Predicting and perhaps mitigating against rare, extreme events in fluid flows is an important challenge. Due to the time-localised nature of these events, Fourier-based methods prove inefficient in capturing them. Instead, this paper uses wavelet-based methods to understand the underlying patterns in a forced flow over a 2-torus which has intermittent high-energy burst events interrupting an ambient low-energy ‘quiet’ flow. Two wavelet-based methods are examined to predict burst events: (i) a wavelet proper orthogonal decomposition (WPOD) based method which uncovers and utilises the key flow patterns seen in the quiet regions and the bursting episodes; and (ii) a wavelet resolvent analysis (WRA) based method that relies on the forcing structures which amplify the underlying flow patterns. These methods are compared with a straightforward energy tracking approach which acts as a benchmark. Both the wavelet-based approaches succeed in producing better predictions than a simple energy criterion, i.e. earlier prediction times and/or fewer false positives and the WRA-based technique always performs better than WPOD. However, the improvement of WRA over WPOD is not as substantial as anticipated. We conjecture that this is because the mechanism for the bursts in the flow studied is found to be largely modal, associated with the unstable eigenfunction of the Navier–Stokes operator linearised around the mean flow. The WRA approach should deliver much better improvement over the WPOD approach for generically non-modal bursting mechanisms where there is a lag between the imposed forcing and the final response pattern.

The three-dimensional stability of two-dimensional natural convection flows in a heated, square enclosure inclined to the horizontal is investigated numerically. First, the computational procedure is validated by comparison of base flow solutions to results reported in literature across a range of inclinations. A bi-global linear stability analysis is then conducted to investigate the stability of these two-dimensional base flows to infinitesimal three-dimensional perturbations, and the effect that buoyancy forces (defined by a buoyancy number $R_N$) and enclosure inclination $\theta$ have on these stability characteristics. The flow is first observed to become three-dimensionally unstable at buoyancy number $R_N = 213.8$ when $\theta$ is $180^\circ$; this increases to $R_N = 2.54 \times 10^4$ at inclination $\theta =58^\circ$. It is found that the two-dimensional base flow is more unstable to three-dimensional perturbations with the critical $R_N$ corresponding to three-dimensional instability being significantly lower than its two-dimensional counterpart across all considered inclinations except $83^\circ \leq \theta \leq 88^\circ$, where the most unstable mode is a two-dimensional oscillatory mode that develops in the boundary layers along the conducting walls. Eight different leading three-dimensional instability modes are identified, with inclinations $58^\circ \leq \theta < 88^\circ$ transitioning through an oscillatory mode, and inclinations $88^\circ \leq \theta \leq 180^\circ$ transitioning through a stationary mode. The characteristics of the primary instability modes corresponding to inclinations $88^\circ \leq \theta \leq 179^\circ$ indicate the presence of a Taylor–Görtler instability.

We undertake an experimental investigation into the instabilities that emerge when a shear-thinning fluid intrudes a less viscous Newtonian fluid axisymmetrically in a lubricated Hele-Shaw cell. Pre-formed lubrication layers of Newtonian fluid that separate the shear-thinning fluid from the cell walls are incorporated into the experimental design. Provided the lubrication layers remain effective at reducing shear stress, so that extensional stresses dominate the flow of the intruding fluid, the instabilities evolve to form branch-like structures, which exhibit fracturing or tearing behaviour at their troughs. Thicker lubrication layers enable the branches to propagate radially outwards, whilst thinner, less effective ones hinder their development and progression. In the absence of lubrication layers, the shear-thinning fluid spreads radially and remains axisymmetric. For lubricated flows, we show that the number of branches is dependent primarily on the strain rate at the radial distance where they first emerge, and that the number of branches decreases with increasing strain rate.

The manipulation of the Richtmyer–Meshkov instability growth at a heavy–light interface via successive shocks is theoretically analysed and experimentally realized in a specific shock-tube facility. An analytical model is developed to forecast the interface evolution before and after the second shock impact, and the possibilities for the amplitude evolution pattern are systematically discussed. Based on the model, the parameter conditions for each scenario are designed, and all possibilities are experimentally realized by altering the time interval between two shock impacts. These findings may enhance the understanding of how successive shocks influence hydrodynamic instabilities in practical applications.

Mangroves are a natural defence of the coastal strip against extreme waves. Furthermore, innovative techniques of naturally based coast defence are used increasingly, according to the canons of eco-hydraulics. Therefore, it is important to correctly evaluate the transmission of waves through cylinder arrays. In the present paper, the attenuation of solitary waves propagating through an array of rigid emergent and submerged cylindrical stems on a horizontal bottom is investigated theoretically, numerically and experimentally. The results of the theoretical model are compared with the numerical simulations obtained with the smoothed particle hydrodynamics meshless Lagrangian numerical code and with experimental laboratory data. In the latter case, solitary waves were tested on a background current, in order to reproduce more realistic sea conditions, since the absence of circulation currents is very rare in the sea. The comparison confirmed the validity of the theoretical model, allowing its use for the purposes indicated above. Furthermore, the present study allowed for an evaluation of the bulk drag coefficient of the rigid stem arrays used, as a function of their density, the stem diameter, and their submergence ratio.

Numerical simulations are conducted to investigate particle suspension and deposition within turbidity currents. Utilizing Lagrangian particle tracking and a discrete element model, our numerical approach enables a detailed examination of autosuspension, deposition and bulk behaviours of turbidity current. We specifically focus on flow regimes where particle settling and buoyancy-induced hydrodynamics play equally important roles. Our discussion is divided into three parts. Firstly, we examine the main body of the current formed by suspended particles, revealing a temporal evolution consisting of initial slumping, propagation and dissipation stages. Our particle calculation allows for the tracking of autosuspended particles, enabling a deeper understanding of the connection between autosuspension and current propagation through energy budget analysis. In the second part, we delve into particle deposition, highlighting transverse and longitudinal variations. Transverse variations arise from lobe-and-cleft (LC) flow features, while longitudinal variations result from vortex detachment, particularly notable with large-sized particles. We observe that as particle size increases, leading to a particle Stokes number greater than 0.1, rapid particle settling suppresses the LC flow structure, resulting in wider lobes at the deposition height. Lastly, we propose a new scaling law for the propagation speed and current length. Our simulation results demonstrate close agreement with this new scaling law, providing valuable insights into turbidity current dynamics.

The collapse of an initially spherical cavitation bubble near a free surface leads to the formation of two jets: a downward jet into the liquid, and an upward jet penetrating the free surface. In this study, we examine the surprising interaction of a bubble trapped in a stable cavitating vortex ring approaching a free surface. As a result, a single fast and tall liquid jet forms. We find that this jet is observed only above critical Froude numbers ($Fr$) and Weber numbers ($We$) when ${Fr}^2 (1.6-2.73/{We}) > 1$, illustrating the importance of inertia, gravity and surface tension in accelerating this novel jet and thereby reaching heights several hundred times the radius of the vortex ring. Our experimental results are supported by numerical simulations, revealing that the underlying mechanism driving the vortex ring acceleration is the disruption of the equilibrium of high-pressure regions at the front and rear of the vortex ring caused by the free surface. Quantitative analysis based on the energy relationships elucidates that the velocity ratio between the maximum velocity of the free-surface jet and the translational velocity of the vortex ring is relatively stable yet is attenuated by surface tension when the jet is mild.

We investigate the drag reduction effect of the streamwise travelling wave-like wall deformation in a high-Reynolds-number turbulent channel flow by large-eddy simulation (LES). First, we assess the validity of subgrid-scale models in uncontrolled and controlled flows. For friction Reynolds numbers $Re_\tau = 360$ and $720$, the Smagorinsky and wall-adapting local eddy-viscosity (WALE) models with a damping function can reproduce well the mean velocity profile obtained by direct numerical simulation (DNS) in both the uncontrolled and controlled flows, leading to a small difference in drag reduction rate between LES and DNS. The LES with finer grid resolution can reproduce well the key structures observed in the DNS of the controlled flow. These results show that the high-fidelity LES is valid for appropriately predicting the drag reduction effect. In addition, a small computational domain is sufficient for reproducing the turbulence statistics, key structures and drag reduction rate obtained by DNS. Subsequently, to investigate the trend of drag reduction rate at higher Reynolds numbers, we utilize the WALE model with the damping function to investigate the control effect at higher Reynolds numbers up to $Re_\tau = 3240$. According to the analyses of turbulence statistics and instantaneous flow fields, the drag reduction at higher Reynolds numbers occurs basically through the same mechanism as that at lower Reynolds numbers. In addition, the drag reduction rate obtained by the present LES approaches that predicted using the semi-empirical formula (Nabae et al., Intl J. Heat Fluid Flow, vol. 82, 2020, 108550) as the friction Reynolds number increases, which supports the high predictability of the semi-empirical formula at significantly high Reynolds numbers.

Ekman pumping is a phenomenon induced by no-slip boundary conditions in rotating fluids. In the context of Rayleigh–Bénard convection, Ekman pumping causes a significant change in the linear stability of the system compared with when it is not present (that is, stress-free). Motivated by numerical solutions to the marginal stability problem of the incompressible Navier–Stokes equation (iNSE) system, we seek analytical asymptotic solutions which describe the departure of the no-slip solution from the stress-free one. The substitution of normal modes into a reduced asymptotic model yields a linear system for which we explore analytical solutions for various scalings of wavenumber. We find very good agreement between the analytical asymptotic solutions and the numerical solutions to the iNSE linear stability problem with no-slip boundary conditions.

The transformation of internal waves on a stepwise underwater obstacle is studied in the linear approximation. The transmission and reflection coefficients are derived for a two-layer fluid. The results are obtained and presented as functions of incident wave wavenumber, density ratio of layers, pycnocline position, and height of the bottom step. Excitation coefficients of evanescent modes are also calculated, and their importance is demonstrated. This allows one to estimate the number of evanescent modes necessary to take into account to attain the required accuracy for the transformation coefficients.

When atmospheric storms pass over the ocean, they resonantly force near-inertial waves (NIWs), internal waves with a frequency close to the local Coriolis frequency $f$. It has long been recognised that the evolution of NIWs is modulated by the ocean's mesoscale eddy field. This can result in NIWs being concentrated into anticyclones which provide an efficient pathway for NIW propagation to depth. Here we analyse the eigenmodes of NIWs in the presence of mesoscale eddies and heavily draw on parallels with quantum mechanics. Whether the eddies are effective at modulating the behaviour of NIWs depends on the wave dispersiveness $\varepsilon ^2 = f\lambda ^2/\varPsi$, where $\lambda$ is the deformation radius and $\varPsi$ is a scaling for the eddy streamfunction. If $\varepsilon \gg 1$, NIWs are strongly dispersive, and the waves are only weakly affected by the eddies. We calculate the perturbations away from a uniform wave field and the frequency shift away from $f$. If $\varepsilon \ll 1$, NIWs are weakly dispersive, and the wave evolution is strongly modulated by the eddy field. In this weakly dispersive limit, the Wentzel–Kramers–Brillouin approximation, from which ray tracing emerges, is a valid description of the NIW evolution even if the large-scale atmospheric forcing apparently violates the requisite assumption of a scale separation between the waves and the eddies. The large-scale forcing excites many wave modes, each of which varies on a short spatial scale and is amenable to asymptotic analysis analogous to the semi-classical analysis of quantum systems. The strong modulation of weakly dispersive NIWs by eddies has the potential to modulate the energy input into NIWs from the wind, but we find that this effect should be small under oceanic conditions.

We investigate experimentally the planar paths displayed by cylinders falling freely in a thin-gap cell containing liquid at rest, by varying the elongation ratio and the Archimedes number of the cylinders, and the solid-to-fluid density ratio. In the investigated conditions, the oscillatory falling motion features two main characteristics: the mean fall velocity $\overline {u_v}$ does not scale with the gravitational velocity, which overestimates $\overline {u_v}$ and is unable to capture the influence of the density ratio on it; and high-amplitude oscillations of the order of $\overline {u_v}$ are observed for both translational and rotational velocities. To model the body behaviour, we propose a force balance, including proper and added inertia terms, the buoyancy force and vortical contributions accounting for the production of vorticity at the body surface and its interaction with the cell walls. Averaging the equations over a temporal period provides a mean force balance that governs the mean fall velocity of the cylinder, revealing that the coupling between the translational and rotational velocity components induces a mean upward inertial force responsible for the decrease of $\overline {u_v}$. This mean force balance also provides a normalization for the frequency of oscillation of the cylinder in agreement with experimental measurements. We then consider the instantaneous force balance experienced by the body, and propose three contributions for the modelling of the vortical force. These can be interpreted as drag, lift and history forces, and their dependence on the control parameters is adjusted on the basis of the experimental measurements.