This paper investigates the shock-induced instability of the interfaces between gases and dense granular media with finite length via the coarse-grained compressible computational fluid dynamics–discrete parcel method. Despite generating a typical spike-bubble structure reminiscent of the Richtmyer–Meshkov instability (RMI), the shock-driven granular instability (SDGI) is governed by fundamentally different mechanisms. Unlike the RMI arising from baroclinic vorticity deposition on the interface, the SDGI is closely associated with the interfacial and bulk granular dynamics, which evolve with the transient coupling between particles and gases. Consequently, the SDGI follows a growth law distinctly different from that of the RMI, namely a semilinear slow regime followed by an exponentially expedited regime and a quadratic asymptotic regime. We further establish the instability criteria of the SDGI for granular media with infinite and finite lengths, which do not exist in the RMI. A scaling growth law of the SDGI for dense granular media with finite length is derived by normalizing the time with the rarefaction propagation time, which successfully collapses the data from cases with varying shock strength, particle column length and particle volume fraction and ought to hold for granular media with varying particle parameters. The effect of the initial perturbation magnitude can be properly considered in the scaling growth law by incorporating it into the length normalization.

New insight into the contribution of the microscale vortex evolution to convection heat transfer in porous media is presented in this paper. The objective is to determine how the microscale vortices influence convection heat transfer in turbulent flow inside porous media. The microscale temperature distribution is analysed using flow visualization in two dimensions using streamlines and in three dimensions using the Q-criterion. The pertinent observations are supplemented with a comparison of surface skin friction and heat transfer using: (i) surface skin-friction lines and (ii) the joint probability density function of the pressure and skin-friction coefficients, along with the Nusselt number. The microscale flow phenomena observed are corroborated with the features of the frequency spectra of the drag coefficient and macroscale Nusselt number. The large eddy simulation technique is used in this study to investigate the flow field inside a periodic porous medium. The Reynolds numbers of the flow are 300 and 500. The porous medium consists of solid obstacles in the shape of square and circular cylinders. Two distinct flow regimes are represented by using the porosities of 0.50 and 0.87. The results show that the surface Nusselt number distribution is dependent on whether the micro-vortices are attached to or detached from the surface of the obstacle. The spectra of the macroscale Nusselt number and the pressure drag are similar, signifying a correlation between the dynamics of heat transfer and the microscale turbulent structures. Both vortex shedding and secondary flow instabilities are observed that significantly influence the Nusselt number. The fundamental insight gained in this paper can inform the development of more robust macroscale models of convection heat transfer in turbulent flow in porous media.

The problem of hydroelastic wave diffraction by a surface-piercing vertical circular cylinder mounted on the bottom of an ice-covered channel is considered. The ice sheet is modelled as an elastic thin plate with homogeneous properties, while the linearized velocity potential theory is adopted to describe the motion of the fluid. The solution starts from the Green function satisfying all other boundary conditions apart from that on the body surface. This is obtained through applying a Fourier transform in the longitudinal direction of the channel and adopting an eigenfunction expansion in the vertical direction. The boundary conditions on the side walls and ice edges are imposed through an orthogonal product. Through the Green function, the velocity potential due to a surface-piercing structure with arbitrary shape can be expressed through a source distribution formula derived in this work, in which only integrals over the body surface and its interaction line with the ice sheet need to be retained. For a vertical circular cylinder, the unknown source distribution can be expanded further into a Fourier series in the circumferential direction, and then the analytical solution of the velocity potential can be obtained further. Extensive results and discussions are provided for the hydrodynamic forces and vertical shear forces on the cylinder, as well as the deflection and strain of the ice sheet. In particular, the behaviour of the solution near one of the natural frequencies of the channel is investigated in detail.

Marangoni spreading on thin films is widely observed in nature and applied in industry. It has serious implications for airway drug delivery, especially in surfactant displacement therapy. This paper reports the results of experimental investigations of a surfactant-laden droplet spreading on films made of more viscous Newtonian fluids as well as on films made of viscoelastic fluids. The experiments used particle seeding, the transmission-speckle method and particle tracking velocimetry (PTV) to determine the deformation of the film–droplet interface and to measure velocity fields. Radially aligned patterns were observed on Newtonian films. Similar patterns, but with much smaller wavenumber, were observed on viscoelastic films in combination with rapid azimuthal variations of the film thickness. The Saffman–Taylor instability at the film–droplet interface explains the formation of patterns on a more viscous Newtonian film, and their onset requires exceeding the critical capillary number. The pattern formation on viscoelastic films is correlated with an instability at the film–droplet–air contact line when the liquid is expelled radially by the spreading droplet. PTV revealed azimuthal variations of the velocity field in the vicinity of the contact line. The observed contact line instability is different from previously reported fingering instabilities of Newtonian thin films. A simple scaling law accounting for the Marangoni-stress-induced elastic shear deformation is proposed to describe the flow field in the patterns formed in the viscoelastic films.

Thin, roughly horizontal low-permeability layers are a common form of large-scale heterogeneity in geological porous formations. In this paper, the dynamics of a buoyancy-driven plume in a two-dimensional layered porous medium is studied theoretically, with the aid of high-resolution numerical simulations. The medium is uniform apart from a thin, horizontal layer of a much lower permeability, located a dimensionless distance $L\gg 1$ below the dense plume source. If the dimensionless thickness $2\unicode[STIX]{x1D700}L$ and permeability $\unicode[STIX]{x1D6F1}$ of the low-permeability layer are small, the effect of the layer is found to be well parameterized by its impedance $\unicode[STIX]{x1D6FA}=2\unicode[STIX]{x1D700}L/\unicode[STIX]{x1D6F1}$. Five different regimes of flow are identified and characterized. For $\unicode[STIX]{x1D6FA}\ll L^{1/3}$, the layer has no effect on the plume, but as $\unicode[STIX]{x1D6FA}$ is increased the plume widens and spreads over the layer as a gravity current. For still larger $\unicode[STIX]{x1D6FA}$, the flow becomes destabilized by convective instabilities both below and above the layer, until, for $\unicode[STIX]{x1D6FA}\gg L$, the spread of the plume is dominated by convective mixing and buoyancy is transported across the layer by diffusion alone. Analytical models for the spread of the plume over the layer in the various different regimes are presented.

The present work studies the nonlinear dynamics of a shear layer, driven by a body force and confined between parallel walls, a simplified setting to study transitional and turbulent shear layers. It was introduced by Nogueira & Cavalieri (J. Fluid Mech., vol. 907, 2021, A32), and is here studied using a reduced-order model based on a Galerkin projection of the Navier–Stokes system. By considering a confined shear layer with free-slip boundary conditions on the walls, periodic boundary conditions in streamwise and spanwise directions may be used, simplifying the system and enabling the use of methods of dynamical systems theory. A basis of eight modes is used in the Galerkin projection, representing the mean flow, Kelvin–Helmholtz vortices, rolls, streaks and oblique waves, structures observed in the cited work, and also present in shear layers and jets. A dynamical system is obtained, and its transition to chaos is studied. Increasing Reynolds number $Re$ leads to pitchfork and Hopf bifurcations, and the latter leads to a limit cycle with amplitude modulation of vortices, as in the direct numerical simulations by Nogueira & Cavalieri. Further increase of $Re$ leads to the appearance of a chaotic saddle, followed by the emergence of quasi-periodic and chaotic attractors. The chaotic attractors suffer a merging crisis for higher $Re$, leading to a chaotic dynamics with amplitude modulation and phase jumps of vortices. This is reminiscent of observations of coherent structures in turbulent jets, suggesting that the model represents a dynamics consistent with features of shear layers and jets.

The effects of insoluble surfactants, satisfying a Langmuir equation of state, on transverse Stokes flow over a superhydrophobic surface of unidirectional grooves with flat menisci are examined. The phenomenon of surface immobilisation, whereby surfactants cause part or all of the Cassie-state menisci to become effectively no-slip zones thereby degrading the slip properties of the surface, is of primary interest. The study employs a combined analytical and numerical approach allowing an exploration of surfactant effects over the full range of surface Péclet numbers, Marangoni numbers and surfactant loads. For small surface Péclet and Marangoni numbers, perturbation theory is used to gain basic insights into the physical mechanisms at work. That analysis also provides checks on a robust numerical scheme, built around a complex variable formulation of the problem, used to compute solutions across a wide range of non-dimensional parameter values. Two distinct mechanisms are found to be responsible for surface immobilisation. In the first, most commonly seen at higher surface Péclet numbers, a stagnant cap forms because swept surfactant immobilises a section of the meniscus before any portion of the meniscus reaches maximum packing. Such a cap exists even for a linear equation of state and grows in length with increasing Marangoni number. A second immobilisation mechanism is associated with the nonlinear equation of state: an immobilised region forms because the surfactant concentration reaches its maximum value near the downstream edge of the meniscus. Immobilisation of the latter form can occur at much lower surface Péclet numbers, even if the Marangoni number is small, as long as there is sufficient surfactant in the system. The study enhances understanding of how insoluble surfactants can degrade slip over superhydrophobic surfaces.

It is well known that the Poiseuille mass flow rate along microchannels shows a stationary point as the fluid density decreases, referred to as the Knudsen minimum. Surprisingly, if the flow characteristic length is comparable to the molecular size, the Knudsen minimum disappears, as reported for the first time by Wu et al. (J. Fluid Mech., vol. 794, 2016, pp. 252–266). However, there is still no fundamental understanding why the mass flow rate monotonically increases throughout the entire range of flow regimes. Although diffusion is believed to dominate the fluid transport at the nanoscale, here we show that the Fick's first law fails in capturing this behaviour, and so diffusion alone is insufficient to explain this confined flow phenomenon. Rather, we show that the Knudsen minimum disappears in tight confinements because the decay of the mass flow rate due to the decreasing density effects is overcome by the enhancing contribution to the flow provided by the fluid velocity slip at the wall.

Topological transition and helicity conversion of vortex torus knots and links are studied using direct numerical simulations of the incompressible Navier–Stokes equations. We find three topological transitional routes (viz. merging, reconnection and transition to turbulence) in the evolution of vortex knots and links over a range of torus aspect ratios and winding numbers. The topological transition depends not only on the initial topology but also on the initial geometry of knots/links. For small torus aspect ratios, the initially knotted or linked vortex tube rapidly merges into a vortex ring with a complete helicity conversion from the writhe and link components to the twist. For large torus aspect ratios, the vortex knot or link is untied into upper and lower coiled loops via the first vortex reconnection, with a helicity fluctuation including loss of writhe and link, and generation of twist. Then, the relatively unstable lower loop can undergo a secondary reconnection to split into multiple small vortices with a similar helicity fluctuation. Surprisingly, for moderate torus aspect ratios, the incomplete reconnection of tangled vortex loops together with strong vortex interactions triggers transition to turbulence, in which the topological helicity decomposition fails due to the breakdown of vortex core lines.

An analytical model is developed which explores the impact of irregular sea-floor roughness on large-scale oceanic flows. The previously reported asymptotic ‘sandpaper’ theory of flow-topography interaction represents relatively swift currents and exhibits singular behaviour in the weak flow limit. The present investigation systematically spans a wider parameter space and identifies the principal dissimilarities in the topographic regulation of slow and fast currents. The fast flows are controlled by the Reynolds stresses produced by topographically generated eddies. In contrast, relatively weak flows are more affected by the eddy-induced bottom form drag. The asymptotic models for fast and slow currents are then combined to arrive at a concise description of flow forcing by small-scale topography in homogeneous and multilayer models. The proposed closure is validated by comparing corresponding topography-resolving and parametric simulations.

To isolate the multiscale dynamics of the logarithmic layer of wall-bounded turbulent flows, a novel numerical experiment is conducted in which the mean tangential Reynolds stress is eliminated except in a subregion corresponding to the typical location of the logarithmic layer in channels. Various statistical comparisons against channel flow databases show that, despite some differences, this modified flow system reproduces the kinematics and dynamics of natural logarithmic layers well, even in the absence of a buffer and an outer zone. This supports the previous idea that the logarithmic layer has its own autonomous dynamics. In particular, the results suggest that the mean velocity gradient and the wall-parallel scale of the largest eddies are determined by the height of the tallest momentum-transferring motions, which implies that the very large-scale motions of wall-bounded flows are not an intrinsic part of the logarithmic-layer dynamics. Using a similar set-up, an isolated layer with a constant total stress, which represents the logarithmic layer without a driving force, is simulated and examined.

We interpret the Taylor–Green cellular vortex model in terms of the Kolmogorov length and velocity scales, in order to study the balance between aggregation and breakup of cohesive sediment in fine-scale turbulence. One-way coupled numerical simulations, which capture the effects of cohesive, lubrication and direct contact forces on the flocculation process, reproduce the non-monotonic relationship between the equilibrium floc size and shear rate observed in previous experiments. The one-way coupled results are confirmed by select two-way coupled simulations. Intermediate shear gives rise to the largest flocs, as it promotes preferential concentration of the primary particles without generating sufficiently strong turbulent stresses to break up the emerging aggregates. We find that the optimal intermediate shear rate increases for stronger cohesion and smaller particle-to-fluid density ratios, and we propose a simple model for the equilibrium floc size that agrees well with experimental data reported in the literature.

This paper describes, from a theoretical point of view, the appearance and characteristics of granular roll waves in chute flow, and the maximal size these waves can attain for a given influx of material into the system. Granular roll waves are steady travelling wave solutions of the generalized Saint-Venant equations for flowing granular matter, appearing when the Froude number $Fr$ of the incoming flow exceeds a critical value, $Fr>Fr_{cr}$. We focus upon the phase space of the corresponding dynamical system, where the roll waves take the form of a stable limit cycle around an unstable fixed point; this limit cycle gives precise information on the size and periodicity of the roll wave. It is found that, for any given value of $Fr$, the limit cycle cannot become arbitrarily large because it is constrained by a homoclinic loop in phase space. Roll waves of larger amplitude can be generated by increasing the Froude number $Fr$.