We use direct numerical simulation of stress-driven turbulent Couette flows over waving surfaces to study turbulence in the vicinity of water waves. Mechanistic study is performed through systematic investigation of different wavy surface conditions including plane progressive Airy and Stokes waves with and without wind-induced surface drift, as well as stationary wavy walls and vertically waving walls for comparison. Two different wave steepness valuesak= 0.1 and 0.25 are considered, whereais the wave amplitude andkis the wavenumber. For effects of wave age, defined as the ratio between the wave phase speedcand the turbulence friction velocityu_*, we consider three values, namelyc/u_*= 2, 14 and 25, corresponding to slow, intermediate and fast waves, respectively. Detailed analysis of turbulence structure and statistics shows their dependence on the above-mentioned parameters. Our result agrees with previous measurement and simulation results and reveals many new features unreported in the literature. Over progressive waves, although no apparent flow separation is found in mean flow, considerable intermittent separations in instantaneous flow are detected in slow waves with large steepness. The near-surface coherent vortical structures are examined. We propose two conceptual vortex structure models: quasi-streamwise and reversed horseshoe vortices for slow waves and bent quasi-streamwise vortices for intermediate and fast waves. Detailed examination of Reynolds stress with quadrant analysis, turbulent kinetic energy (TKE) and TKE budget with a focus on production shows large variation with wave phase; analysis shows that the variation is highly dependent on wave age and wave nonlinearity. Comparison between Airy waves and Stokes waves indicates that although the nonlinearity of surface water waves is a high-order effect compared with the wave age and wave steepness, it still makes an appreciable difference to the turbulence structure. The effect of wave nonlinearity on surface pressure distribution causes substantial difference in the wave growth rate. Wind-induced surface drift can cause a phase shift in the downstream direction and a reduction in turbulence intensity; this effect is appreciable for slow waves but negligible for intermediate and fast waves. In addition to providing detailed information on the turbulence field in the vicinity of wave surfaces, the results obtained in this study suggest the importance of including wave dynamics in the study of wind–wave interaction.

A hybrid numerical capability is developed for the simulation of offshore wind farms, in which large-eddy simulation is performed for the wind turbulence, and a potential flow based method is used for the simulation of the ocean wave field. The wind and wave simulations are dynamically coupled. The effect of wind turbines on the wind field is represented by an actuator disk model. This study focuses on the effect of wind-seas, and the turbine motion is treated as negligibly small. A variety of fully-developed and fetch-limited wind-sea conditions and turbine spacings are considered in the study. Statistical analyses are performed for the simulation results, with a focus on the mean wind profile, kinetic energy budget in the wind field, and the wind turbine power extraction rate. The results indicate that the waves have appreciable effect on the wind farm performance. The wind turbines obtain a higher wind power extraction rate under the fully developed wind-sea condition compared with that under the fetch-limited condition. This higher extraction rate is caused by the faster propagating waves and the lower sea-surface resistance on the wind when the wind-seas are fully developed. The wave-induced difference can be as high as 8% with the commonly used turbine spacing in commercial land-based wind farms, s_x = 7 (with s_x being the ratio of streamwise turbine spacing to the turbine diameter). Such level of difference is noteworthy considering the previous understanding that direct wave-induced disturbance to the wind field decays exponentially away from wave surface.

Wind blowing over the ocean surface can be treated as a turbulent boundary layer over a multiscale rough surface with moving roughness elements, the waves. Large-eddy simulation (LES) of such flows is challenging because LES resolves wind–wave interactions only down to the grid scale, $\Delta $ , while the effects of subgrid-scale (SGS) waves on the wind need to be modelled. Usually, a surface-layer model based on the law of the wall is used; but the surface roughness has been known to depend on the local wind and wave conditions and is difficult to parameterize. In this study, a dynamic model for the SGS sea-surface roughness is developed, with the roughness corresponding to the SGS waves expressed as ${\alpha }_{w} \hspace{0.167em} { \sigma }_{\eta }^{\Delta } $ . Here, ${ \sigma }_{\eta }^{\Delta } $ is the effective amplitude of the SGS waves, modelled as a weighted integral of the SGS wave spectrum based on the geometric and kinematic properties of the waves for which five candidate expressions are examined. Moreover, ${\alpha }_{w} $ is an unknown dimensionless model coefficient determined dynamically based on the first-principles constraint that the total surface drag force or average surface stress must be independent of the LES filter scale $\Delta $ . The feasibility and consistency of the dynamic sea-surface roughness models are assessed bya prioritests using data from high-resolution LES with near-surface resolution, appropriately filtered. Also, these data are used fora posterioritests of the dynamic sea-surface roughness models in LES with near-surface modelling. It is found that the dynamic modelling approach can successfully capture the effects of SGS waves on the wind turbulence withoutad hocprescription of the model parameter ${\alpha }_{w} $ . Also, for ${ \sigma }_{\eta }^{\Delta } $ , a model based on the kinematics of wind–wave relative motion achieves the best performance among the five candidate models.

Characteristics of laboratory-scale bubble-driven buoyant plumes in a stably stratified quiescent fluid are studied using large-eddy simulation (LES). As a bubble plume entrains stratified ambient water, its net buoyancy decreases due to the increasing density difference between the entrained and ambient fluids. A large fraction of the entrained fluid eventually detrains and falls along an annular outer plume from a height of maximum rise (peel height) to a neutral buoyancy level (trap height), during which less buoyant scalars (e.g. small droplets) are trapped and dispersed horizontally, forming quasi-horizontal intrusion layers. The inner/outer double-plume structure and the peel/intrusion process are found to be more distinct for cases with small bubble rise velocity, while weak and unstable when the slip velocity is large. LES results are averaged to generate distributions of mean velocity and turbulent fluxes. These distributions provide data for assessing the performance of previously developed closures used in one-dimensional integral plume models. In particular, the various LES cases considered in this study yield consistent behaviour for the entrainment coefficients for various plume cases. Furthermore, a new continuous peeling model is derived based on the insights obtained from LES results. Comparing to previous peeling models, the new model behaves in a more self-consistent manner, and it is expected to provide more reliable performance when applied in integral plume models.

Vortical structures in turbulence over progressive surface waves are studied using the data from direct numerical simulation of a stress-driven turbulent Couette flow above a waving surface. Instantaneous flow field and its evolution, vorticity statistics, and conditionally averaged flow field with various sampling methods are examined. Unique vortical structures are identified, which are found to be strongly dependent on the wave motion. For a slow wave (with a small value of wave age $c/u_{\ast }=2$ ; here $c$ is the phase speed of the wave and $u_{\ast }$ is the friction velocity), the vortical structures are characterized by reversed horseshoe vortices and quasistreamwise vortices. The former is concentrated above the wave trough and is associated with sweep events there; the latter has high intensity over the windward face of the wave and is associated with ejection events. Relative to the waveform, the coherent vortical structures propagate in the downstream direction. Vortex turning and vortex stretching play an important role in the vortex transformation and evolution processes. For an intermediate wave $\left(c/u_{\ast }=14\right)$ and a fast wave $\left(c/u_{\ast }=25\right)$ , the dominant vortical structure is bent quasistreamwise vortices, which are predominantly horizontal but have a distinctive downward bending in their upstream ends near the wave trough. The vortices are found to propagate in the upstream direction with respect to the waveform. The above-wave coherent vortices identified in this study are found to play an important role in the turbulent transport process.