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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. 

The momentum and energy exchanges at the ocean surface are central factors determining the sea state, weather patterns and climate. To investigate the effects of surface waves on the air–sea energy exchanges, we analyse high-resolution laboratory measurements of the airflow velocity acquired above wind-generated surface waves using the particle image velocimetry technique. The velocity fields were further decomposed into the mean, wave-coherent and turbulent components, and the corresponding energy budgets were explored in detail. We specifically focused on the terms of the budget equations that represent turbulence production, wave production and wave–turbulence interactions. Over wind waves, the turbulent kinetic energy (TKE) production is positive at all heights with a sharp peak near the interface, indicating the transfer of energy from the mean shear to the turbulence. Away from the surface, however, the TKE production approaches zero. Similarly, the wave kinetic energy (WKE) production is positive in the lower portion of the wave boundary layer (WBL), representing the transfer of energy from the mean flow to the wave-coherent field. In the upper part of the WBL, WKE production becomes slightly negative, wherein the energy is transferred from the wave perturbation to the mean flow. The viscous and Stokes sublayer heights emerge as natural vertical scales for the TKE and WKE production terms, respectively. The interactions between the wave and turbulence perturbations show an energy transfer from the wave to the turbulence in the bulk of the WBL and from the turbulence to the wave in a thin layer near the interface. 

Reliable estimates of the fluxes of momentum, heat and moisture at the air–sea interface are essential for accurate long-term climate projections, as well as the prediction of short-term weather events such as tropical cyclones. In recent years, it has been suggested that these estimates need to incorporate an accurate description of the transport of sea spray within the atmospheric boundary layer and the drop-induced fluxes of momentum, heat and moisture, so that the resulting effects on atmospheric flow can be evaluated. In this paper we propose a model based on a theoretical and mathematical framework inspired from kinetic gas theory. This approach reconciles the Lagrangian nature of spray transport with the Eulerian description of the atmosphere. In turn, this enables a relatively straightforward inclusion of the spray fluxes and the resulting spray effects on the atmospheric flow. A comprehensive dimensional analysis has led us to identify the spray effects that are most likely to influence the speed, temperature and moisture of the airflow. We also provide an example application to illustrate the capabilities of the model in specific environmental conditions. Finally, suggestions for future work are offered. 

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. 

Abstract We experimentally investigate the depth distributions and dynamics of air bubbles entrained by breaking waves in a wind‐wave channel over a range of breaking wave conditions using high‐resolution imaging and three‐dimensional bubble tracking. Below the wave troughs, the bubble concentration decays exponentially with depth. Patches of entrained bubbles are identified for each breaking wave, and statistics describing the horizontal and vertical transport are presented. Aggregating our results, we find a stream‐wise transport faster than the associated Stokes drift and modified Stokes drift for buoyant particles, which is an effect not accounted for in current models of bubble transport. This enhancement in transport is attributed to the flow field induced by the breaking waves and is relevant for the transport of bubbles, oil droplets, and microplastics at the ocean surface.