Models are developed to grasp the combined effect of rheology and spatial layering on buoyancy-driven dispersion in geologic media. We consider a power-law (PL) or Herschel–Bulkley (HB) constitutive equation for the fluid, and an array of $N$ independent layers in a vertical fracture or porous medium subject to the same upstream overpressure. Under these assumptions, analytical solutions are derived in self-similar form (PL) or based on an expansion (HB) for the nose of single-phase gravity currents advancing into the layers ahead of a pressurized body. The position and size of the body and nose and the shape of the latter are significantly influenced by the interplay of model parameters: flow behaviour index $n$, dimensionless yield stress $\kappa$ for HB fluids, number of layers $N$ and upstream overpressure. It is seen that layering produces (i) a relatively modest increase of the total flow rate with respect to the single layer of equal thickness, and (ii) macro-dispersion at the system scale in addition to local dispersion. The second longitudinal spatial moment of the solute cloud scales with time as $t^{2n/(n+1)}$ for power-law fluids. The macro-dispersion induced by the layering prevails upon local dispersion beyond a threshold time. Theoretical results for the fracture are validated against a set of experiments conducted within a Hele-Shaw cell consisting of six layers. Comparison with experimental results shows that the proposed model is able to capture the propagation of the current and the macro-dispersion due to the velocity difference between layers, typically over-predicting the former and under-predicting the latter.

The flow with low shear inside a bladeless mixer is characterized experimentally. This soft mixer, inspired by the precession of the Earth, consists of a cylindrical container rotating around its axis and tilted from the vertical. For low Froude numbers, the free surface remains horizontal, thus generating a forcing on the tilted rotating fluid. As in the case of a precessing cylinder, this forcing excites global inertial modes (Kelvin modes) which become resonant when the height of fluid is equal to a multiple of a half-wavelength. Ekman pumping saturates the amplitude of the mode at a value proportional to the square root of the Reynolds number. For sufficiently large tilt angles and Reynolds numbers, the global mode destabilizes via a parametric triadic instability involving two additional Kelvin modes. The viscous threshold of the instability can be predicted analytically with no fitting parameter and is in excellent agreement with the experimental results. This instability generates a strong mixing which is as efficient as the one achieved using a classical Rushton turbine, but with a shear 20 times smaller. This simple bladeless mixer is thus an excellent candidate for large scale bioreactors where mixing is needed to enhance gas exchanges but where shear is harmful for fragile cells. Preliminary results obtained for the growth of microalgae (dinoflagellates) in such photobioreactors suggest that it could be a technological breakthrough in biotechnologies.

Experimental methods are employed to investigate vortex rings generated by impulsively emitting pressurised air through a rectangular outlet of high aspect ratio into quiescent surroundings. The flow is characterised by a rapid transverse expansion as thick-cored, almost spherical vortex rings with a diameter more than 40 times the outlet width and entrainment rates of $\eta >0.9$ are generated. They continue to absorb vorticity far beyond the universal formation time of $t^*\approx 4$ applicable to axisymmetric parallel starting jets introduced by Gharib et al. (J. Fluid Mech., vol. 360, 1998, pp. 121–140). Here, the maximum circulation and the corresponding formation time depend on the magnitude of over-pressure in the outlet plane. After momentarily reaching a non-dimensional energy close to or even below a value of $\alpha =0.16$ associated with Hill's spherical vortex, vorticity is continuously shed into a trailing jet, and the vortex rings evolve into unsteady thinner-core states. No separation between the vortex ring and the trailing jet (pinch-off) is observed. The present study provides new insights into the flow physics of non-parallel planar starting jets that significantly differ from parallel starting flows investigated previously. The potential for active flow control applications is discussed.

Premixed flame propagation is a rich interface problem. Instabilities and nonlinearities lead to the formation of cusps pointing toward the burnt gas. These cusps, which undergo complex dynamics, enhance the reaction rate by increasing the flame surface. These crests can be interpreted as pole solutions of the Michelson–Sivashinsky equation that evolve according to ordinary differential equations. Thanks to a quasi-bidimensional experimental facility (a Hele-Shaw burner) we evaluate the accuracy of the description of flame dynamics by elementary interaction between cusps. In particular, we address the time for which a direct comparison between experiments and numerical integration is feasible. The sensitivity to initial conditions and noise is discussed. We demonstrate that at any time of evolution, interesting features can be recovered by describing the flame surface evolution as pole dynamics.

We investigate the transport of size-selected particles suspended in turbulent boundary layers at friction Reynolds numbers up to $Re_\tau = 19\,000$. We use microscopic glass spheres in air, spanning a wide range of viscous Stokes numbers, $St^+ = 18\text {--}870$. These are imaged simultaneously with the flow tracers, and particle image and tracking velocimetry are used to measure the two-phase flow along a wall-normal plane in the logarithmic region. The air flow statistics are not altered by the particles at the present mass loading. In comparison to the classic equilibrium solution, the particle concentration profiles display weaker wall-normal gradients. This is shown to be an effect of particle inertia: this manifests itself through different mechanisms in different strata of the flow, and the effects on the concentration are captured by a three-layer parameterization of the profile. The particles lag the fluid across the boundary layer, with a mean slip velocity of the order of the friction velocity and increasing with particle inertia. Near the wall this lag is mainly due to the instantaneous slip of the particles relative to the surrounding fluid, while away from the wall the leading cause is the preferential sampling of low-speed fluid regions. Larger particles (in the size range of sand, as opposed to dust) display a qualitatively different behaviour, likely because of nonlinear drag effects. All considered particles oversample specific regions of the fluid flow: they favour regions of negative streamwise fluctuations, especially ejection events, and are likely to be found about the centre of strain cells with backward-leaning compressive axis and forward-leaning extensive axis. This pattern is visible for a wide range of Stokes numbers, underscoring the multi-scale nature of preferential concentration. The present findings highlight how high-Reynolds-number features of turbulent boundary layers impact the transport of suspended inertial particles, and thus are especially relevant to environmental and geophysical flows.

In this study, direct numerical simulation of the dispersion and motion of inertial particles in a spatially developing compressible turbulent boundary layer at a Mach number of 2 is performed with the Eulerian–Lagrangian point particle method. Two cases are simulated with different particle diameters (Stokes number) but identical inflow particle numbers. Statistical characteristics and preferential accumulation of particles in the very-near-wall and wake regions are systematically investigated through conditional sampling and mechanism analysis. The results reveal that particle streaks are formed in low-speed regions near the wall because of the influence of dominating ejection events. After normalization with the local minimum particle number density, the particle number density profile reveals a self-similar feature at different streamwise positions. Compared with small particles, large particles are more significantly influenced by turbophoresis and demonstrate stronger preferential accumulation; thus, more large particles are clustered in the near-wall regions and the deviation between the mean velocities of the particle and the fluid increases. With the wall effect, both large and small particles are selectively accumulated in high-vorticity regions in the buffer layer in contrast to turbulence without walls. In comparison with incompressible wall-bounded turbulence, a new mechanism for particle preferential accumulation based on local fluid density is discovered. Large particles are located in low-density regions in the inner zones and high-density regions in the outer zones. Nevertheless, small particles remain located in regions with low fluid density, as illustrated by the mechanism analysis of particle dilatation.

We extend upon the known flow transitions in neutrally buoyant particle-laden Taylor–Couette flows by accessing higher suspension Reynolds numbers $(Re_{{susp}} \sim O(10^3))$ in a geometry with radius ratio $\eta = 0.917$ and aspect ratio $\varGamma = 21.67$. Flow transitions for several particle volume fractions ($0 \leq \phi \leq 0.40$) are investigated by means of flow visualization experiments, in a flow driven by a rotating inner cylinder. Despite higher effective ramp rates, we observe non-axisymmetric patterns, such as spirals, in the presence of particles. A novel observation in our experiments is the azimuthally localized wavy vortex flow, characterized by waviness present on a fraction of the otherwise axisymmetric Taylor vortices. The existence of this flow state suggests that in addition to the already established, destabilizing effect of particles, they may also inhibit the growth of instabilities. Flow topologies corresponding to higher-order transitions in particle-laden suspensions appear to be qualitatively similar to those observed in single-phase flows. A key difference, however, is the visible reduction in the appearance of a second, incommensurate frequency at higher particle loadings, which could have implications for the onset of chaos. Simultaneous torque measurements allow us to estimate an empirical scaling law between the Nusselt number ($Nu_{\omega }$), the Taylor number ($Ta$) and the relative viscosity ($\chi ^{e}): Nu_{\omega } \propto Ta^{0.24} \chi ^{e \, 0.41}$. The scaling exponent of $Ta$ is non-trivially independent of the particle loading. Apparently, particles do not trigger a qualitative change in the nature of angular momentum transfer between the cylinders.

Adaptive control of flow separation based on online dynamic mode decomposition (DMD) is formulated and implemented on a canonical separated laminar boundary layer via a pulse-modulated zero-net mass-flux jet actuator located just upstream of separation. Using a linear array of thirteen flush-mounted microphones, dynamical characteristics of the separated flow subjected to forcing are extracted by online DMD. This method provides updates of the modal characteristics of the separated flow while forcing is applied at a rate commensurate with the characteristic time scales of the flow. In particular, online DMD provides a time-varying linear estimate of the nonlinear evolution of the controlled flow without any prior knowledge. Using this adaptive model, feedback control is then implemented in which the linear quadratic regulator gains are computed recursively. This physics-based, autonomous approach results in more efficient flow reattachment compared with commensurate open-loop control. Four Reynolds numbers are tested to assess robustness, $Re_c = 0.9\times 10^5$, $Re_c = 1\times 10^5$, $Re_c = 1.1\times 10^5$ and $Re_c = 1.25\times 10^5$. All controlled cases exhibit a significant reduction in mean separation bubble height, requiring approximately 10 characteristic time periods to establish control.

Submesoscale processes along coastal boundaries provide a potential mechanism for the dissipation of mesoscale kinetic energy in the ocean. Since these processes occur on scales not generally resolved by global ocean models, a physically motivated parametrisation is required to accurately describe their effects. Submesoscale dynamics is characterised by strong turbulent mixing, nonlinearity and topographic effects; all of which significantly modify the flow. A major component of the submesoscale boundary response to mesoscale forcing is the Kelvin – or coastally trapped – wave field, which has been shown to transport energy over large distances. This paper thus examines the influence of vertical mixing, nonlinearity and steep-slope topography on baroclinic Kelvin waves with the aim of assessing the importance of these effects. We consider the limit of a steep coastal boundary, weak mixing and weak nonlinearity and perform an asymptotic analysis to determine the modification of the classical Kelvin wave solution by these effects. Linear and nonlinear solutions are given and different mixing limits are discussed and compared with previous work. We find that vertical mixing acts to damp slowly propagating Kelvin waves while nonlinearity can cause wave breaking which may be important for fast waves. Steep-slope topography acts to modify the wave speed and structure consistent with previous work.

Recent experimental and computational studies indicate that near-wall turbulent flows can be characterized by universal small-scale autonomous dynamics that is modulated by large-scale structures. We formulate numerical simulations of near-wall turbulence in a small domain localized to the boundary, whose size scales in viscous units. To mimic the environment in which the near-wall turbulence evolves, the formulation accounts for the flux of mean momentum through the upper boundary of the domain. Comparisons of the model's two-dimensional energy spectra and low-order single-point statistics with the corresponding quantities computed from direct numerical simulations indicate that it successfully captures the dynamics of the small-scale near-wall turbulence.

This paper investigates the use of inviscid flow theory accompanied by surfaces of discontinuity as a means of representing viscous effects. The problem studied is that of starting flow separation past a sharp wedge. We use the vortex-entrainment sheet model of DeVoria & Mohseni (J. Fluid Mech., vol. 866, 2019, pp. 660–688) to augment the set of self-similar solutions with zero entrainment as calculated by Pullin (J. Fluid Mech., vol. 88, 1978, pp. 401–430). Even under the constraints of similarity, the inclusion of entrainment allows for several new degrees of freedom, which correspond to different classes of boundary conditions, and thus solutions, that are excluded by classical potential models. Some computed examples are presented and compared to a previous experimental study. The results offer encouraging evidence that viscous or finite Reynolds number effects can, in an integrated sense, be captured by an inviscid model with singularity distributions. A normal boundary condition that contains the information pertaining to the entrainment must be supplied and represents the trade-off in surrendering the Navier–Stokes equations for the lower-order inviscid model.

We analyse the near-rolling motion of non-wetting droplets down a gently inclined plane. Inspired by the scaling analysis of Mahadevan & Pomeau (Phys. Fluids, vol. 11, 1999, pp. 2449–2453), we focus upon the limit of small Bond numbers, where the drop shape is nearly spherical and the internal flow is approximately a rigid-body rotation except close to the flat spot at the base of the drop. In that region, where the fluid interface appears flat, we obtain an analytical approximation for the flow field. By evaluating the dissipation associated with that flow we obtain a closed-form approximation for the drop speed. This approximation reveals that the missing prefactor in the Mahadevan–Pomeau scaling law is $(3{\rm \pi} /16)\sqrt {3/2}\approx 0.72$ – in good agreement with experiments. An unexpected feature of the flow field is that it happens to satisfy the no-slip and shear-free conditions simultaneously over both the solid flat spot and the mobile fluid interface in its vicinity. Furthermore, we show that close to the near-circular contact line the velocity field lies primarily in the plane locally normal to the contact line; it is analogous there to the local solution in the comparable problem of a two-dimensional rolling drop. This analogy breaks down near the two points where the contact line propagates parallel to itself, the local flow being there genuinely three dimensional. These observations illuminate a unique ‘peeling’ mechanism by which a rolling droplet avoids the familiar non-integrable stress singularity at a moving contact line.

The effective dilatational and shear viscosities of a particle-laden fluid interface are computed in the dilute limit under the assumption of an asymptotically vanishing viscosity ratio between the two fluids. Spherical particles with a given contact angle of the fluid interface at the particle surface are considered. A planar fluid interface and a small Reynolds number are assumed. The theoretical analysis is based on a domain perturbation expansion in the deviation of the contact angle from $90^{\circ }$ up to the second order. The resulting effective dilatational viscosity shows a stronger dependence on the contact angle than the effective shear viscosity, and its magnitude is larger for all contact angles. The limits of validity of the theory are discussed.

The instability of the flow in a two-dimensional meandering channel of slowly varying depth is considered. The flow is characterised by $\delta$ the typical slope of the channel walls and the modified Reynolds number $R_m$ which is the usual Reynolds number multiplied by $\delta$. The modified Reynolds number is shown to be the appropriate parameter controlling the instability of the flow to streamwise vortices periodic in the spanwise direction. In particular, channels periodic in the streamwise direction are considered and it is found that the most unstable mode can correspond to either a subharmonic or synchronous disturbance. The instability problem at finite $R_m$ is discussed first and then the inviscid and large wavenumber regimes are discussed in detail. The instability is shown to be a hybrid form of centrifugal instability having properties of both Görtler vortices and a parametric resonance usually referred to as an elliptic instability. The limiting case of small wall modulation amplitudes is investigated and the results suggest that at small amplitudes the subharmonic mode is always dominant.

Wedge-induced oblique detonation waves (ODWs) have been studied widely, but their interactions with complicated geometries have not been fully addressed. In this study, we investigate ODW interaction with a deflected upper corner due to confinement change upstream of the ODW. Numerical simulations are conducted using the reactive Euler equations with a two-step induction–reaction kinetic model. Two ODWs without the upper wall deflection are first simulated to resolve the basic structures with inflow Mach numbers $M_0 = 6$ and 7. Thereafter, we introduce a deflected upper confinement, resulting in a new wave configuration. This wave is characterized by a post-turning, triangular recirculation zone coupled with a gaseous wedge connecting the deflection point and ODW surface. A parametric study is performed to analyse the effects of the deflection location, deflection angle and activation energy of the heat release reaction. The results reveal that the wave configuration is due to the evolution of ODW decoupling in an expanded supersonic flow. We further study the surface stability and structural unsteadiness arising for $M_0 = 6$. Upstream-travelling transverse waves are observed for the first time, and effects of different parameters on the surface instability are analysed via fast Fourier transforms. Two destabilizing mechanisms of ODW structures are proposed, one from the post-surface thermal choking and the other from the enhanced surface instability.

A growing body of studies in wall-bounded turbulence has shown that the generation of wall-shear stress fluctuations is directly connected with outer-layer large-scale motions. In the present study, we investigate the scale-based structures of the streamwise wall-shear stress fluctuations ($\tau _x'$) in turbulent channel flows at different Reynolds numbers. The wall-shear stress structures are identified using a two-dimensional clustering methodology, and two indispensable factors, scale and sign, are considered for the analysis. The structures are classified into positive and negative families according to the sign of $\tau _x'$. The statistical properties of the structures, including geometrical characteristics, spatial distribution, population density, fluctuating intensity, and correlations with outer motions are comprehensively investigated. Particular attention is paid to the asymmetries between positive and negative structures and their connection with wall-attached energy-containing eddies. In virtue of our results, only the large-scale structures of negative $\tau _x'$ contain the footprints of the inactive part of wall-attached eddies populating the logarithmic region.

We propose a linear asymptotic theory to describe the propagation of planar detonation fronts through heterogeneous mixtures of reactive gases consisting of random fluctuations in the fuel mass fraction. The analysis starts with the derivation of the transfer functions that relate the upstream fuel mass fraction inhomogeneities with the burnt-gas perturbations via normal mode analysis. These results are then used in a Fourier analysis of a detonation wave interacting with two- and three-dimensional isotropic heterogeneous fields. This yields integral formulae for the turbulent kinetic energy, sonic energy and averaged vorticity and entropy production rates. Second-order corrections for the turbulent Rankine–Hugoniot conditions are also obtained, along with analytical expressions for the deviation of the detonation velocity with respect to that of the equivalent homogeneous mixture. Upstream inhomogeneities are found to speed up the detonation front in the vast majority of scenarios studied, with a velocity amplification factor that depends on the properties of the fuel–air mixture, particularly on the variation of the density and the heat release with the fuel mass fraction.

Wave shape (i.e. skewness or asymmetry) plays an important role in beach morphology evolution, remote sensing and ship safety. The wind's influence on ocean waves has been extensively studied theoretically in the context of growth, but most theories are phase averaged and cannot predict wave shape. Most laboratory and numerical studies similarly focus on wave growth. A few laboratory experiments have demonstrated that wind can change wave shape, and two-phase numerical simulations have also noted wind-induced wave-shape changes. However, the wind's effect on wave shape is poorly understood, and no theory for it exists. For weakly nonlinear waves, wave-shape parameters are the phase of the first harmonic relative to the primary frequency (or harmonic phase HP, zero for a Stokes wave) and relative amplitude of the first harmonic to the primary wave. Here, surface pressure profiles (denoted Jeffreys, Miles and generalized Miles) are prescribed based on wind–wave generation theories. Theoretical solutions are derived for quasi-periodic progressive waves and the wind-induced changes to the HP, relative harmonic amplitude, as well as the already known phase speed changes and growth rates. The wave-shape parameters depend upon the chosen surface pressure profile, pressure magnitude and phase relative to the wave profile and non-dimensional depth. Wave asymmetry is linked to the non-dimensional growth rate. Atmospheric large eddy simulations constrain pressure profile parameters. The HP predictions are qualitatively consistent with laboratory observations. This theory, together with the HP and relative harmonic amplitude observables, can provide insight into the actual wave surface pressure profile.

In this study, identical experiments of bottom-cooled solidification fluidic mixtures that exhibit faceted and dendritic microstructures were performed. The strength of compositional convection, created due to the rejection of a lighter solute, was correlated with the solidifying microstructure morphology via separate Rayleigh numbers in the mushy and bulk-fluid zones. While the bulk fluid in dendritic solidification experienced a monotonic decrease in the temperature, solidification of the faceted case revealed an unconventional, anomalous temperature rise in the bulk liquid after the formation of a eutectic solid. Based on the bulk-liquid temperatures, three distinct regimes of heat transfer were observed in the liquid, namely, convection-dominated, transition and conduction-dominated. The observations were analysed and verified with the help of different initial compositions and cooling conditions, as well as other mixtures that form faceted morphology upon freezing. The observed temperature rise was further ascertained by performing an energy balance in an indicative control volume ahead of the solid–liquid interface. The plausible mechanism of permeability-driven flow causing a gain in the temperature of the liquid during freezing was generalized with the help of a semi-analytical investigation of a one-dimensional system comprising solid, porous mush and liquid regions. The analytical scaling relations for fluid velocity and vorticity, for the faceted and dentritic cases, revealed contrasting vorticity values, which are much larger in low permeability (faceted case) and cause enhanced mixing in the bulk. The study sheds new insights into the role of microstructural morphology in governing the transport phenomena in the bulk liquid.

We present the rich and complex relaxation dynamics of turbulent plane Couette flow when the Reynolds number is lowered. In particular, we reveal the existence of well-defined transient states around which the dynamics of turbulent retreat is organized. We characterize these states in physical space and we propose a projection of these states in phase space to understand their nature. The results presented have been obtained in an experiment in which we perform annealing and quenching, i.e. gentle or sudden decreases in Reynolds number. The nature of asymptotic states is also studied and shown to depend on the final Reynolds number, but not at all on the rate of change of the Reynolds number.