Open cavity flows are known to select and enhance locked-on modes or tones. High-energy self-sustained oscillations arise within the shear layer, impinging onto the trailing edge of the cavity. These self-sustained oscillations are subject to amplitude modulations (AMs) at multiple low frequencies. However, only a few studies have addressed the identification of the lowest modulating frequencies. The present work brings to light salient AMs of the shear layer waves and identifies their source as three-dimensional dynamics existing inside the cavity. Indeed, the recirculating inner flow gives rise to centrifugal instabilities, which entail broad-band frequencies down two orders of magnitude lower than those of the self-sustained oscillations. Using time-resolved PIV (TRPIV) in two planes, the nonlinearly saturated dynamics is analysed in both space and time by means of proper orthogonal decomposition, global Fourier decomposition and Hilbert–Huang transforms. The inner flow can be decomposed as three-dimensional waves carried by the main recirculation. Bicoherence distributions are computed to highlight the nonlinear interactions between these spanwise-travelling waves inside the cavity and the locked-on modes. The modulated envelope of the shear layer oscillations is extracted and investigated with regards to the inner-flow dynamics. Strong cross-correlations, in time rather than in space, reveal a global coupling mechanism, possibly related to the beating of the spanwise-travelling waves.

We consider a twisted cylinder that was designed by rotating the elliptic cross-section along the spanwise direction, resulting in a passive control. The flow over the twisted cylinder is investigated at a subcritical Reynolds number (Re) of 3000 using large eddy simulation based on the finite volume method. For comparison, the flow past smooth and wavy cylinders is also calculated. The twisted cylinder achieves reductions of approximately 13 and 5 % in mean drag compared with smooth and wavy cylinders, respectively. In particular, the root mean square (r.m.s.) value of the lift fluctuation of the twisted cylinder shows a substantial decrease of approximately 96 % compared with the smooth cylinder. The shear layer of the twisted cylinder covering the recirculation region is more elongated than those of the smooth and wavy cylinders, and vortex shedding from the twisted cylinder is considerably suppressed. Consequently, the elongation of the shear layer from the body and the near disappearance of vortex shedding in the near wake with weak vortical strength contributes directly to the reduction of drag and lift oscillation. Various fundamental mechanisms that affect the flow phenomena, three-dimensional separation, pressure coefficient, vortex formation length and turbulent kinetic energy are examined systematically to demonstrate the effect of the twisted cylinder surface. In addition, for the twisted cylinder at $\mathit{Re}=3000$, the effect of the cross-sectional aspect ratio is investigated from 1.25 to 2.25 to find an optimal value that can reduce the drag and lift forces. Moreover, the effect of the Reynolds number on the aerodynamic characteristics is investigated in the range of $3\times 10^{3}\leqslant \mathit{Re}\leqslant 1\times 10^{4}$. We find that as Re increases, the mean drag and the r.m.s. lift coefficient of the twisted cylinder increase, and the vortex formation length decreases.

Mixing induced through the life-cycle of Kelvin–Helmholtz (KH) billows is studied for a range of low and intermediate Reynolds numbers using direct numerical simulations (DNS). The amount of stirring, and therefore mixing, is significantly controlled by the process of vortex pairing of two KH billows. For low Reynolds numbers, vortex pairing of the billows is complete in the pre-turbulent stage or early stages of turbulence, generating a high amount of stirring. At higher Reynolds numbers, vortex pairing is suppressed by the growth of three-dimensional instabilities, and the amount of stirring is significantly reduced. For single KH billows, as the Reynolds number increases, there is a transition in the characteristics of the mixing, similar to the laboratory measurements of Breidenthal (J. Fluid Mech., vol. 109, 1981, pp. 1–24) and Koochesfahani & Dimotakis (J. Fluid Mech., vol. 170, 1986, pp. 83–112). The transition in mixing is associated with the growth and sustainability of three-dimensional motions at sufficiently high Reynolds numbers. We examine this ‘mixing transition’ and the influence of vortex pairing on it by examining the flow properties at different stages and the exchange between the energy partitions. As the Reynolds number increases, three-dimensional motions develop over a wider range of length scales, and smaller scale eddies form. However, this does not necessarily result in a greater amount of mixing. The maximum total amount of mixing induced over the lifetime of a KH instability, for billows both with and without vortex pairing, occurs when the large-scale eddies that cause the stirring are the most energetic. The mixing efficiency reveals a non-monotonic dependence on the Reynolds number.

We study here Green–Naghdi type equations (also called fully nonlinear Boussinesq, or Serre equations) modelling the propagation of large-amplitude waves in shallow water without a smallness assumption on the amplitude of the waves. The novelty here is that we allow for a general vorticity, thereby allowing complex interactions between surface waves and currents. We show that the a priori ($2+1$)-dimensional dynamics of the vorticity can be reduced to a finite cascade of two-dimensional equations. With a mechanism reminiscent of turbulence theory, vorticity effects contribute to the averaged momentum equation through a Reynolds-like tensor that can be determined by a cascade of equations. Closure is obtained at the precision of the model at the second order of this cascade. We also show how to reconstruct the velocity field in the ($2+1$)-dimensional fluid domain from this set of two-dimensional equations and exhibit transfer mechanisms between the horizontal and vertical components of the vorticity, thus opening perspectives for the study of rip currents, for instance.

The propagation of transient inertio-gravity waves in a shear flow is examined using the Gaussian beam formulation. This formulation assumes Gaussian wavepackets in the spectral space and uses a second-order Taylor expansion of the phase of the wave field. In this sense, the Gaussian beam formulation is also an asymptotic approximation like spatial ray tracing; however, the first one is free of the singularities found in spatial ray tracing at caustics. Therefore, the Gaussian beam formulation permits the examination of the evolution of transient inertio-gravity wavepackets from the initial time up to the destabilization of the flow close to the critical levels. We show that the transience favours the development of the dynamical instability relative to the convective instability. In particular, there is a well-defined threshold for which small initial amplitude transient inertio-gravity waves never reach the convective instability criterion. This threshold does not exist for steady-state inertio-gravity waves for which the wave amplitude increases indefinitely towards the critical level. The Gaussian beam formulation is shown to be a powerful tool to treat analytically several aspects of inertio-gravity waves in simple shear flows. In more realistic shear flows, its numerical implementation is readily available and the required numerical calculations have a low computational cost.

The bed entrainment rate in a gravity mass flow (GMF) is uniquely determined by the properties of the bed and the flow. In depth-averaging, however, critical information on the flow variables near the bed is lost and empirical assumptions usually are made instead. We study the interplay between bed and flow assuming a perfectly brittle bed, characterized by its shear strength ${\it\tau}_{c}$, and erosion along the bottom surface of the flow; frontal entrainment is neglected here. The brittleness assumption implies that the shear stress at the bed surface cannot exceed ${\it\tau}_{c}$. For quasi-stationary flows in a simplified setting, analytic solutions are found for Bingham and frictional–collisional (FC) fluids. Extending this theory to non-stationary flows requires some assumptions for the velocity profile. For the Bingham fluid, the profile of a ‘proxy’ quasi-stationary eroding flow is used; the rheological parameters are chosen to match the instantaneous velocity and shear-layer depth of the non-stationary flow. For the FC fluid, a two-parameter family of functions that closely match the profiles obtained in depth-resolved numerical simulations is assumed; the boundary conditions determine the instantaneous parameter values and allow computation of the erosion rate. Preliminary tests with the FC erosion formula incorporated in a simple slab model indicate that the non-stationary erosion formula matches the depth-resolved simulations asymptotically, but differs in the start-up phase. The non-stationary erosion formulae are valid only up to a limit velocity (and to a limit flow depth if there is Coulomb friction). This appears to mark the transition to another erosion regime – to be described by a different model – where chunks of bed material are intermittently ripped out and gradually entrained into the flow.

The parametric subharmonic instability (PSI) in stratified fluids depends on the frequency and the amplitude of the primary plane wave. In this paper, we present experimental and numerical results emphasizing that the finite width of the beam also plays an important role on this triadic instability. A new theoretical approach based on a simple energy balance is developed and compared with numerical and experimental results. Owing to the finite width of the primary wave beam, the secondary pair of waves can leave the interaction zone which affects the transfer of energy. Experimental and numerical results are in good agreement with the prediction of this theory, which brings new insights on energy transfers in the ocean where internal waves with finite-width beams are dominant.

The flow past a transversely rotating sphere at Reynolds numbers of $\mathit{Re}=500{-}1000$ is directly simulated using an unstructured finite volume collocated code. The effect of rotation rate on the flow is studied by increasing the dimensionless rotation rate, ${\it\Omega}^{\ast }$, from 0 to 1.20, where ${\it\Omega}^{\ast }$ is the maximum sphere surface velocity normalised by the free stream velocity. This study investigates the marked unsteadiness of the flow structures at $\mathit{Re}=500{-}1000$. Comparison with previous numerical data (Giacobello et al., J. Fluid Mech., vol. 621, 2009, pp. 103–130; Kim, J. Mech. Sci. Technol., vol. 23, 2009, pp. 578–589) reveals a new flow regime, namely a ‘shear layer–stable foci’ regime, besides the widely reported ‘vortex shedding’ and ‘shear layer instability’ regimes. The ‘shear layer–stable foci’ regime is observed at $\mathit{Re}=500$ and ${\it\Omega}^{\ast }=1.00$; $\mathit{Re}=640{-}1000$ and ${\it\Omega}^{\ast }\geqslant 0.80$. In this flow regime, the shear layer on the advancing side of the sphere (where the sphere surface velocity vector opposes the free stream velocity) shortens significantly while fluid from the retreating side (opposite to the advancing side) is drawn towards the mid-plane normal to the peripheral velocity. This results in the formation of a stable focus near the onset of the shear layer instability. This stable focus becomes more pronounced with increasing $\mathit{Re}$ and ${\it\Omega}^{\ast }$. It increases the oscillation magnitude and decreases the oscillation frequency of the hydrodynamic forces.

We investigate the response of a laboratory aquifer submitted to artificial rainfall, with an emphasis on the early stage of a rain event. In this almost two-dimensional experiment, the infiltrating rainwater forms a groundwater reservoir which exits the aquifer through one side. The resulting outflow resembles a typical stream hydrograph: the water discharge increases rapidly during rainfall and decays slowly after the rain has stopped. The Dupuit–Boussinesq theory, based on Darcy’s law and the shallow-water approximation, quantifies these two asymptotic regimes. At the early stage of a rainfall event, the discharge increases linearly with time, at a rate proportional to the rainfall rate to the power of ${\textstyle \frac{3}{2}}$. Long after the rain has stopped, it decreases as the squared inverse of time (Boussinesq, C. R. Acad. Sci., vol. 137, 1903, pp. 5–11). We compare these predictions with our experimental data.

We present new families of gravity–capillary solitary waves propagating on the surface of a two-dimensional deep fluid. These spatially localised travelling-wave solutions are non-symmetric in the wave propagation direction. Our computation reveals that these waves appear from a spontaneous symmetry-breaking bifurcation, and connect two branches of multi-packet symmetric solitary waves. The speed–energy bifurcation curve of asymmetric solitary waves features a zigzag behaviour with one or more turning points.

We investigate the settling speeds and root mean square (r.m.s.) velocities of inertial particles in isotropic turbulence with gravity using experiments with water droplets in air turbulence from 32 loudspeaker jets and direct numerical simulations (DNS). The dependence on particle inertia, gravity and the scales of both the smallest and largest turbulent eddies is investigated. We isolate the mechanisms of turbulence settling modification and find that the reduced settling speeds of large particles in experiments are due to nonlinear drag effects. We demonstrate using DNS that reduced settling speeds with linear drag (e.g. see Nielsen, J. Sedim. Petrol., vol. 63, 1993, pp. 835–838) only arise in artificial flows that, by design, eliminate preferential sweeping by the eddies. Gravity and inertia both reduce the particle r.m.s. velocities and falling particles are more responsive to vertical than to horizontal fluctuations. The model by Wang & Stock (J. Atmos. Sci., vol. 50, 1993, pp. 1897–1913) captures these trends.