This work reports high-fidelity shock-tube experiments on the convergent Richtmyer–Meshkov (RM) instability at a heavy gas layer. The convergent shock tube is designed based on shock dynamics theory, significantly mitigating interface deceleration and reflected shock. As a result, long-term observation of instability growth up to nonlinear stage, free of interface deceleration and reshock, is achieved. Various types of SF$_6$ layers surrounded by air with controllable thicknesses and shapes, created using a soap film technique, are examined. For thick layers, the evolutions of the outer and inner interfaces are nearly decoupled regardless of the layer shape. The weakly nonlinear model of Wang (Phys. Plasmas,vol. 22, 2015, p. 082702), designed for cylindrical RM instability at a single interface, provides a reasonable prediction of perturbation growth at the inner interface, while slightly underestimating instability growth at the outer interface, as it neglects the effects of rarefaction wave. For thin layers, perturbation growth is fastest at either interface when both interfaces initially possess in-phase perturbations, moderate when only one interface is initially perturbed and slowest when the two interfaces have anti-phase perturbations. This variation in growth rates is due to the fact that the evolution of a thin layer is influenced by both reverberating waves and interface coupling, with each factor being highly sensitive to the layer shape. The original vortex method is extended to address the convergent RM instability by incorporating the influences of unsteady background flow, interface coupling and reverberating waves into the transport of a vortex sheet. This extended vortex method enables accurate prediction of convergent RM instability at a gas layer, covering the full range from early linear to late nonlinear stages.

Turbulent flows over porous substrates are studied via a systematic exploration of the dependence of the flow properties on the substrate parameters, including permeability $K$, grain pitch $L$ and depth $h$. The study uses direct numerical simulations mainly for staggered-cube substrates with $L^+\approx 10$–$50$, $\sqrt {K}/L\approx 0.01$–$0.25$ and depths from $h=O(L)$ to $h\gg L$, ranging from typical impermeable rough surfaces to deep porous substrates. The results indicate that the permeability has significantly greater relevance than the grain size and microscale topology for the properties of the overlying flow, including the mean-flow slip and the shear across the interface, the drag increase relative to smooth-wall flow and the statistics and spectra of the overlying turbulence, whereas the direct effect of grain size is only noticeable near the interface as grain-coherent flow fluctuations. The substrate depth also has a significant effect, with shallower substrates suppressing the effective transpiration at the interface. Based on the direct-simulation results, we propose an empirical ‘equivalent permeability’ $K_{eq}^t$ that incorporates this effect and scales well the overlying turbulence for substrates with different depths, permeabilities, etc. This result suggests that wall normal transpiration driven by pressure fluctuations is the leading contributor to the changes in the drag and the overlying turbulence. Based on this, we propose a conceptual $h^+$–$\sqrt {K^+}$ regime diagram where, for any given substrate topology, turbulence transitions smoothly from that over impermeable rough surfaces with $h=O(L)$ to that over deep porous substrates with $h^+\gtrsim 50$, with the latter limit determined by the typical lengthscale of the overlying pressure fluctuations.

Rogue waves (RWs) can form on the ocean surface due to the well-known quasi-four-wave resonant interaction or superposition principle. The first is known as the nonlinear focusing mechanism and leads to an increased probability of RWs when unidirectionality and narrowband energy of the wave field are satisfied. This work delves into the dynamics of extreme wave focusing in crossing seas, revealing a distinct type of nonlinear RWs, characterised by a decisive longevity compared with those generated by the dispersive focusing (superposition) mechanism. In fact, through fully nonlinear hydrodynamic numerical simulations, we show that the interactions between two crossing unidirectional wave beams can trigger fully localised and robust development of RWs. These coherent structures, characterised by a typical spectral broadening then spreading in the form of dual bimodality and recurrent wave group focusing, not only defy the weakening expectation of quasi-four-wave resonant interaction in directionally spreading wave fields, but also differ from classical focusing mechanisms already mentioned. This has been determined following a rigorous lifespan-based statistical analysis of extreme wave events in our fully nonlinear simulations. Utilising the coupled nonlinear Schrödinger framework, we also show that such intrinsic focusing dynamics can be captured by weakly nonlinear wave evolution equations. This opens new research avenues for further explorations of these complex and intriguing wave phenomena in hydrodynamics as well as other nonlinear and dispersive multi-wave systems.

As new concepts to protect marine structures from ocean waves, we propose the use of a floating elastic annulus. In this paper, two types of annuli are demonstrated. The first is a ‘wave shield’, which creates a calm free surface within an inner domain of the annulus by preventing wave penetration. The second is a ‘cloak’, which not only creates a calm space within the inner domain but also prevents wave scattering outside the annulus. To evaluate the calmness of the inner domain of the annulus, an inlet wave energy factor is newly defined. The wave shield is designed to minimise the inlet wave energy factor to nearly zero. However, the cloak is designed to minimise both the inlet wave energy factor and scattered-wave energy which evaluates the amount of wave scattering at far-field. Each annulus consists of several horizontal concentric annular plates, and the flexural rigidities of the plates are optimised to minimise objective functions at a target frequency. Numerical simulations demonstrate that both the wave shield and the cloak can create calm free surfaces within their inner domains. In addition, the cloak effectively suppresses the outgoing scattering waves and reduces the resultant wave drift force.

We conduct direct numerical simulations (DNS) to investigate the attenuation of turbulence in a periodic cube due to the addition of prolate spheroidal solid particles. Even with a dilute volume fraction of $O(10^{-2})$, particles can drastically attenuate the turbulence. Our DNS show that the turbulent kinetic energy reduces more significantly when the particles’ Stokes number is larger, size is smaller or aspect ratio is larger. We can explain these results based on the formula proposed by Oka and Goto (2022 J. Fluid Mech. 949, A45), which relates the turbulence attenuation rate to the energy dissipation rate $\epsilon _p$ around particles. More precisely, under the condition that the volume fraction of particles is fixed, $\epsilon _p$ is larger when the Stokes number and, therefore, the relative velocity between fluid and particles are larger, the particle size is smaller or the aspect ratio is larger. These results also imply that the rotation of the anisotropic particles plays only a limited role in the attenuation of turbulence when the Stokes number of particles is sufficiently large, because the main cause of the attenuation is the relative translational velocity between fluid and particles.

Here we evaluate the skin coefficient of friction for steady turbulent radial wall jets across smooth and rough surfaces. Although the Colebrook equation has been used successfully for many decades to evaluate friction factors for flows through smooth and rough pipes, how roughness affects the skin friction coefficient for steady turbulent radial wall jets remains unclear. Here we explore a Colebrook-type equation for skin friction coefficients associated with single-phase turbulent radial wall jets arising from orthogonally impinging circular jets. The fully iterative solution, based on well-established concepts of turbulent wall-bounded flow, is presented along with a power-law approximation and a non-iterative approximation for the friction coefficient derived therefrom. We find the skin coefficient of friction defined on the peak radial velocity to be a function of position over rough but not smooth surfaces in contrast to pipe friction factors that remain independent of axial position. These results follow expected trends, explain prior heterogeneity in power-law expressions for the skin friction coefficient and have significant implications for the industrial use of jets in mixing vessels.

In Rayleigh–Bénard convection and Taylor–Couette flow cellular patterns emerge at the onset of instability and persist as large-scale coherent structures in the turbulent regime. Their long-term dynamics has been thoroughly characterised and modelled for the case of turbulent convection, whereas turbulent Taylor rolls have received much less attention. Here we present direct numerical simulations of axisymmetric Taylor–Couette flow in the corotating regime and reveal a transition to spatio–temporal chaos as the system size increases. Beyond this transition, Taylor rolls suddenly undergo erratic drifts evolving on a very slow time scale. We estimate an effective diffusion coefficient for the drift and compare the dynamics with analogous motions in Rayleigh–Bénard convection and Poiseuille flow, suggesting that this spontaneous diffusive displacement of large coherent structures is common among different types of wall-bounded turbulent flows.

Wind turbines operate in the atmospheric boundary layer (ABL), where Coriolis effects are present. As wind turbines with larger rotor diameters are deployed, the wake structures that they create in the ABL also increase in length. Contemporary utility-scale wind turbines operate at rotor diameter-based Rossby numbers, the non-dimensional ratio between inertial and Coriolis forces, of $\mathcal {O}(100)$ where Coriolis effects become increasingly relevant. Coriolis forces provide a direct forcing on the wake, but also affect the ABL base flow, which indirectly influences wake evolution. These effects may constructively or destructively interfere because both the magnitude and sign of the direct and indirect Coriolis effects depend on the Rossby number, turbulence and buoyancy effects in the ABL. Using large eddy simulations, we investigate wake evolution over a wide range of Rossby numbers relevant to offshore wind turbines. Through an analysis of the streamwise and lateral momentum budgets, we show that Coriolis effects have a small impact on the wake recovery rate, but Coriolis effects induce significant wake deflections which can be parsed into two regimes. For high Rossby numbers (weak Coriolis forcing), wakes deflect clockwise in the northern hemisphere. By contrast, for low Rossby numbers (strong Coriolis forcing), wakes deflect anti-clockwise. Decreasing the Rossby number results in increasingly anti-clockwise wake deflections. The transition point between clockwise and anti-clockwise deflection depends on the direct Coriolis forcing, pressure gradients and turbulent fluxes in the wake. At a Rossby number of 125, Coriolis deflections are comparable to wake deflections induced by ${\sim} 20^{\circ }$ of yaw misalignment.

Lift and drag forces on moving intruders in flowing granular materials are of fundamental interest but have not yet been fully characterized. Drag on an intruder in granular shear flow has been studied almost exclusively for the intruder moving across flow streamlines, and the few studies of the lift explore a relatively limited range of parameters. Here, we use discrete element method simulations to measure the lift force, $F_{{L}}$, and the drag force on a spherical intruder in a uniformly sheared bed of smaller spheres for a range of streamwise intruder slip velocities, $u_{{s}}$. The streamwise drag matches the previously characterized Stokes-like cross-flow drag. However, $F_{{L}}$ in granular shear flow acts in the opposite direction to the Saffman lift in a sheared fluid at low $u_{{s}}$, reaches a maximum value and then decreases with increasing $u_{{s}}$, eventually reversing direction. This non-monotonic response holds over a range of flow conditions, and the $F_{{L}}$ versus $u_{{s}}$ data collapse when both quantities are scaled using the particle size, shear rate and overburden pressure. Analogous fluid simulations demonstrate that the flow around the intruder particle is similar in the granular and fluid cases. However, the shear stress on the granular intruder is notably less than that in a fluid shear flow. This difference, combined with a void behind the intruder in granular flow in which the stresses are zero, significantly changes the lift-force-inducing stresses acting on the intruder between the granular and fluid cases.

We study the dynamics of a thin liquid sheet that flows upwards along the sides of a vertically aligned, impacting plate. Upon impact of the vertical solid plate onto a liquid pool, the liquid film is ejected and subsequently continues to flow over the solid surface while the plate enters the water. With increasing impact velocity, the liquid film is observed to rise up faster and higher. We focus on the time evolution of the liquid film height and the thickness of its upper rim and discuss their dynamics in detail. Similar to findings in previous literature on sheet fragmentation during drop impact, we find the rim thickness to be governed by the local instantaneous capillary number based on gravity and the deceleration of the liquid sheet, showing that the retraction of the rim is primarily due to capillarity. In contrast, for the liquid film height, we demonstrate that the viscous dissipation in the thin boundary layer is the dominant factor for the vertical deceleration of the liquid sheet, by modelling the time evolution of the film height and showing that the influences of capillarity, gravity and deceleration due to the air phase are all negligible compared with the viscous term. Finally, we introduce characteristic viscous time and length scales based on the initial rim thickness and show that the maximum height of the film and the corresponding time can be determined from these viscous scales.

The real-fluid effect induced by large density variation at supercritical pressure (SCP) modulates the turbulent dynamics and heat transfer, and poses challenges to existing turbulence models that are based on ideal-gas conditions. This study conducts direct numerical simulations of fully developed channel flows at SCP, with the upper and lower channel walls being isothermally heated and cooled, respectively. Emphasis is placed on examining the effects of various levels of density variations on near-wall turbulence as well as turbulent heat transfer by changing wall temperatures. The results show that the density fluctuation significantly impacts both first-order and second-order turbulence statistics near the heated wall owing to the close vicinity of pseudo-boiling point. Such real-fluid impact increases substantially with increasing density ratio, and tends to weaken the turbulent kinetic energy by damping turbulence production, while simultaneously inducing an additional turbulent mass flux that partially offsets this reduction. Detailed quadrant analysis reveals that the ‘ejection’ events dominate diverse effects of density fluctuation on Reynolds shear stresses, with density fluctuation contributing positively on the cooled wall side, and negatively on the heated wall side. Regarding the turbulent heat transfer, density fluctuation enhances the enthalpy–pressure–gradient correlation, tending to weaken the turbulent heat flux, which is slightly compensated by additional terms induced by density fluctuations. The overall negative contribution of density fluctuation to turbulent heat flux stems primarily from ‘hot ejection’ motions. Instantaneous flow characteristics provide additional support for these findings. Additionally, the mechanisms by which density fluctuations affect Reynolds shear stress and turbulent heat flux could also be extended to the skin friction coefficient and Nusselt number, respectively.