Local shearing motions in turbulence form small-scale shear layers, which are unstable to perturbations at approximately 30 times the Kolmogorov scale. This study conducts direct numerical simulations of passive-scalar mixing layers in a shear-free turbulent front to investigate mixing enhancements induced by such perturbations. The initial turbulent Reynolds number based on the Taylor microscale is $ Re_\lambda = 72$ or 202. The turbulent front develops by entraining outer fluid. Weak sinusoidal velocity perturbations are introduced locally, either inside or outside the turbulent front, or globally throughout the flow. Perturbations at this critical wavelength promote small-scale shear instability, complicating the boundary geometry of the scalar mixing layer at small scales. This increases the fractal dimension and enhances scalar diffusion outward from the scalar mixing layer. Additionally, the promoted instability increases the scalar dissipation rate and turbulent scalar flux at small scales, facilitating faster scalar mixing. The effects manifest locally; external perturbations intensify mixing near the boundary, while internal perturbations affect the entire turbulent region. The impact of perturbations is consistent across different Reynolds numbers when the amplitudes normalised by the Kolmogorov velocity are the same, indicating that even weaker perturbations can enhance scalar mixing at higher Reynolds numbers. The mean scalar dissipation rate increases by up to 50 %, even when the perturbation energy is only 2.5 % of the turbulent kinetic energy. These results underscore the potential to leverage small-scale shear instability for efficient mixing enhancement in applications such as chemically reacting flows.

Using clean numerical simulation (CNS) in which artificial numerical noise is negligible over a finite, sufficiently long interval of time, we provide evidence, for the first time, that artificial numerical noise in direct numerical simulation (DNS) of turbulence is approximately equivalent to thermal fluctuation and/or stochastic environmental noise. This confers physical significance on the artificial numerical noise of DNS of the Navier–Stokes equations. As a result, DNS on a fine mesh should correspond to turbulence under small internal/external physical disturbance, whereas DNS on a sparse mesh corresponds to turbulent flow under large physical disturbance. The key point is that all of them have physical meanings and so are correct in terms of their deterministic physics, even if their statistics are quite different. This is illustrated herein. Our paper provides a positive viewpoint regarding the presence of artificial numerical noise in DNS.

We study the onset of spontaneous dynamics in the follower force model of an active filament, wherein a slender elastic filament in a viscous liquid is clamped normal to a wall at one end and subjected to a tangential compressive force at the other. Clarke et al. (Phys. Rev. Fluids, vol. 9, 2024, 073101) recently conducted a thorough investigation of this model using methods of computational dynamical systems; inter alia, they showed that the filament first loses stability via a supercritical double-Hopf bifurcation, with periodic ‘planar-beating’ states (unstable) and ‘whirling’ states (stable) simultaneously emerging at the critical follower-force value. We complement their numerical study by carrying out a weakly nonlinear analysis close to this unconventional bifurcation, using the method of multiple scales. The main outcome is an ‘amplitude equation’ governing the slow modulation of small-magnitude oscillations of the filament in that regime. Analysis of this reduced-order model provides insights into the onset of spontaneous dynamics, including the creation of the nonlinear whirling states from particular superpositions of linear planar-beating modes as well as the selection of whirling over planar beating in three-dimensional scenarios.

A point force acting on a Brinkman fluid in confinement is always counterbalanced by the force on the porous medium, the force on the walls and the stress at open boundaries. We discuss the distribution of those forces in different geometries: a long pipe, a medium with a single no-slip planar boundary, a porous sphere with an open boundary and a porous sphere with a no-slip wall. We determine the forces using the Lorentz reciprocal theorem and additionally validate the results with explicit analytical flow solutions. We discuss the relevance of our findings for cellular processes such as cytoplasmic streaming and centrosome positioning.

Particle-laden horizontal turbulent pipe flow is studied experimentally in the two-way coupling regime with a focus on delineating the effects of particle-to-fluid density ratio $\rho _{p}/\rho _{f}=1$ and 1.05 on the fluid and particle statistics. Particle volume fraction $\phi _{v}$ up to $1\,\%$ and viscous Stokes numbers ranging from $St^+ \approx 1.2$ to $St^+ \approx 3.8$ are investigated at friction Reynolds number $Re_\tau \approx 195$ using time-resolved two-dimensional particle image and tracking velocimetry. Substantial differences are observed between the statistics of neutrally buoyant (i.e. $\rho _{p}/\rho _{f}=1$) and denser (i.e. $\rho _{p}/\rho _{f}=1.05$) settling particles (with settling velocities 0.12–0.32 times the friction velocity), which, at most instances, show opposing trends compared to unladen pipe flow statistics. Neutrally buoyant particles show a slightly increased overall drag and suppressed turbulent stresses, but elevated particle–fluid interaction drag and results in elongated turbulent structures compared to the unladen flow, whereas $\rho _{p}/\rho _{f}=1.05$ particles exhibit a slight overall drag reduction even with increased radial turbulent stresses, and shorter streamwise structures compared to the unladen flow. These differences are enhanced with increasing $St^+$ and $\phi _v$, and can be attributed to the small but non-negligible settling velocity of denser particles, which also leads to differing statistics in the upper and lower pipe halves.

We perform simulations of a two-fluid–structure interaction problem involving liquid–gas flow past a fully submerged stationary circular cylinder. Interactions between the liquid–gas interface with finite surface tension and flow disturbances arising from the cylinder induce a variety of interfacial phenomena and wake structures. We map different interface regimes in a parameter space defined by the Bond number $Bo \in [100, 5000]$ and the submergence depth $h/D \in [1, 2.5]$ of the cylinder while keeping the Reynolds (Re) and Weber (We) numbers fixed at 150 and 1000, respectively. The emerging interface features are classified into three distinct regimes: interfacial waves generated by Strouhal vortices, the entrainment of multi-scale gas bubbles and the reduced deformation state. In the interfacial wave regime, we demonstrate that the frequency of transverse interface fluctuations at a specific streamwise location is identical to the vortex shedding frequency. Additionally, the wavelength of interfacial waves is determined by the size of vortex pairs consisting of alternating Strouhal vortices. In the gas entrainment regime at $ Bo = 1000$, our bubble-size distributions reveal that the entrained bubbles have sizes ranging from one to two orders of magnitude smaller than the cylinder. These multi-scale bubbles are formed primarily through plunging and surfing breakers at $h/D = 2.5$. In contrast, at $h/D = 1$, smaller bubbles initially emerge from the breakup of a gas finger. Over time, some of these bubbles grow in size through coalescence cascades. The influence of $ Re \in [50, 150]$ and $ We \in [700, 1100]$ on gas entrainment is quantified in terms of mean bubble size and count. Lastly, we demonstrate how the deformability of the liquid–gas interface drives the hydrodynamic lift force acting on the cylinder. The net downward lift materializes only in the gas entrainment and reduced deformation regimes due to the broken symmetry of the front stagnation point. While our study focuses on two-dimensional simulations, we also provide insights into the three-dimensional gas entrainment mechanism for one of the extreme cases at $h/D = 1$.

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.