A direct numerical simulation study is conducted to investigate sinusoidal oscillatory flow over a two-dimensional wavy wall. The height and wavelength of the bottom profile, and the period and amplitude of the free-stream oscillation, are selected to mimic a wave-driven boundary layer over vortex ripples on a sandy seabed. Two cases with different Reynolds numbers $(Re)$ are considered, and the higher-$Re$ case achieves a fully developed turbulent state with a wide separation between the energy-containing and dissipative scales. The oscillatory flow is characterized by coherent columnar vortices, which are the main transport agents of turbulent kinetic energy and enstrophy. Two classes of coherent vortices are observed: (i) a primary vortex formed at the lee side of the ripple by flow separation at the crest; (ii) a secondary vortex formed beneath the primary vortex by vortex-induced separation. When the free-stream velocity weakens, these vortices form a counter-rotating vortex dipole and eject themselves over the crest with their mutual induction. Turbulence production peaks twice in a half-cycle; during the formation of the primary vortex and during the ejection of the vortex dipole. The intensity of the former peak remains low in the lower-$Re$ case, as the vortex dipole follows a higher altitude trajectory limiting its interactions with the bottom, and leaving minimal residual turbulence around the ripples for the subsequent half-cycle. Flow snapshots and spectral analysis reveal two dominant three-dimensional features: (i) an energetic vortex mode with a preferred spanwise wavelength close to the ripple wavelength; (ii) streamwise vortical structures in near-wall regions with a relatively shorter spanwise spacing influenced by viscous effects. The vortex mode becomes strong when the cores of the vortices are strained to an elliptical form while moving towards the crest. Following the detachment of the vortices from the ripple, the vortex mode in the higher-$Re$ case breaks down the spanwise coherence of the columnar vortices and decomposes them into intermittent patches of turbulent vortex clusters. The distribution of wall shear stress over the ripple is also analysed in detail. The peak values are observed near the ripple crest around the ejection of the vortex dipole and the maximum free-stream velocity. In the former, both the vortex mode and streamwise vortices have strong footprints on the wall, yielding a bimodal wall-shear-stress spectrum with two distinctive peaks. In the second high-stress regime, decaying coherent vortices impose strong inhomogeneity on the wall shear stress as their wall-attached parts sweep the ripples. These spanwise variations in the wall shear provide insights into the instability of two-dimensional sand ripples.

Recent experiments have revealed the existence of very long streamwise features, denoted as very-large-scale motions (VLSMs), in the thermally neutral atmospheric boundary layer (ABL) (Hutchins et al., Boundary-Layer Meteorol., vol. 145(2), 2012, pp. 273–306). The aim of our study is to elaborate the role of these large-scale anisotropic patterns in wind-energy harvesting with special emphasis on the organization of turbulent fields around wind turbines. To this end, we perform large-eddy simulation (LES) of a turbine row operating under neutral conditions. The ABL data are produced separately in a very long domain of $240\unicode[STIX]{x1D6FF}$, where $\unicode[STIX]{x1D6FF}$ is the ABL thickness, to ensure a realistic representation for very large scales of $O(10\unicode[STIX]{x1D6FF})$. VLSMs are extracted from the LES database using a cutoff at streamwise wavelength $\unicode[STIX]{x1D706}_{x}=5\unicode[STIX]{x1D6FF}$, or $\unicode[STIX]{x1D706}_{x}=50D$ in terms of turbine diameter. Reynolds averaging of low-pass filtered fields shows that the interaction of VLSMs and turbines produce very-long-wavelength motions in the wake region, which contain approximately $20\,\%$ of the resolved Reynolds shear stress, and $30\,\%$ of the resolved streamwise kinetic energy in the shear layers. To further elucidate these statistics, we conduct a geometrical analysis using conditional averaging based on large-scale low- and high-velocity events. The conditional eddies provide evidence for very long (${\sim}10\unicode[STIX]{x1D6FF}$) and wide (${\sim}\unicode[STIX]{x1D6FF}$) streak–roller structures around the turbine row. Although all of these eddies share the same streak–roller topology, there are remarkable modifications in the morphology of the conditional eddies whose cores are located sideways to the turbines. In these cases, the turbine row pushes the whole low- or high-momentum streak aside, and prevails as a sharp boundary to the low–high-momentum streak pair. In this process, accompanying rollers remain relatively unaffected. This creates a two-way flux towards the turbine row. These observations provide some insights about the high lateral spreading observed in the large-scale Reynolds stress fields.

We study the near field of a zero-net-mass-flux (ZNMF) actuated round jet using direct numerical simulations. The Reynolds number of the jet ReD = 2000 and three ZNMF actuators are used, evenly distributed over a circle, and directed towards the main jet. The actuators are triggered in phase, and have a relatively low momentum coefficient of Cμ = 0.0049 each. We study four different control frequencies with Strouhal numbers ranging from StD = 0.165 to StD = 1.32; next to that, also two uncontrolled baseline cases are included in the study. We find that this type of ZNMF actuation leads to strong deformations of the near-field jet region that are very similar to those observed for non-circular jets. At the end of the jet's potential core (x/D = 5), the jet-column cross section is deformed into a hexagram-like geometry that results from strong modifications of the vortex structures. Two mechanisms lead to these modifications, i.e., (i) self-deformation of the jet's primary vortex rings started by distortions in their azimuthal curvature by the actuation, and (ii) production of side jets by the development and subsequent detachment of secondary streamwise vortex pairs. Further downstream (x/D = 10), the jet transforms into a triangular pattern, as the sharp corner regions of the hexagram entrain fluid and spread. We further investigate the global characteristics of the actuated jets. In particular when using the jet preferred frequency, i.e., StD = 0.33, parameters such as entrainment, centerline decay rate, and mean turbulent kinetic energy are significantly increased. Furthermore, high frequency actuation, i.e., StD = 1.32, is found to suppress the mechanisms leading to large scale structure growth and turbulent kinetic energy production. The simulations further include a passive scalar equation, and passive scalar mixing is also quantified and visualized.

The use of active flow control with unsteady means gains increasing interest in engineering designs. The main bottleneck of the methodology is the strong dependence on trial and error to find the right set of control parameters. In this context, adjoint-based control using high-fidelity simulations is a promising method to explore optimal values in large parameter spaces. However, the applicability of the methodology to complex engineering geometries remains extremely limited. In this work, we employ adjoint-based optimal control using unsteady high-fidelity simulations in a generic unstructured grid framework. To this end, an optimal flow control study is conducted in OpenFOAM R using the continuous adjoint method and DNS simulations. To demonstrate the methodology, we study control of an incompressible axisymmetric jet at Re D = 2000, with focus on improving its mixing properties. The gradient of the cost functional is calculated with a newly developed unsteady-adjoint solver based on a classical incremental projection scheme. Particular attention is paid into the presentation of mathematical and algorithmic details. Moreover, we address three main issues that remained relatively undiscussed in common practise: the choice of adjoint boundary conditions on computational boundaries, the failure of the adjoint methodology for long optimization horizons in turbulent flows and the treatment of the additional transposed convective term in the adjoint equations. Practical solutions are employed for these issues. Two optimization cases with different initial conditions are designed. To this end, we considered