriously challenging to measure and predict using physics-based approaches. This work proposes a supervised machine learning (ML) model that estimates the spatial distribution of the skin-friction drag over wind waves using solely wave elevation and wave age, which are relatively easy to acquire. The input–output pairs are high-resolution wave profiles and their corresponding surface viscous stresses collected from laboratory experiments. The ML model is built upon a convolutional neural network architecture that incorporates the Mish nonlinearity as its activation function. Results show that the model can accurately predict the overall distribution of viscous stresses; it captures the peak of viscous stress at/near the crest and its dramatic drop to almost null just past the crest in cases of intermittent airflow separation. The predicted area-aggregate skin friction is also in excellent agreement with the corresponding measurements. The proposed method offers a practical pathway for estimating both local and area-aggregate skin friction and can be easily integrated into existing numerical models for the study of air–sea interactions. 

A light breeze rising over calm water initiates an intricate chain of events that culminates in a centimetres-deep turbulent shear layer capped by gravity–capillary ripples. At first, viscous stress accelerates a laminar wind-drift layer until small surface ripples appear. The surface ripples then catalyse the growth of a second instability in the wind-drift layer, which eventually sharpens into along-wind jets and downwelling plumes, before devolving into three-dimensional turbulence. In this paper, we compare laboratory experiments with simplified, wave-averaged numerical simulations of wind-drift layer evolution beneath monochromatic, constant-amplitude surface ripples seeded with random initial perturbations. Despite their simplicity, our simulations reproduce many aspects of the laboratory-based observations – including the growth, nonlinear development and turbulent breakdown the wave-catalysed instability – generally validating our wave-averaged model. But we also find that the simulated development of the wind-drift layer is disturbingly sensitive to the amplitude of the prescribed surface wave field, such that agreement is achieved through suspiciously careful tuning of the ripple amplitude. As a result of this sensitivity, we conclude that wave-averaged models should really describe the coupled evolution of the surface waves together with the flow beneath to be regarded as truly ‘predictive’. 

The paper is devoted to two-phase flow simulations and investigates the ability of a diffusive interface Cahn–Hilliard volume-of-fluid model to capture the dynamics of the air–sea interface at geophysically relevant Reynolds numbers. It employs a hybrid filtered/averaging improved detached eddy simulation method to model turbulence and utilizes a continuum model to account for surface tension if the diffuse interface is under-resolved by the grid. A numerical wind-wave tank is introduced, and results obtained for two known wind-wave conditions are analyzed in comparison to experimental data at matched Reynolds numbers. The focus of the comparison is on both time-averaged and wave-coherent quantities, and includes pressure, velocity as well as modeled and resolved Reynolds stresses. In general, numerical predictions agree well with the experimental measurements and reproduce many wave-dependent flow features. Reynolds stresses near the water surface are found to be especially important in modulating the critical layer height. It is concluded that the diffusive interface approach proves to be a promising method for future studies of air–sea interface dynamics in geophysically relevant flows. 

Highly resolved laboratory measurements of the airflow over wind-generated waves are examined using a novel wave growth diagnostic that quantifies the presence of Miles’ critical layer mechanism of wind-wave growth. The wave growth diagnostic is formulated based on a linear stability analysis, and results in growth rates that agree well with those found by a pressure reconstruction method as well as other, less direct, methods. This finding, combined with a close agreement between the airflow measurements and the predictions of linear stability (critical layer) theory, demonstrate that the Miles’ critical layer mechanism can cause significant wave growth in young (wave age $$c/u_* = 6.3$$ , where $$c$$ is the wave phase speed, and $$u_*$$ the friction velocity) wind-forced waves. 

Abstract The quantification of pressure fields in the airflow over water waves is fundamental for understanding the coupling of the atmosphere and the ocean. The relationship between the pressure field, and the water surface slope and velocity, are crucial in setting the fluxes of momentum and energy. However, quantifying these fluxes is hampered by difficulties in measuring pressure fields at the wavy air-water interface. Here we utilise results from laboratory experiments of wind-driven surface waves. The data consist of particle image velocimetry of the airflow combined with laser-induced fluorescence of the water surface. These data were then used to develop a pressure field reconstruction technique based on solving a pressure Poisson equation in the airflow above water waves. The results allow for independent quantification of both the viscous stress and pressure-induced form drag components of the momentum flux. Comparison of these with an independent bulk estimate of the total momentum flux (based on law-of-the-wall theory) shows that the momentum budget is closed to within approximately 5%. In the partitioning of the momentum flux between viscous and pressure drag components, we find a greater influence of form drag at high wind speeds and wave slopes. An analysis of the various approximations and assumptions made in the pressure reconstruction, along with the corresponding sources of error, is also presented.