We investigate the influence of capillary effects on wave breaking through direct numerical simulations of the Navier–Stokes equations for a two-phase air–water flow. A parametric study in terms of the Bond number, $\mathit{Bo}$, and the initial wave steepness, ${\it\epsilon}$, is performed at a relatively high Reynolds number. The onset of wave breaking as a function of these two parameters is determined and a phase diagram in terms of $({\it\epsilon},\mathit{Bo})$ is presented that distinguishes between non-breaking gravity waves, parasitic capillaries on a gravity wave, spilling breakers and plunging breakers. At high Bond number, a critical steepness ${\it\epsilon}_{c}$ defines the onset of wave breaking. At low Bond number, the influence of surface tension is quantified through two boundaries separating, first gravity–capillary waves and breakers, and second spilling and plunging breakers; both boundaries scaling as ${\it\epsilon}\sim (1+\mathit{Bo})^{-1/3}$. Finally the wave energy dissipation is estimated for each wave regime and the influence of steepness and surface tension effects on the total wave dissipation is discussed. The breaking parameter $b$ is estimated and is found to be in good agreement with experimental results for breaking waves. Moreover, the enhanced dissipation by parasitic capillaries is consistent with the dissipation due to breaking waves.

The stability and turbulence characteristics of a vortex filament emanating from a single-bladed rotor in hover are investigated using proper orthogonal decomposition (POD). The rotor is operated at a tip chord Reynolds number and tip Mach number of 218 000 and 0.23, respectively, and with a blade loading of $C_{T}/{\it\sigma}=0.066$. In-plane components of the velocity field (normal to the axis of the vortex filament) are captured by way of two-dimensional particle image velocimetry with corrections for vortex wander being performed using the ${\it\Gamma}_{1}$ method. The first POD mode alone is found to encompass nearly 75 % of the energy for all vortex ages studied and is determined using a grid of sufficient resolution to avoid numerical integration errors in the decomposition. The findings reveal an equal balance between the axisymmetric and helical modes during vortex roll-up, which immediately transitions to helical mode dominance at all other vortex ages. This helical mode is one of the modes of the elliptic instability. The spatial eigenfunctions of the first few Fourier-azimuthal modes associated with the most energetic POD mode is shown to be sensitive to the choice of the wander correction technique used. Higher Fourier-azimuthal modes are observed in the outer portions of the vortex and appeared not to be affected by the choice of the wander correction technique used.

An analytical consideration has been made to explore the velocity, temperature and nanoparticle distributions and heat transfer characteristics associated with thermal dispersion and nanoparticle mechanical dispersion within a nanofluid-saturated homogeneous metal foam. A volume-averaging theory was rigorously applied to integrate locally a set of governing equations based on the modified Buongiorno model at the pore scale. Thus, a macroscopic set of volume-averaged governing equations were derived allowing interstitial heat transfer between the nanofluid and metal phases. Unknown terms were modelled mathematically to obtain a closed set of volume-averaged governing equations. Subsequently, a pore-scale analysis was carried out to find possible functional forms for describing thermal dispersion and nanoparticle mechanical dispersion in a nanofluid-saturated metal foam. Using the resulting set of volume-averaged governing equations, forced convective flows in nanofluid-saturated metal foams were analytically investigated for the steady-state case. Eventually, it has been predicted that an unconventionally high level of the heat transfer rate (about 80 times more than the case of base fluid convection without a metal foam) may be achieved by combination of metal foam and nanofluid.

The three-dimensional propagation of internal gravity wave beams in a uniformly stratified Boussinesq fluid is discussed, assuming that variations in the along-beam and transverse directions are of long length scale relative to the beam width. This situation applies, for instance, to the far-field behaviour of a wave beam generated by a horizontal line source with weak transverse dependence. In contrast to the two-dimensional case of purely along-beam variations, where nonlinear effects are minor even for beams of finite amplitude, three-dimensional nonlinear interactions trigger the transfer of energy to a circulating horizontal time-mean flow. This resonant beam–mean-flow coupling is analysed, and a system of two evolution equations is derived for the propagation of a small-amplitude beam along with the induced mean flow. This model explains the salient features of the experimental observations of Bordes et al. (Phys. Fluids, vol. 24, 2012, 086602).

Diffusive bottom boundary layers can produce upslope flows in a stratified fluid. Accumulating observations suggest that these boundary layers may drive upwelling and mixing in mid-ocean ridge flank canyons. However, most studies of diffusive bottom boundary layers to date have concentrated on constant bottom slopes. We present a study of how diffusive boundary layers interact with various idealized topography, such as changes in bottom slope, slopes with corrugations and isolated sills. We use linear theory and numerical simulations in the regional ocean modeling system (ROMS) model to show changes in bottom slope can cause convergences and divergences within the boundary layer, in turn causing fluid exchanges that reach far into the overlying fluid and alter stratification far from the bottom. We also identify several different regimes of boundary-layer behaviour for topography with oceanographically relevant size and shape, including reversing flows and overflows, and we develop a simple theory that predicts the regime boundaries, including what topographies will generate overflows. As observations also suggest there may be overflows in deep canyons where the flow passes over isolated bumps and sills, this parameter range may be particularly significant for understanding the role of boundary layers in the deep ocean.

The statistical properties of wall turbulence in the logarithmic region are investigated using structure functions of the streamwise velocity. To this end, datasets that span several orders of magnitude of Reynolds numbers are used, up to $Re_{{\it\tau}}=O(10^{6})$, providing uniquely large scale separations for scrutinising previously proposed scaling laws. For the second-order structure functions strong support is found simultaneously for power-law scalings in the Kolmogorov inertial subrange and for logarithmic scaling at larger scales within the inertial range ($z<r\ll {\it\delta}$, where $z$ is the distance from the wall, $r$ the scale, and ${\it\delta}$ the boundary layer thickness). The observed scalings are shown to agree between the datasets, which include both temporal and spatial velocity signals and span from laboratory to atmospheric flows, showing a degree of universality in the results presented. An examination of higher even-order structure functions also shows support for logarithmic scaling behaviour for $z<r\ll {\it\delta}$, provided that the Reynolds number is sufficiently high. These findings are interpreted by generalising the work of Meneveau & Marusic (J. Fluid Mech., vol. 719, 2013) and introducing bridging relations between higher-order moments of velocity fluctuations and structure functions. Further, a physical model based on the attached-eddy hypothesis is utilised to derive various properties of the structure functions for the energy-containing scales of the logarithmic region. The descriptions derived from the model are shown to be supported by the experimental data.

This paper addresses the problem of designing low-order and linear robust feedback controllers that provide a priori guarantees with respect to stability and performance when applied to a fluid flow. This is challenging, since whilst many flows are governed by a set of nonlinear, partial differential–algebraic equations (the Navier–Stokes equations), the majority of established control system design assumes models of much greater simplicity, in that they are: firstly, linear; secondly, described by ordinary differential equations (ODEs); and thirdly, finite-dimensional. With this in mind, we present a set of techniques that enables the disparity between such models and the underlying flow system to be quantified in a fashion that informs the subsequent design of feedback flow controllers, specifically those based on the $\mathscr{H}_{\infty }$ loop-shaping approach. Highlights include the application of a model refinement technique as a means of obtaining low-order models with an associated bound that quantifies the closed-loop degradation incurred by using such finite-dimensional approximations of the underlying flow. In addition, we demonstrate how the influence of the nonlinearity of the flow can be attenuated by a linear feedback controller that employs high loop gain over a select frequency range, and offer an explanation for this in terms of Landahl’s theory of sheared turbulence. To illustrate the application of these techniques, an $\mathscr{H}_{\infty }$ loop-shaping controller is designed and applied to the problem of reducing perturbation wall shear stress in plane channel flow. Direct numerical simulation (DNS) results demonstrate robust attenuation of the perturbation shear stresses across a wide range of Reynolds numbers with a single linear controller.

An error in the complex representation of the porous-coating model used in the study by Fedorov et al. (J. Fluid Mech., vol. 479, 2003, pp. 99–124), investigating the stabilization effect of ultrasonically absorptive coatings on hypersonic boundary layers, is pointed out and corrected. This error has been acknowledged by Fedorov et al. (J. Fluid Mech., vol. 769, 2015, pp. 725–728). The corrected version of the erroneous linear stability results of the original work is presented and previously made conclusions are reassessed. The novel numerical results indicate that second-mode instabilities are shifted to lower frequencies on felt-metal porous coatings, similar to the behaviour observed on porous coatings with regular microstructure.

Motivated by the need to characterize the spatio-temporal structure of turbulence in wall-bounded flows, we study wavenumber–frequency spectra of the streamwise velocity component based on large-eddy simulation (LES) data. The LES data are used to measure spectra as a function of the two wall-parallel wavenumbers and the frequency in the equilibrium (logarithmic) layer. We then reformulate one of the simplest models that is able to reproduce the observations: the random sweeping model with a Gaussian large-scale fluctuating velocity and with additional mean flow. Comparison with LES data shows that the model captures the observed temporal decorrelation, which is related to the Doppler broadening of frequencies. We furthermore introduce a parameterization for the entire wavenumber–frequency spectrum $E_{11}(k_{1},k_{2},{\it\omega};z)$, where $k_{1}$, $k_{2}$ are the streamwise and spanwise wavenumbers, ${\it\omega}$ is the frequency and $z$ is the distance to the wall. The results are found to be in good agreement with LES data.

Recent experimental research on rotating cylinder wakes has found that a previously numerically predicted subharmonic instability mode, mode C, occurs for considerably lower rotation rates than predicted through stability analysis, yet other mode transitions occur closer to the predicted onset. One difference between the theoretical and experimental set-ups is the use of a small-diameter hydrogen bubble visualisation wire placed upstream of the rotating cylinder. The current paper tests the hypothesis that a wire, of only $1/100$th of the cylinder diameter, placed five diameters upstream of the cylinder, sufficiently perturbs the flow to substantially affect certain wake transitions, including the onset of mode C. This is achieved using stability analysis of a flow that includes the upstream wire. The results indeed show that the wire of a tiny diameter induces a non-negligible asymmetry in the flow, triggering the subharmonic mode at substantially lower rotation rates. Furthermore, at higher rotation rates, the onset of two other three-dimensional modes are delayed to higher Reynolds numbers. These results make the point that even seemingly minute perturbations caused by minimally intrusive methods may result in substantially altered experimental flow behaviour.