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 velocity prediction for wall-bounded turbulence is useful for constructing a wall model and estimating dissipation and wall shear stress. A convolutional neural network is developed to improve the near-wall velocity prediction and spatial resolution for wall-bounded turbulent velocity fields obtained using particle image velocimetry (PIV). To establish the relationship between the low-resolution and high-resolution fields, this machine learning model is trained on a synthetic PIV dataset generated based on velocity fields obtained from the direct numerical simulation of turbulent channel flows at Re_τ = 1000. Using a test dataset with a higher Reynolds number of Re_τ = 5200, the performance of this model is assessed in terms of instantaneous fields, error analysis, velocity statistics, and energy spectra. The influences of the interrogation window, image resolution, and particle concentration on the performance of this network are also considered. We further apply this network to practical PIV data from a turbulent boundary layer at Re_τ = 2200 to assess the network performance under real experimental conditions. The results indicate that the proposed machine-learning-based model can predict missing near-wall velocity fields and enhance the spatial resolution of PIV fields, but the accuracy for Reynolds shear stress prediction needs to be further improved. The presented approach shows the potential ability to predict the near-wall instantaneous velocity of high-Reynolds-number turbulence from low-Reynolds-number flow fields.

Direct numerical simulations (DNS) of turbulent channel flows up to ${Re}_{\tau} \approx 1000$ are conducted to investigate the three-dimensional (consisting of streamwise wavenumber, spanwise wavenumber and frequency) spectrum of wall pressure fluctuations. To develop a predictive model of the wavenumber–frequency spectrum from the wavenumber spectrum, the time decorrelation mechanisms of wall pressure fluctuations are investigated. It is discovered that the energy-containing part of the wavenumber–frequency spectrum of wall pressure fluctuations can be well predicted using a similar random sweeping model for streamwise velocity fluctuations. To refine the investigation, we further decompose the spectrum of the total wall pressure fluctuations into the autospectra of rapid and slow pressure fluctuations, and the cross-spectrum between them. We focus on evaluating the assumption applied in many predictive models, that is, the magnitude of the cross-spectrum is negligibly small. The present DNS shows that neglecting the cross-spectrum causes a maximum error up to 4.7 dB in the subconvective region for all Reynolds numbers under test. Our analyses indicate that the approximation of neglecting the cross-spectrum needs to be applied carefully in the investigations of acoustics at low Mach numbers, in which the subconvective components of wall pressure fluctuations make important contributions to the radiated acoustic power.

In this paper, highly disturbed turbulent flows confined within a square duct with uniformly spaced V-shaped ribs mounted on one wall are investigated using large-eddy simulation (LES). Two V-shaped ($60^{°}$ and $45^{°}$ ) rib cases are studied in comparison with the perpendicular ($90^{°}$ ) rib case. The LES results are validated against a set of water-channel measurement data newly acquired by the authors. The effects of different shaped ribs on turbulent flow are systematically studied in terms of the mean velocity field, turbulence statistics, and coherent structures. The results show that strong secondary flows in the pattern of a pair of large symmetrical streamwise-elongated vortices exist in all three rib cases. The impacts of rib geometry on turbulent coherent structures are investigated using vortex identifiers, temporal autocorrections, spatial two-point autocorrelations, and velocity spectra.