We study wind turbulence over breaking waves based on direct numerical simulation (DNS) of two-fluid flows. In the DNS, the air and water are simulated as a coherent system, with the interface captured using the coupled level-set and volume-of-fluid method. Because the wave breaking is an unsteady process, we use ensemble averaging over 100 runs to define turbulence statistics. We focus on analysing the turbulence statistics of the airflow over breaking waves. The effects of wave age and wave steepness are investigated. It is found that before wave breaking, the turbulence statistics are largely influenced by the wave age. The vertical gradient of mean streamwise velocity is positive at small and intermediate wave ages, but it becomes negative near the wave surface at large wave age as the pressure force changes from drag to thrust. Furthermore, wave-coherent motions make increasingly important contributions to the momentum flux and kinetic energy of velocity fluctuations (KE-F) as the wave age increases. During the wave breaking process, spilling breakers do not influence the wind field significantly; in contrast, plunging breakers alter the structures of wind turbulence near the wave surface drastically. It is observed from the DNS results that during wave plunging, a high pressure region occurs ahead of the wave front, which further accelerates the wind in the downstream direction. Meanwhile, a large spanwise vortex is generated, which greatly disturbs the airflow around it, resulting in large magnitudes of Reynolds stress and turbulence kinetic energy (TKE) below the wave crest. Above the crest, the magnitude of KE-F is enhanced during wave plunging at small and large wave ages, but at intermediate wave age, the transient enhancement of KE-F is absent. The effect of wave breaking on the magnitude of KE-F is further investigated through the analysis of the KE-F production. It is discovered that at small wave age, the transient enhancement of KE-F is caused by the appearance of a local maximum in the profile of total momentum flux; but at large wave age, it results from the change in the sign of the KE-F production from negative to positive, due to the sign change in the wave-coherent momentum flux. At intermediate wave age, neither of these two processes is present, and the transient growth of KE-F does not take place.

Detecting the turbulent/non-turbulent interface is a challenging topic in turbulence research. In the present study, machine learning methods are used to train detectors for identifying turbulent regions in the flow past a circular cylinder. To ensure that the turbulent/non-turbulent interface is independent of the reference frame of coordinates and is physics-informed, we propose to use invariants of tensors appearing in the transport equations of velocity fluctuations, strain-rate tensor and vortical tensor as the input features to identify the flow state. The training samples are chosen from numerical simulation data at two Reynolds numbers, . The objectivity of the detector is verified by changing the input features and the flow region for choosing the turbulent training samples. Compared with the conventional methods, the proposed method based on machine learning shows its novelty in two aspects. First, no threshold value needs to be specified explicitly by the users. Second, machine learning can treat multiple input variables, which reflect different properties of turbulent flows, including the unsteadiness, vortex stretching and three-dimensionality. Owing to these advantages, XGBoost generates a detector that is more robust than those obtained from conventional methods.

Near-wall streamwise vortices are closely related to the generation of high skin friction in wall-bounded turbulent flows. A common feature of controlled, friction-reduced turbulent flows is weakened near-wall streamwise vortices. In the present study, the streak transient growth (STG) mechanism for generating near-wall streamwise vortices by Schoppa & Hussain (J. Fluid Mech., vol. 453, 2002, pp. 57–108) is employed, and the opposition control proposed by Choi, Moin & Kim (J. Fluid Mech., vol. 262, 1994, pp. 75–110) is imposed during the transient growth process of perturbations to determine how active control affects the generation of quasi-streamwise vortices. In the transient growth stage, when the detection plane is located near the wall ( ${ y}_{d}^{+ } = 15$ ), the control can suppress the production of streamwise vorticity by weakening the near-wall vertical velocity; when the detection plane moves away from the wall ( ${ y}_{d}^{+ } = 28$ ), the control has the opposite effect. In the vortex generation stage, the control cannot change the dominance of the stretching effect. Controls imposed at different stages reveal the importance of the STG stage in vortex generation. Strengthened out-of-phase control and lessened in-phase control are proposed as an extension of the original opposition-control scheme. Application in a fully developed turbulent channel flow shows that strengthened ${ y}_{d}^{+ } = 10$ control can yield an even higher drag reduction rate than the original ${ y}_{d}^{+ } = 15$ control. Moreover, lessened ${ y}_{d}^{+ } = 28$ control can also achieve drag reduction and turbulence suppression.

Direct numerical simulations of turbulent channel flows are performed with opposition control at Re_τ = 180 and 1000. The drag reduction rate at the higher Reynolds number is reduced by 25% compared with that at the lower Reynolds number. In order to investigate the reason for the degradation of the control effectiveness, we examine the response of Reynolds stresses and coherent structures in both the outer and inner regions to the control and the role that large-scale motions play therein. In the outer region, the Reynolds stresses at different length scales are reduced at the same rate as the drag reduction rate, and conditionally averaged large-scale motions with spanwise scale larger than half channel width are still large-scale low-speed streaks flanked by a pair of large-scale counter-rotating streamwise vortices but with reduced velocity amplitudes. In the inner region, the effectiveness of the control in suppressing the turbulence deteriorates at the higher Reynolds number. In response to the superimposition effect of large-scale motions, the contribution to near-wall wall-parallel velocity fluctuations from large-scale motions becomes larger at the higher Reynolds number, while the suppression of large-scale motions by the control is weaker than that of near-wall coherent structures. In both controlled and uncontrolled cases, large-scale motions can modulate the amplitudes of near-wall coherent structures, and the attenuation of streamwise vortices by the control under large-scale high-speed streaks is significantly less effective than that under large-scale low-speed streaks. As a result, the effectiveness of control in suppressing near-wall coherent structures and Reynolds shear stresses becomes weaker at the higher Reynolds number. The quantitative analysis of the contributions to the drag reduction rate from outer and inner regions shows that the effectiveness of the control is mainly determined by the suppression degree of near-wall motions. Furthermore, budgets of streamwise enstrophy are analysed to reveal the interaction of large-scale motions with near-wall streamwise vorticity. The titling effect induced by large-scale motions is positive under large-scale high-speed streaks, but negative under large-scale low-speed streaks, which could be a possible way of large-scale motion to modulate streamwise vorticity. In the controlled cases, the positive titling effect induced by large-scale motions under large-scale high-speed streaks is even enhanced, while other terms in the budgets are reduced, which could explain the degradation of control effectiveness in suppressing near-wall streamwise vortices under large-scale high-speed streaks. Therefore, the loss in the drag reduction rate at the higher Reynolds number is due to the weakened control effectiveness on near-wall coherent structures, which are exposed to the modulation effect of large-scale motions.

An opposition control scheme with strengthened control input is proposed and tested in turbulent channel flows at friction Reynolds number Re_τ = 180 by direct numerical simulations. When the detection plane is located at less than 20 wall units, the drag reduction rate can be greatly enhanced by increasing the control amplitude parameter. The maximum drag reduction rate achieved in the present study is around 33%, which is much higher than the best value of 25% reported in literature. The strengthened control can be more efficient to attain a given drag reduction rate. Based on the total shear stress at the virtual wall established between the real wall and the detection plane by the control, a new friction velocity is proposed and the corresponding coordinate transform is made. Scaled by the proposed friction velocity, the wall-normal velocity fluctuation and the Reynolds shear stress of the controlled flows are collapsed well with those of the uncontrolled flow in the new coordinate. Based on the similarity, a relation between drag reduction rate and the effectiveness of the virtual wall is deduced, which disclosed that the elevation and residual Reynolds shear stress at the virtual wall are the key parameters to determine the drag reduction rate. The conclusion are also validated at Re_τ = 395 and 590. The decrease of the drag reduction rate with the increase of the Reynolds number is attributed to the enhanced residual Reynolds shear stress at the virtual wall.

We perform large-eddy simulation (LES) and theoretical analysis to investigate the effects of opposing waves on overlying turbulent wind. The LES results show that opposing waves induce nearly antisymmetric vertical velocity , and generates a mean wave-coherent stress and the form drag on the wave surface. The wave attenuation rates quantified using the form drag agree with the published experiments.