Hydromagnetic surface waves propagating on the surface of a finitely conducting fluid are studied experimentally and theoretically. An alternating magnetic field is used, so that the field is largely excluded from the bulk of the fluid. Thus, the magnetic damping of the waves is negligible, and the perfectly conducting d.c. case is simulated. The effects of a finite electromagnetic skin depth, δ, are included in the calculation of the theoretical wave dispersion relation. It is predicted that as δ is increased and becomes comparable to the wavelength of the surface wave, the effect of the magnetic field on the fluid motion is decreased. This prediction is confirmed experimentally.

The boundary layers due to finite viscosity and magnetic diffusivity are studied in relation to two models of the flow of a conducting fluid past a body in an aligned magnetic field. In each case it is deduced that the growth of the boundary layer may have substantial effects, such as to raise doubts about the validity of the assumed basic flow patterns.

An experimental investigation of the instability of a laminar air flow over water shows two distinct modes of unstable oscillations as predicted by theory. The Tollmien–Schlichting waves instability could be excited by a ribbon vibrating in the air, and the neutral stability curve determined. The water wave instability mode could be excited by a ribbon vibrating in the water. The growth rates of these waves show only fair agreement with theoretical predictions.

The dynamics of a fluid-filled square cavity with stable thermal stratification subjected to harmonic vertical oscillations is investigated numerically. The nonlinear responses to this parametric excitation are studied over a comprehensive range of forcing frequencies up to two and a half times the buoyancy frequency. The nonlinear results are in general agreement with the Floquet analysis, indicating the presence of nested resonance tongues corresponding to the intrinsic $m:n$ eigenmodes of the stratified cavity. For the lowest-order subharmonic $1:1$ tongue, the responses are analysed in great detail, with complex dynamics identified near onset, most of which involves interactions with unstable saddle states of a homoclinic or heteroclinic nature.

We calculate suspended sediment transport, erosion and deposition under reflected long waves on a plane beach. Our method employs the shallow-water equations, and is based on the calculation of the concentration field in Lagrangian coordinates: this allows results to be obtained readily throughout the whole domain, including the often troublesome shoreline region. These results suggest that the tendency of wave-dominated muddy shores to export sediment and erode over long time scales is not due to wave forcing at infragravity frequencies, since the sediment transport under such waves is localized close to the shoreline, and is principally directed shorewards. They also provide easily reproduced test cases against which to validate the numerical methods used in more detailed studies of coastal sediment transport and morphodynamics.

We consider the general motion (translation and rotation) of a deformable or rigid body of arbitrary shape in a linear shear flow of an effectively inviscid and incompressible fluid possessing uniform vorticity. The ambient vorticity may be time-dependent. For two-dimensional configurations a solution with uniform vorticity is possible for all times and for three-dimensional, it is possible only initially or during a short time interval after the body is impulsively introduced into the fluid. General analytic expressions for the vortical force and moment exerted on an arbitrary moving body are presented. Bearing in mind applications for large non-spherical bubble dynamics, the general expressions for the hydrodynamic loads are further reduced for symmetric quadratic shapes such as two-dimensional ellipses or three-dimensional ellipsoids. The simplified expressions are given in terms of the body's added-mass tensor, its six velocities and the ambient vorticity. The few available degenerate solutions for cylinders and spheres are readily obtained as limiting cases.

The Rayleigh–Taylor instability induced turbulence is studied under the Boussinesq approximation focusing on vorticity and mixing. A direct numerical simulation has been carried out with an auto-adaptive multidomain Chebyshev–Fourier–Fourier numerical method. The spatial resolution is increased up to $(24\times 40)\times 940^{2}=848\,M$ collocation points. The Taylor Reynolds number is $\mathit{Re}_{\unicode[STIX]{x1D706}_{zz}}\approx 142$ and a short inertial range is observed. The nonlinear growth rate of the turbulent mixing layer is found to be close to $\unicode[STIX]{x1D6FC}_{b}=0.021$ . Our conclusions may be summarized as follows.

(i) The simulation data are in agreement with the scalings for the pressure ( $k^{-7/3}$ ) and the vertical mass flux ( $k^{-7/3}$ ).

(ii) Mean quantities have a self-similar behaviour, but some inhomogeneity is still present. For higher-order quantities the self-similar regime is not fully achieved.

(iii) In the self-similar regime, the mean dissipation rate and the enstrophy behave as $\langle \overline{\unicode[STIX]{x1D700}}\rangle \propto t$ and $\langle \overline{\unicode[STIX]{x1D714}_{i}\,\unicode[STIX]{x1D714}_{i}}^{1/2}\rangle \propto t^{1/2}$ , respectively.

(iv) The large-scale velocity fluctuation probability density function (PDF) is Gaussian, while vorticity and dissipation PDFs show large departures from Gaussianity.

(v) The pressure PDF exhibits strong departures from Gaussianity and is skewed. This is related to vortex coherent structures.

(vi) The intermediate scales of the mixing are isotropic, while small scales remain anisotropic. This leaves open the possibility of a small-scale buoyancy. Velocity intermediate scales are also isotropic, while small scales remain anisotropic. Mixing and dynamics are therefore consistent.

(vii) Properties and behaviours of vorticity and enstrophy are detailed. In particular, equations for these quantities are written down under the Boussinesq approximation.

(viii) The concentration PDF is quasi-Gaussian. The vertical concentration gradient is both non-Gaussian and strongly skewed.

We develop a model of the skin-friction coefficient based on scalar images in the compressible, spatially evolving boundary-layer transition. The images are extracted from a passive scalar field by a sliding window filter on the streamwise and wall-normal plane. The multi-scale and multi-directional geometric analysis is applied to characterize the averaged inclination angle of spatially evolving filtered component fields at different scales ranging from a boundary-layer thickness to several viscous length scales. In general, the averaged inclination angles increase along the streamwise direction, and the variation of the angles for large-scale structures is smaller than that for small-scale structures. Inspired by the coincidence of the increasing averaged inclination angle and the rise of the skin-friction coefficient, we propose a simple image-based model of the skin-friction coefficient. The model blends empirical formulae of the skin-friction coefficient in laminar and fully developed turbulent regions using the normalized averaged inclination angle of scalar structures at intermediate and small scales. The model prediction calculated from scalar images is validated by the results from the direct numerical simulation at two Mach numbers, 2.25 and 6, and the relative error can be less than 15 %.

We have performed numerical calculations of fluid mixing driven by Rayleigh–Taylor instability for density profiles based on the stratified density experiments of Lawrie & Dalziel (J. Fluid Mech., vol. 688, 2011, pp. 507–527) and Davies Wykes & Dalziel (J. Fluid Mech., vol. 756, 2014, pp. 1027–1057). We find that the late-time mixing profiles are similar to their experimental results for similar initial conditions; we consider a range of additional initial conditions to investigate the robustness of the results. A model for the late-time structure of the mixing layer, based on the maximization of configurational entropy, is compared with the results of the numerical calculations, and shows good agreement.

The governing equations of a surface wave field and a coexisting roll–streak circulation typical of Langmuir circulations or submesoscale frontal circulations are derived to better describe their two-way interactions. The gradients and vertical velocities of the roll–streak circulation induce wave refraction, amplitude modulation and higher-order waves. These changes then produce wave–wave nonlinear forces and divergence of the wave-induced mass transport, both of which in turn affect the circulation. To accurately represent these processes, both a wave theory and a wave-averaged theory are developed without relying on any extrapolation, any spatiotemporal mapping or an approximation that treats the wave-induced mass divergence as being concentrated at the surface. This wave theory finds seven types of current-induced higher-order wave motions. It also determines the wave dynamics such as the governing equation of the wave action density valid in the presence of the complex circulation. The evolution of the wave action density is clearly affected by the upwelling or downwelling. The new wave-averaged theory presents the governing equations of the wave-averaged circulation which satisfies the wave-averaged mass conservation. This circulation is different from the circulation considered to satisfy the mass conservation in the Craik–Leibovich theory, and the difference becomes critical when the wave field evolves due to refraction. In this case, compared to the Craik–Leibovich theory, long waves are more important and also the rolls are more weakly forced.

Bulk-to-shear viscosity ratios of three orders of magnitude are often reported in carbon dioxide but are always neglected when predicting aerothermal loads in external (Mars exploration) or internal (turbomachinery, heat exchanger) turbulent flows. The recent (and first) numerical investigations of that matter suggest that the solenoidal turbulence kinetic energy is in fact well predicted despite this seemingly arbitrary simplification. The present work argues that such a conclusion may reflect limitations from the choice of configuration rather than provide a definite statement on the robustness of kinetic-energy transfers to the use of Stokes’ hypothesis. Two distinct asymptotic regimes (Euler–Landau and Stokes–Newton) in the eigenmodes of the Navier–Stokes equations are identified. In the Euler–Landau regime, the one captured by earlier studies, acoustic and entropy waves are damped by transport coefficients and the dilatational kinetic energy is dissipated, even more rapidly for high bulk-viscosity fluids and/or forcing frequencies. If the kinetic energy is initially or constantly injected through solenoidal motions, effects on the turbulence kinetic energy remain minor. However, in the Stokes–Newton regime, diffused bulk compressions and advected isothermal compressions are found to prevail and promote small-scale enstrophy via vorticity–dilatation correlations. In the absence of bulk viscosity, the transition to the Stokes–Newton regime occurs within the dissipative scales and is not observed in practice. In contrast, at high bulk viscosities, the Stokes–Newton regime can be made to overlap with the inertial range and disrupt the enstrophy at small scales, which is then dissipated by friction. Thus, flows with substantial inertial ranges and large bulk-to-shear viscosity ratios should experience enhanced transfers to small-scale solenoidal kinetic energy, and therefore faster dissipation rates leading to modifications of the heat-transfer properties. Observing numerically such transfers is still prohibitively expensive, and the present simulations are restricted to two-dimensional turbulence. However, the theory laid here offers useful guidelines to design experimental studies to track the Stokes–Newton regime and associated modifications of the turbulence kinetic energy, which are expected to persist in three-dimensional turbulence.

The present work consists of an investigation of the turbulence radiation interaction (TRI) in a radiative turbulent channel flow of grey gas bounded by isothermal hot and cold walls. The optical thickness $\unicode[STIX]{x1D70F}$ of the channel is varied from 0.1 to 10 to observe different regimes of TRI. A high-resolution finite volume method for radiative heat transfer is employed and coupled with the direct numerical simulation (DNS) of the flow. The resulting effects of TRI on temperature statistics are strongly dependent on the considered optical depth. In particular, the contrasting role of emission and absorption is highlighted. For a low optical thickness the effect of radiative fluctuations on temperature statistics is low and causes the reduction of temperature variance through the dissipating action of emission. On the other hand, while increasing optical thickness to relatively high levels, the dissipation of temperature variance is balanced, at low wavenumbers in the turbulence spectrum, through the preferential action of absorption, which increases the large-scale temperature fluctuations. A significant rise in the effect of radiation on the temperature variance can be observed as a consequence of the reduction of radiative heat transfer length scales.

The instability of the Kármán vortex street is revisited under a spatio-temporal perspective that allows the taking into account of the advection of the vortices by the external flow. We analyse a simplified point vortex model and show through numerical simulations of its linear impulse response that the system becomes convectively unstable above a certain critical advection velocity. This critical velocity decreases as the aspect ratio approaches its specific value for temporal stability, and increases with the confinement induced by lateral walls. In the limiting unconfined case, direct application of the Briggs–Bers criterion to the dispersion relation gives results in excellent agreement with the numerical simulations. Finally, a direct numerical simulation of the $Re=100$ flow past a confined cylinder is performed, and the actual advection velocity of the resulting vortex street is found to be much larger than the critical advection velocity for convective instability given by our model. The Kármán vortex street is therefore strongly convectively unstable.