This paper proposes a theoretical model to describe previous laboratory observations of the dynamics of debris accumulations around bridge piers of cylindrical shape. The model is based on the assumption that the observed dynamics is mainly governed by dynamic changes of the point of application of the drag force exerted on a solid body formed by debris accumulated around a pier. A phase-plane analysis of the resulting nonlinear system of ordinary differential equations shows that the model captures the main patterns observed in previous laboratory experiments, including an oscillatory motion and the removal of debris from the pier by the flow. The model provides a theoretical basis for the analysis of the conditions required for debris jams to remain stable over long periods of exposure to impinging flow. Namely, the model indicates that the stability of debris accumulations primarily depends on geometrical asymmetry and on the length of the extension downstream of the pier. The former induces the torque required to rotate the jam about the pier, while the latter produces a stabilising effect after the body rotates.

The motion of an assembly of rigid fibres is investigated for different classes of closed streamline flows, steady or time dependent, two-dimensional or three-dimensional. In our study, the dynamics of the fibre assembly is fully coupled to the flow field by means of a state of the art immersed boundary method. We show that, for sufficiently small Stokes times of the assembly, the whole flow gradient tensor can be accurately reconstructed by simply tracking the fibre assembly and measuring suitable fibre velocity differences evaluated at the fibre ends. Our results strongly suggest the possibility of using rigid fibres (or assemblies of them) to perform multi-point flow measures, either in laboratory or in field: future experiments are therefore mandatory to inquire the feasibility of a new ‘fibre tracking velocimetry’ technique.

With the aim of assessing internal wave-driven mixing in the ocean, we develop a new technique for direct numerical simulations of stratified turbulence. Since the spatial scale of oceanic internal gravity waves is typically much larger than that of turbulence, fully incorporating both in a model would require a high computational cost, and is therefore out of our scope. Alternatively, we cut out a small domain periodically distorted by an unresolved large-scale internal wave and locally simulate the energy cascade to the smallest scales. In this model, even though the Froude number of the outer wave, $Fr$, is small such that density overturn or shear instability does not occur, a striped pattern of disturbance is exponentially amplified through a parametric subharmonic instability. When the disturbance amplitude grows sufficiently large, secondary instabilities arise and produce much smaller-scale fluctuations. Passing through these two stages, wave energy is transferred into turbulence energy and will be eventually dissipated. Different from the conventional scenarios of vertical shear-induced instabilities, a large part of turbulent potential energy is supplied from the outer wave and directly used for mixing. The mixing coefficient $\varGamma =\epsilon _P/\epsilon$, where $\epsilon$ is the dissipation rate of kinetic energy and $\epsilon _P$ is that of available potential energy, is always greater than 0.5 and tends to increase with $Fr$. Although our results are mostly consistent with the recently proposed scaling relationship between $\varGamma$ and the turbulent Froude number, $Fr_t$, the values of $\varGamma$ obtained here are larger by a factor of about two than previously reported.

We examine the scaling of the two-point correlation function for $\unicode[STIX]{x1D716}$, the energy dissipation rate, over a range of values of the separation $r$ between the two points and the Taylor microscale Reynolds number $Re_{\unicode[STIX]{x1D706}}$. The correlation function is estimated from hot-wire measurements in grid turbulence, along the axes of wakes and jets, and along the centreline of a fully developed channel flow. When $Re_{\unicode[STIX]{x1D706}}$ exceeds a value of approximately 300, a condition which is achieved for both plane and circular jets, the correlation function collapses over nearly all values of $r$ when the normalization uses Kolmogorov scales. However, there is no collapse in either the power-law range or dissipative range when the normalization is on the integral (or external) length scale, which indicates that there is no self-similarity based on external scales. Although the maximum value of $Re_{\unicode[STIX]{x1D706}}$ is not much larger than $10^{3}$, the behaviour of the energy dissipation correlation function on the axes of plane and circular jets seems consistent with the first similarity hypothesis of Kolmogorov (Dokl. Akad. Nauk SSSR, vol. 30, 1941, pp. 299–303) but not with the revised phenomenology of Kolmogorov (J. Fluid Mech., vol. 13, 1962, pp. 82–85).

Given the current lack of experimental data for shock waves interacting with incoming transitional boundary layers, the goal of this study was to characterize the dynamics of such an interaction to better understand the fundamental fluid physics of these complex phenomena. Here, the mean flow field and time-dependent characteristics of a three-dimensional Mach 5 cylinder-induced shock-wave/boundary-layer interaction where the upstream boundary layer is transitional, have been studied experimentally. The interactions were generated with a right circular cylinder mounted on a flat plate. Streamwise–spanwise planar laser scattering from a condensed alcohol fog and schlieren imaging were used to characterize the mean and instantaneous structure of the interaction, and fast-response wall-pressure measurements on the centreline upstream of the cylinder enabled characterization of the unsteadiness. The pressure measurements show a mean pressure profile that resembles a composite of an upstream laminar profile and a downstream turbulent profile. The upstream influence location of the transitional interaction was approximately 8.5 diameters ($d$) upstream of the cylinder leading edge, which is between that of a laminar and a turbulent interaction, and is followed by a plateau region to approximately $4d$ upstream of the cylinder. The plateau region is a region with a thicker boundary layer and possible flow separation. The plateau pressure was within 7 % of the value predicted by Hill's correlation for free-interaction phenomena. Furthermore, a statistical analysis of the pressure histories suggests that the entire interaction stretches and contracts in concert. Power spectral densities of the pressure fluctuations showed unsteadiness throughout the interaction with energy content primarily centred between a region defined by a separation-length-based Strouhal number $St_{L} = 0.05\text {--}0.2$, comparing well with other related studies of cylinder-induced interactions. Cross-correlations and coherence functions in the interaction suggest that the unsteadiness in the laminar region may be due to the entire ‘laminar’ region oscillating in response to the ‘turbulent’ unsteadiness of the intermittent region.

Chemically active, or autophoretic, particles that isotropically emit or absorb solute molecules undergo spontaneous self-propulsion when their activity is increased beyond a critical Péclet number ($Pe$). Here, we conduct numerical computations, using a spectral element based method, of a rigid, spherical autophoretic particle in unsteady rectilinear translation. The particle can be freely suspended (or ‘unforced’) or subject to an external force field (or ‘forced’). The motion of an unforced particle progresses through four regimes as $Pe$ is increased: quiescent, steady, stirring and chaos. The particle is stationary in the quiescent regime, and the solute profile is isotropic about the particle. At $Pe=4$ the fore–aft symmetry in the solute profile is broken, resulting in its steady self-propulsion. Our computations indicate that the self-propulsion speed scales linearly with $Pe-4$ near the onset of self-propulsion, as has been predicted in previous studies. A further increase in $Pe$ gives rise to the stirring regime at $Pe\approx 27$, where the fluid undergoes recirculation, while the particle remains essentially stationary. As $Pe$ is increased even further, the particle dynamics is marked by chaotic oscillations at $Pe\approx 55$ and higher, which we characterize in terms of the mean square displacement and velocity autocorrelation of the particle. Our results for an autophoretic particle under a weak external force are in good agreement with recent asymptotic predictions (Saha, Yariv & Schnitzer, J. Fluid Mech., vol. 916, 2021, p. A47). Additionally, we demonstrate that the strength and temporal scheduling of the external force may be tuned to modulate the chaotic dynamics at large $Pe$.

A numerical insight into the radial displacement of two viscously stable reactants undergoing an infinitely fast chemical reaction is obtained. This work broadens the numerical knowledge about the interaction between chemical reaction and hydrodynamic instability. A suitable transformation is utilised to deal with an infinite dimensionless parameter and reduce computational cost. Viscous fingering instability originates when the product has a different viscosity than the reactants. We calculate the onset time $t_{on}$ when the instability begins to appear for different reactants by varying the log mobility ratio $R_c$ and the Péclet number $Pe$. Based on $t_{on}$, we divide the time domain into stable and unstable zones with respect to instability. This helps to characterise reactants so as to have a flow with/without instability. For a fixed $Pe$ and $\vert R_c \vert$, it is found that $t_{on}$ is early for $R_c > 0$ in contrast to the result for rectilinear displacement. This results in a wider stable zone for $R_c < 0$. Interestingly, it is found that the stable zone can be made independent of $Pe$ by using a careful rescaling and we obtain the dependence of the onset time of instability on $R_c$ and $Pe$ as $t_{on} \propto (\vert R_c\vert Pe^{\beta _1}-\beta _2)^{\beta _3}$ where the constant of proportionality and $\beta _i$, $i=1,2,3$, depend upon the sign of $R_c$. In the unstable zone, we find that the length of the fingers depends upon the sign of $R_c$, which is not observed for any radial displacement of reactants undergoing a slow or moderately fast chemical reaction.

The general asymptotic theory for wave propagation in a slowly varying medium, classically known as the Wentzel–Kramers–Brillouin–Jeffreys (WKBJ) approximation, is revisited here with the aim of constructing a new data diagnostic technique useful in atmospheric and oceanic sciences. Using the Wigner transform, a kind of mapping that associates a linear operator with a function, we analytically decompose a flow field into mutually independent wave signals. This method takes account of the variations in the polarisation relations, an eigenvector that represents the kinematic characteristics of each wave component, so as to project the variables onto their eigenspace quasi-locally. The temporal evolution of a specific mode signal obeys a single wave equation characterised by the dispersion relation that also incorporates the effect from the local gradient in the medium. Combining this method with transport theory and applying them to numerical simulation data, we can detect the transfer of energy or other conserved quantities associated with the propagation of each wave signal in a wide variety of situations.

We show that, in the case of turbulent Rayleigh–Bénard convection, shadowgraph can be used to gain quantitative results on the plume statistics and velocity. For this purpose, we compare the experimental shadowgraph of a Rayleigh–Bénard cell with the synthetic shadowgraph obtained by calculating the integrated two-dimensional Laplacian of the temperature field from a numerical simulation very similar to the experiment. We use image processing tools to enhance the quality of the shadowgraph image, and obtain quantitative statistics for the thermal plumes, such as plume density and plume velocity distribution. To highlight the efficiency of this new process of plume counting, we use, both in the experiment and in the numerical simulation, a turbulent Rayleigh–Bénard convection cell with a rough bottom surface and a smooth top surface, where the statistics of the plumes can be influenced (or not) by the roughness. In addition, the distribution of velocity obtained from processing the synthetic shadowgraph images of the direct numerical simulations (DNS) or the experimental shadowgraph images, are compared to the velocity fluid at mid-plane of the DNS or particle image velocimetry measurement in the experiment, respectively. It will be shown that the mean velocity profile measured using the advection of the plumes is different from the average Eulerian velocity profile.

Shock reflection experiments are performed to study the large-scale convective mixing created by the forward jetting phenomenon. Experiments are performed at a wedge angle of $\theta _{{w}} = 30^{\circ }$ in nitrogen, propane–oxygen and hexane with incident shock Mach numbers up to $M = 4$. Experiments are complemented by shock-resolved viscous simulations of triple-point reflection in hexane for $M = 2.5$ to $6$. Inviscid simulations are performed over a wider range of parameters. Reynolds numbers up to $Re \lesssim 10^3$ are covered by simulations and Reynolds numbers of $Re \sim 10^5$ are covered by experiments. The study shows that as the isentropic exponent is lowered, and as the Mach number and Reynolds number are increased, the forward jet approaches the Mach stem, forms a vortex, deforms the shock front and in some cases bifurcates the Mach stem. Experiments show that Kelvin–Helmholtz instabilities in the vortex cause large-scale convective mixing behind the Mach stem at low isentropic exponents ($\gamma \le 1.15$). The limits of Mach stem bifurcation (triple Mach–White reflection) in inviscid simulations are plotted in the phase space of $M$–$\theta _{{w}}$–$\gamma$. A maximum isentropic exponent of $\gamma \approx 1.3$ is found beyond which bifurcation does not occur (at $\theta _{{w}} = 30^{\circ }$). This closely matches the boundary between irregular and regular detonation cellular structures.

The compressibility effects on energy exchange mechanisms in a three-dimensional, spatially developing plane free shear layer are investigated via data produced by direct numerical simulation. The compressible shear layer is simulated using a high-order discontinuous spectral element method for convective Mach numbers $M_c = 0.3$, 0.5 and 0.7. The energy exchange mechanisms in the flow are examined by analysing the budget terms of mean kinetic, internal and turbulent kinetic energy transport equations, in both transition and turbulent regions. The results show that turbulent production, turbulent viscous dissipation, mean viscous dissipation, pressure dilatation and enthalpic production are the main mechanisms responsible for energy exchange among different forms of energy. The effects of compressibility on energy transfer mechanisms are studied based on the analyses of those five budget terms. The primary budget terms evolve differently in the transition and turbulent regions and change significantly for varying compressibility. In the transition region, a double-peak variation becomes a single peak in the streamwise profile of the turbulent production as $M_c$ increases from 0.3 to 0.7, due to significant changes in the vortex pairing structures. The shear layer centre slightly shifts to the high-speed side due to the appearance of the velocity deficit. The velocity deficit presence distance (VDPD) becomes longer as compressibility increases. However, in the turbulent region, the cross-stream profiles of the main budget terms significantly shift to the low-speed side because of the asymmetric mass entrainment and shift even further as $M_c$ increases.

The classical theory by Jeffery predicts that, in the absence of Brownian fluctuations, a thin rigid platelet rotates continuously in a shear flow, performing periodic orbits. However, a stable orientation is possible if the surface of the platelet displays a hydrodynamic slip length $\lambda$ comparable to or larger than the thickness of the platelet. In this article, by solving the Fokker–Plank equation for the orientation distribution function and corroborating the analysis with boundary integral simulations, we quantify a threshold Péclet number, ${Pe}_{c}$, above which such alignment occurs. We found that for ${Pe}$ smaller than ${Pe}_{c}$, but larger than a second threshold, a regime emerges where Brownian fluctuations are strong enough to break the platelet's alignment and induce rotations, but with a period of rotation that depends on the value of $\lambda$. For ${Pe}$ below this second threshold, slip has a negligible effect on the orientational dynamics. We use these thresholds to classify the dynamics of graphene-like nanoplatelets for realistic values of $\lambda$ and apply our results to the quantification of the orientational contribution to the effective viscosity of a dilute suspension of nanoplatelets with slip. We find a non-monotonic variation of this term, with a minimum occurring when the slip length is comparable to the thickness of the particle.

Direct numerical simulations (DNS) of turbulent channel flows up to ${Re}_{\tau} \approx 1000$ are conducted to investigate the three-dimensional (consisting of streamwise wavenumber, spanwise wavenumber and frequency) spectrum of wall pressure fluctuations. To develop a predictive model of the wavenumber–frequency spectrum from the wavenumber spectrum, the time decorrelation mechanisms of wall pressure fluctuations are investigated. It is discovered that the energy-containing part of the wavenumber–frequency spectrum of wall pressure fluctuations can be well predicted using a similar random sweeping model for streamwise velocity fluctuations. To refine the investigation, we further decompose the spectrum of the total wall pressure fluctuations into the autospectra of rapid and slow pressure fluctuations, and the cross-spectrum between them. We focus on evaluating the assumption applied in many predictive models, that is, the magnitude of the cross-spectrum is negligibly small. The present DNS shows that neglecting the cross-spectrum causes a maximum error up to 4.7 dB in the subconvective region for all Reynolds numbers under test. Our analyses indicate that the approximation of neglecting the cross-spectrum needs to be applied carefully in the investigations of acoustics at low Mach numbers, in which the subconvective components of wall pressure fluctuations make important contributions to the radiated acoustic power.

Understanding flow and transport of bacteria in porous media is crucial to technologies such as bioremediation, biomineralization and enhanced oil recovery. While physicochemical bacteria filtration is well documented, recent studies showed that bacterial motility plays a key role in the transport process. Flow and transport experiments performed in microfluidic chips containing randomly placed obstacles confirmed that the distributions of non-motile bacteria stays compact, whereas for the motile strains, the distributions are characterized by both significant retention as well as fast downstream motion. For motile bacteria, the detailed microscopic study of individual bacteria trajectories reveals two salient features: (i) the emergence of an active retention process triggered by motility, (ii) enhancement of dispersion due to the exchange between fast flow channels and low flow regions in the vicinity of the solid grains. We propose a physical model based on a continuous time random walk approach. This approach accounts for bacteria dispersion via variable pore-scale flow velocities through a Markov model for equidistant particle speeds. Motility of bacteria is modelled by a two-rate trapping process that accounts for the motion towards and active trapping at the obstacles. This approach captures the forward tails observed for the distribution of bacteria displacements, and quantifies an enhanced hydrodynamic dispersion effect that originates in the combined effect of pore-scale flow variability and bacterial motility. The model reproduces the experimental observations, and predicts bacteria dispersion and transport at the macroscale.