An experimental study focused on the identification of the flow regimes and quantification of the velocity field at pore scale in microporous media is presented and discussed. Transparent porous media are fabricated by removing a pore forming agent in slightly sintered glass beads of size $50\mu \mathrm{m}$ between two glass slides, leaving typical pores with a size of $500\mu \mathrm{m}$. Pressure-drop measurements and particle image velocimetry measurements are conducted simultaneously in order to evaluate the flow regimes and flow behaviors at pore size based Reynolds numbers from 0.1 to 140. Four different regimes, pre-Darcy, Darcy, Forchheimer, and turbulent, are found and presented. Spatial distribution and characteristics of the time-averaged velocity in all regimes and fluctuation intensity in transitional and turbulent regimes are investigated. Critical Reynolds numbers are identified using both velocity and pressure-drop measurements and the results agree very well, providing direct evidence underpinning the transition. The effects of porosity on these flow properties are also studied, and finally the flow regime boundaries are compared with the literature. These data provide an insight into the flow properties in microporous media with various porosities and an improved understanding that could be further utilized to enhance the flow and heat transfer performance of microporous media. It also demonstrates that velocity and pressure measurements used in combination can be an effective method for studying microporous media.

A key interest in geomorphology is to predict how the shear stress $\tau$ exerted by a turbulent flow of air or liquid onto an erodible sediment bed affects the transport load $M\tilde{g}$ (i.e., the submerged weight of transported nonsuspended sediment per unit area) and its average velocity when exceeding the sediment transport threshold ${\tau }_t$. Most transport rate predictions in the literature are based on the scaling $M\tilde{g}\propto \tau -{\tau }_t$, the physical origin of which, however, has remained controversial. Here we test the universality and study the origin of this scaling law using particle-scale simulations of nonsuspended sediment transport driven by a large range of Newtonian fluids. We find that the scaling coefficient is a universal approximate constant and can be understood as an inverse granular friction coefficient (i.e., the ratio between granular shear stress and normal-bed pressure) evaluated at the base of the transport layer (i.e., the effective elevation of energetic particle-bed rebounds). Usually, the granular flow at this base is gaslike and rapidly turns into the solidlike granular bed underneath: a liquidlike regime does not necessarily exist, which is accentuated by a nonlocal granular flow rheology in both the transport layer and bed. Hence, this transition fundamentally differs from the solid-liquid transition (i.e., yielding) in dense granular flows even though both transitions are described by a friction law. Combining this result with recent insights into the nature of ${\tau }_t$, we conclude that the transport load scaling is a signature of a steady rebound state and unrelated to entrainment of bed sediment.

Turbidity currents are gravity flows of fluids with suspended, denser sediment, which remains aloft due to turbulence generated by the current motion itself. To remain active, turbidity currents must have an ability to entrain material from their base to counteract the sedimentation of particles from the current to the base. A number of decades ago, Bagnold, Engelund, and Fredsøe proposed a physical picture for erosion as a function of the overall velocity of the turbidity current (bed stress). Recently, it has been argued that the high-velocity form of this law is critical in determining the overall mechanics of turbidity currents, particularly their predeliction to erode or deposit sediment in different locations. This letter reexamines the Bagnold-Engelund-Fredsøe picture, and determines the corresponding erosion law in a way that is consistent with turbidity current mechanics, and has a high-velocity plateau that determines the qualitative features of turbidity current deposition and erosion. I also address the differential role of fluid and grain stress transmission in determining erosion; provided the grain stress transmission is less effective than the fluid stress transmission in eroding sediment, there will continue to be a high-velocity plateau in the erosion rate.

From direct numerical simulation (DNS) of turbulence decaying from specified initial conditions for the range of initial Taylor-Reynolds numbers $2.58\le R_{\lambda }\left(0\right)\le 358.6$, it was found that the shape of the iconic curve of dimensionless dissipation versus Reynolds number depended strongly on the choice of measurement time. For our preferred time, a composite based on peak values in the dissipation and inertial transfer curves, the result was virtually identical to the forced, stationary case. In order to try varying the initial conditions, an additional run was performed, using the data from a stationary, forced simulation with $R_{\lambda }=335$ for the initial condition. The results of this suggested that the time taken for energy to pass through the cascade was about one half of an initial eddy turnover time. In the course of studying onset criteria, we found that the exponent for the power-law decay of the energy decreased with increasing Reynolds number and lay in the range $1.35\le n\le 2.60$.

Although the stability properties of the wake past impervious bluff bodies have been widely examined in the literature, similar analyses regarding the flow around and through porous ones are still lacking. In this work, the effect of the porosity and permeability on the wake patterns of porous rectangular cylinders is numerically investigated at low to moderate Reynolds numbers in the framework of numerical simulation combined with local and global stability analyses. A modified Darcy–Brinkman formulation is employed here so as to describe the flow behavior inside the porous media, where also the convective terms are retained to correctly account for the inertial effects at high values of permeability. Different aspect ratios of the cylinder are considered, varying the thickness-to-height ratios, $t/d$, from 0.01 (flat plate) to 1.0 (square cylinder). The results show that the permeability of the bodies has a strong effect in modifying the characteristics of the wakes and of the associated flow instabilities, while the porosity weakly affects the resulting flow patterns. In particular, the fluid flows through the porous bodies and, thus, as the permeability is progressively increased, the recirculation regions, initially attached to the rear part of the bodies, at first detach from the body and, eventually, disappear even in the near wakes. Global stability analyses lead to the identification of critical values of the permeability above which any linear instability is prevented. Moreover, a different scaling of the nondimensional permeability allows us to identify a general threshold for all the configurations here studied that ensures the suppression of vortex shedding, at least in the considered parameter space.

In a microrheological setup a single probe particle immersed in a complex fluid is exposed to a strong external force driving the system out of equilibrium. Here, we elaborate analytically the time-dependent response of a probe particle in a dilute suspension of Brownian particles to a large step force, exact in first order of the density of the bath particles. The time-dependent drift velocity approaches its stationary-state value exponentially fast for arbitrarily small driving in striking contrast to the power-law prediction of linear response encoded in the long-time tails of the velocity autocorrelation function. We show that the stationary-state behavior depends nonanalytically on the driving force and connect this behavior to the persistent correlations in the equilibrium state. We argue that this relation holds generically. Furthermore, we elaborate that the fluctuations in the direction of the force display transient superdiffusive behavior.

Flux of rigid or soft particles (such as drops, vesicles, red blood cells, etc.) in a channel is a complex function of particle concentration, which depends on the details of induced dissipation and suspension structure due to hydrodynamic interactions with walls or between neighboring particles. Through two-dimensional and three-dimensional simulations and a simple model that reveals the contribution of the main characteristics of the flowing suspension, we discuss the existence of an optimal volume fraction for cell transport and its dependence on the cell mechanical properties. The example of blood is explored in detail, by adopting the commonly used modeling of red blood cells dynamics. We highlight the complexity of optimization at the level of a network, due to the antagonist evolution of local volume fraction and optimal volume fraction with the channels diameter. In the case of the blood network, the most recent results on the size evolution of vessels along the circulatory network of healthy organs suggest that the red blood cell volume fraction (hematocrit) of healthy subjects is close to optimality, as far as transport only is concerned. However, the hematocrit value of patients suffering from diverse red blood cel pathologies may strongly deviate from optimality.

We study the influence of wettability on the morphology of fluid-fluid displacement through analog porous media in the limit of vanishing flow rates. We introduce an invasion-percolation model that considers cooperative pore filling and corner-flow mechanisms and captures interface motion at the pore scale for all quasistatic flow regimes between strong drainage and strong imbibition. We validate the method against recent experimental observations of wetting transition in microfluidic cells patterned with circular posts and we use it to explore the sensitivity of fluid invasion to wettability heterogeneity, post spacing, and post height. Our model therefore extends the Cieplak-Robbins description of quasistatic fluid invasion by reproducing the wetting transition in strong imbibition, a feature that requires incorporating three-dimensional effects.

Approximate Bayesian computation (ABC) is a data-driven technique that uses many low-cost numerical simulations to estimate unknown physical or model parameters (e.g., boundary conditions and material properties), as well as their uncertainties, given reference data from real-world experiments or higher-fidelity numerical simulations. In this study, ABC is used to estimate unknown parameters in complex thermal-fluid flows, and the technique is demonstrated on a periodically forced high-temperature jet and a steadily forced helium-air plume. In the first case, computational reference data are used to assess the accuracy of ABC when estimating the frequency, amplitude, and mean of the periodic velocity forcing at the jet inlet. These tests show that ABC provides accurate and reasonably certain estimates of inflow parameters even when the model simulations imperfectly represent the physics underlying the reference data. These tests also show that measurements far from the inlet can be used to perform the estimation, and that temperature measurements can be used to infer velocity inflow parameters. For the second case, ABC is used to estimate the inlet Richardson number and its uncertainty given experimental measurements of the Strouhal number within the plume. Once again, the approach is able to accurately estimate unknown parameters with relatively low uncertainty. As a result, ABC is shown to be a versatile technique for estimating unknown physical parameters when knowledge of a real-world system is limited or incomplete.

The large-scale properties of a self-similar Richtmyer-Meshkov turbulent mixing zone with a small Atwood number and in an infinite domain are investigated. The existence of large-scale invariants is predicted for the velocity spectrum. By contrast, the concentration and concentration flux spectra do not display any such invariants. Their large-scale properties are instead controlled either by the velocity spectrum or by nonlinear backscattering processes depending on the initial conditions. The existence of large-scale invariants for the velocity spectrum allows one to relate the self-similar growth rate of the turbulent mixing zone to the infrared slope of the velocity spectrum. Besides, it also implies that large scales keep their initial anisotropy so that the return to isotropy of the turbulent mixing zone is only partial. Finally, it allows one to estimate the prefactors entering the power laws governing the decay of Richtmyer-Meshkov turbulence, the growth of its length scales, and its mixing level. The different assumptions and predictions of this work are verified by performing implicit large eddy simulations of a Richtmyer-Meshkov turbulent mixing zone.

Inferring physical parameters of turbulent flows by assimilation of data measurements is an open challenge with key applications in meteorology, climate modeling, and astrophysics. Up to now, spectral nudging was applied for empirical data assimilation as a means to improve deterministic and statistical predictability in the presence of a restricted set of field measurements only. Here we explore under which conditions a nudging protocol can be used for two objectives: to unravel the value of the physical flow parameters and to reconstruct large-scale turbulent properties starting from a sparse set of information in space and in time. First, we apply nudging to quantitatively infer the unknown rotation rate and the shear mechanism for turbulent flows. Second, we show that a suitable spectral nudging is able to reconstruct the energy containing scales in rotating turbulence by using a blind setup, i.e., without any input about the external forcing mechanisms acting on the flow. Finally, we discuss the broad potentialities of nudging to other key applications for physics-informed data assimilation in environmental or applied flow configurations.

We investigate the steady expiratory and the oscillatory flow in a planar double bifurcation model with geometric proportions relevant to the respiratory human airways. Expanding on a previous study focused on steady inspiration [Jalal et al., Exp. Fluids 57, 148 (2016)], we use magnetic resonance velocimetry to characterize the three-dimensional velocity field for a range of Reynolds (Re) and Womersley (Wo) numbers. During expiration the velocity profiles are flatter than in inspiration, due to stronger secondary motions. The latter are characterized by counter-rotating streamwise vortices induced by curvature at the branch junctions. With increasing Re, the vortices gain strength, and for $\mathrm{Re}\ge 1000$ they propagate through successive branching generations, profoundly changing the secondary flow pattern. Under oscillatory conditions, as long as the ventilation frequency is in the normal respiration range, the flow topology for both inhalation and exhalation phases is similar to the corresponding steady cases over most of the breathing cycle. On the other hand, in the high-frequency ventilation regime ($\mathrm{Wo}=12$), the acceleration part of both inhalation and exhalation phases show signature features of oscillatory flows, with high-momentum regions located close to the walls. The phenomenon of counterflow is found to be prominent at $\mathrm{Wo}\ge 6$, with reverse flow pockets marking the velocity field especially during the inhalation-exhalation inversion. With increasing oscillation frequency, the secondary motions become more intense during the inhalation phase but are attenuated during the exhalation phase of the cycle. The cycle-averaged drift is found to be significant at low Wo but decreases with increasing ventilation frequency, suggesting that steady streaming is not the main transport mechanism during high-frequency ventilation.

A full understanding of differential molecular diffusion (DMD) in turbulent combustion has its theoretical significance for improving models of turbulent combustion. The scaling of the effect of DMD with respect to the Reynolds number in turbulent combustion is of particular interest for developing physically consistent modeling approaches for DMD. Such a scaling has so far been mostly studied in simple nonreacting flow problems, and a simple power-law scaling has been reported before. The applicability of the power-law scaling to turbulent combustion problems where the chemical reaction is expected to strongly couple with DMD has not been thoroughly studied. In this work, we aim to examine such a scaling by developing a statistical analysis of the dependence of DMD on the Reynolds number in turbulent nonpremixed combustion. Three Sandia temporally evolving planar jet nonpremixed ${\mathrm{CO}/\mathrm{H}}_2$ direct numerical simulation flames [E. R. Hawkes et al., Proc. Combust. Inst. 31, 1633 (2007)] are chosen as the target flames for the study. The Reynolds-number scaling based on a statistical analysis is reported, which is found to be statistically consistent with previous theoretical results in nonreacting problems. The results provide supportive evidence to the existence of a universal power-law scaling of the effect of DMD with respect to the Reynolds number in turbulent nonreacting and reacting flow problems. The results are also important for constraining the development of Reynolds-number-scaling consistent physical models for treating DMD in the modeling and simulations of multicomponent turbulent diffusion systems.

A theoretical model is developed to study the cross-stream migration of a deformable surfactant-laden droplet suspended in a nonisothermal Poiseuille flow. In addition to the thermocapillary migration of the droplet, presence of shape deformation due to the imposed flow redistributes the surfactants along the interface that has a significant effect on its dynamics, which has yet remained unexplored. Owing to the nonlinearity present in the system of governing equations, an asymptotic approach is adopted to capture the intricate and nontrivial coupling between the various influencing parameters. Assuming negligible fluid inertia and thermal convection, the droplet migration velocity is obtained through small-deformation analysis in the limits of convective and diffusive surfactant transport. For the former limiting case, the droplet migrates towards the flow centerline when the temperature of the suspending medium increases in the direction of the imposed flow; however, the direction of its cross-stream migration reverses for a system with a high viscosity ratio of droplet to carrier phase. Under the same limiting scenario and for systems with low viscosity ratio, when the temperature linearly decreases in the direction of the imposed flow, the cross-stream migration velocity reduces with the increase in the applied temperature gradient till a critical point is reached at which there occurs no cross-stream migration. Beyond the critical point, there is a gradual increase in the magnitude of the cross-stream velocity with further rise in the imposed temperature gradient. The droplet, below the critical temperature gradient, migrates towards the flow centerline; however, above it the droplet moves away from the centerline. For the other limiting case where surfactant transport is dominated by surface convection, the magnitude of the cross-stream velocity is found to be significantly larger and at the same time independent of the droplet-carrier phase viscosity ratio.

Solids can be levitated by actively nourishing an air cushion beneath them, using air blown through a porous substrate. It has recently been demonstrated that introducing asymmetry in the airflow close to a hovercraft can lead to its propulsion by viscous entrainment. In this work, we focus on the major consequence of a simple modification in the set-up: instead of engraving the texture on the substrate as in previous works, we directly carve it into the hovercraft. Provided that air-flux is strong enough, propulsion at any Reynolds number is observed. However, motion happens in the direction opposite to the viscous scenario. To understand experimental observations, an analytical model is proposed to account for the force of propulsion and the pressure needed for levitation, emphasizing asymptotic situations at low and high Reynolds numbers, further confirmed by numerical simulations.

In superfluid helium-4, a model of normal-fluid hydrodynamics and their coupling with topological defects (quantized vortices) of the order parameter (superfluid) is formulated. The model requires only material properties as input and applies to both laminar and turbulent flows, to both dilute and dense superfluid vortex tangles. By solving the model for the case of a normal-fluid vorticity Hopf link interacting with systems of quantized vortices, two vortex dynamical mechanisms of energy transfer from the normal fluid to the superfluid are indicated: (a) small superfluid rings expand to the size of the normal-fluid vortex link tubes and (b) superfluid rings with diameters similar to the diameters of the normal-fluid tubes succumb to axial-flow instabilities that excite small-amplitude wiggles which subsequently evolve into spiral waves along the superfluid vortex contours. The normal-fluid vorticity scale determines the upper size of the generated superfluid vorticity structures. A key role in energy transfer processes is played by an axial-flow instability of a superfluid vortex due to mutual-friction excitation by the normal fluid, which mirrors the instability of normal-fluid tubes due to mutual-friction excitation by the superfluid. Although the sites of superfluid vorticity generation are always in the neighborhood of intense normal-fluid vorticity events, the superfluid vortices do not mimic the normal-fluid vorticity structure and perform different motions. These vortex dynamical processes provide explanations for the phenomenology of fully developed finite temperature superfluid turbulence.

A liquid droplet spread on a solid substrate with nonuniform curvature, in the absence of pinning, spontaneously moves. By means of a perturbative scheme, we determine analytically the speed of the droplet and the total capillary force acting on it, by assuming that the only relevant dissipation mechanism is the contact line viscosity. Our solution holds for droplets small with respect to the capillary length and in the limit where the curvature of the substrate is small with respect to the curvature of the droplet. By means of a numerical solution, we validate our perturbative calculation and determine its limit of validity. Our theoretical results are in agreement with recent experimental data on the movement of submillimeter-sized water droplets on conical glass pipettes [Lv et al., Phys. Rev. Lett. 113, 026101 (2014)].

Due to the inherent nonlinearity of fluid dynamics, a large class of oscillating flows gives rise to rectified effects of steady motion. It has recently been shown that particle transport in such flows leads to differential displacement and efficient sorting of microparticles. Here we present a model that generalizes a Maxey-Riley-like equation for particle motion, incorporating important viscous and inviscid effects near oscillating interfaces and efficiently bridging the acoustofluidic and microfluidic approaches. Resulting in direct predictions for particle motion on slower timescales, the model predicts a richer and qualitatively different behavior from that expected from simplified radiation-force formalisms: depending on experimental control parameters, the net effect of interfacial oscillation can be either an attraction to or a repulsion from the interface, and particles can be captured at a fixed distance or released. These results are verified in comparison with experiments.

We consider freely decaying homogeneous anisotropic turbulence whose energy spectrum $E\left(k\right)$ at $k\to 0$ is given by $E\left(k\right)=C{k}^2+o\left(k^2\right)$ at an initial instant, where $k$ is the wave number and $C$ is a $k$-independent positive number. An argument is given to show that there are an infinite number of invariants characterizing the large-scale structure of the turbulence. This is a generalization of Saffman's argument, which shows the existence of a finite number of invariants [P. G. Saffman, J. Fluid Mech. 27, 581 (1967)]. By applying a similar argument to homogeneous anisotropic passive scalar turbulence without any scalar source, we show that there are an infinite number of invariants characterizing the large-scale structure of passive scalar fields. Theoretical analysis based on the invariance and a self-similarity assumption for the large-scale evolution shows that the anisotropy of the velocity and passive scalar fields is persistent at large scales. The decay laws of the velocity and passive scalar fields are derived by a simple dimensional analysis.

High-resolution three-dimensional large-eddy simulations are used to investigate the effects of internal solitary waves (ISWs) breaking over a sloping boundary. The lock release method is applied in a two-layer stratified fluid system to generate three different breaking mechanisms (i.e., plunging, collapsing, and surging breakers). The different breaking types are investigated in terms of their effects on the dynamics of the ISW and the interaction of the ISW with the sloping boundary. During each breaking event, the pycnocline region entrains fresher water from the upper layer and saltier water from the lower one. The associated increase of the intermediate density layer also induces changes of the pycnocline water density. This process occurs with a velocity that can be evaluated using the bulk entrainment parameter. We show how the intermediate layer features depend on the ISW shoaling and breaking dynamics and we discuss entrainment in breaking ISWs. The instabilities induced by boundary layer separation allow entrainment of saltier water, while the run-up of the gravity current causes the decrease of the intermediate layer mean density. Simultaneously, the entrained water mixes into the pycnocline region. For all cases, the temporal evolution of the instantaneous mixing efficiency is discussed. The plunging breaker case shows the largest amount of mixing, which is mostly induced by rear-edge overturning in the onshore direction. The largest entrainment is observed in the surging breaker case in response to the large gravity current flowing upslope. The paper discusses how the different turbulent instabilities induced by the ISWs breaking affect the time delay between the times when entrainment of patches of salty and fresh water from the neighboring layers occurs and the time the density of the intermediate layers becomes fairly uniform via mixing. We finally point out that the entrainment parameter and the mixing efficiency describe two different effects of the turbulent instabilities occurring in a stratified fluid in terms of changes of the bulk density profile.