In typical turbulent flows, noncontinuum effects are extremely small and hence can be ignored. However, for some high-Mach-number flows, the Kolmogorov length scale is of the same order as the molecular mean free path, which could introduce noncontinuum molecular-level effects into the turbulent energy cascade. To investigate this, the compressible Taylor-Green vortex flow is simulated for near-continuum conditions using both noncontinuum molecular gas dynamics (direct simulation Monte Carlo method) and continuum computational fluid dynamics (direct numerical simulation of the Navier-Stokes equations). Although the energy-decay histories are basically the same, molecular-level fluctuations are observed to break the symmetries of the initial conditions and thereby produce different but statistically similar routes (based on velocity spectra) from the initial nonturbulent flow to the long-time turbulent flow.

For two-dimensional (2D) Rayleigh-Bénard convection, classes of unstable, steady solutions were previously computed using numerical continuation [F. Waleffe et al., Phys. Fluids 27, 051702 (2015) and D. Sondak et al., J. Fluid Mech. 784, 565 (2015)]. The “primary” steady solution bifurcates from the conduction state at $\mathrm{Ra}\approx 1708$, and has a characteristic aspect ratio (length/height) of approximately 2. The primary solution corresponds to one pair of counterclockwise-clockwise convection rolls with a temperature updraft in between and an adjacent downdraft on the sides. By adjusting the horizontal length of the domain, Waleffe et al. and Sondak et al. also found steady, maximal heat transport solutions, with a characteristic aspect ratio less than 2 and decreasing with increasing $\mathrm{Ra}$. Compared to the primary solutions, optimal heat transport solutions have modifications to boundary layer thickness, the horizontal length scale of the plume, and the structure of the downdrafts. The current study establishes a direct link between these (unstable) steady solutions and transition to turbulence for $\mathrm{Pr}=7$ and $\mathrm{Pr}=100$. For transitional values of $\mathrm{Ra}$, the primary and optimal-heat-transport solutions both appear prominently in appropriately sized subfields of the time-evolving temperature fields. For $\mathrm{Ra}$ beyond transitional, our data analysis shows persistence of the primary solution for $\mathrm{Pr}=7$, while the optimal heat transport solutions are more easily detectable for $\mathrm{Pr}=100$. In both cases, $\mathrm{Pr}=7$ and $\mathrm{Pr}=100$, the relative prevalence of primary and optimal solutions is consistent with the $\mathrm{Nu}$ vs $\mathrm{Ra}$ scalings for the numerical data and the steady solutions.

The initial thickness and radius of the film that forms upon close contact of two foam bubbles are known to influence the thinning dynamics and lifetime of the film. Various scalings of lifetime $t_r$, with initial radius $R_{\mathrm{film}}$ and thickness $h_o$, have been proposed in literature. In this paper, we present a hydrodynamic thin-film model that includes both surface tension, van der Waals forces, and drainage and that clarifies the various proposed scalings of lifetime. Our model equations were solved numerically for a range of $R_{\mathrm{film}}$ and $h_o$ as direct input parameters. Films with a large radius are found to thin locally at a dimple, while films with a small radius thin across the entire film. The observed dynamics and lifetime were interpreted by developing a simplified model that describes the early stage dimpled drainage and the late stage van der Waals thinning, using known similarity solutions. For large radii films, our simulations confirm earlier theoretical work on semi-infinite films that predicts $t_r\sim R_{\mathrm{film}}^0{h}_0^{5/7}$. For small radii films, our numerical simulations show the opposite trend with lifetime being solely dependent on $R_{\mathrm{film}}$, in fair agreement with the simplified model that predicts $t_r\sim R_{\mathrm{film}}^{10/7}{h}_0^0$.

An analysis of the effects of transpiration on the forces required to maintain the relative movement of parallel plates has been carried out using a two-dimensional model problem. Transpiration was placed either at the stationary or at the moving plates. In both cases its spatial distribution was made of periodic components, but the explicit results are provided only for the commensurable systems. It is shown that the force required to maintain plate movement is affected by the reduction of the effective spacing between the plates caused by formation of a cushion made of the transpiration “bubbles,” by the elimination of the direct contact between the fluid in the slot and the plate with transpiration, and by nonlinear streaming generated by the transpiration. It is possible to reduce the pulling force through the proper selection of the transpiration pattern. The transpiration wave number resulting in the largest reduction corresponds to the maximization of the nonlinear streaming. The largest reduction of resistance is achieved by concentrating transpiration at a single transpiration wave number and avoiding commensurability effects. An analysis of finite-slot transpiration demonstrates the existence of the reduced distribution model, i.e., the performance of such systems can be well approximated using just a few leading modes from the Fourier expansions describing such transpirations. The analysis of energy costs shows that the overall energy cost of the modified flow is higher than the cost of the unmodified flow. Conditions leading to the minimization of this cost have been identified. These conditions describe the most effective use of transpiration as a propulsion augmentation system. Transfer of transpiration to the moving plate does not affect the reduction of resistance and does not change the energy cost associated with transpiration.

A method is proposed in order to optimally decompose the trace of cross-covariances of flow fluctuations, such as Reynolds stresses. Such method, referred to as cross proper orthogonal decomposition (CPOD), leads to a basis of modes extracted from a flow database that are optimal in representing an inner product related to the cross-covariance of interest. A sample application is shown for the representation of Reynolds shear stress in a turbulent channel flow with friction Reynolds number equal to 179. Leading modes are shown to comprise streamwise vortices and streaks with phase opposition between streamwise $\left(u^{\prime }\right)$ and wall-normal $\left(v^{\prime }\right)$ velocities, representing ejections and sweeps, and higher-order modes show similar structures, but with $u^{\prime }$ and $v^{\prime }$ in phase. A combination of such structures leads to an accurate reconstruction of the Reynolds stress, and consequently of the mean flow, with a reasonable near-wall reconstruction with the leading CPOD mode pair (even and odd modes) for each considered wave number, and a close match of the profiles with the five leading CPOD mode pairs. The present method is thus a valuable modal decomposition technique targeting cross-covariances of flow quantities such as Reynolds stresses.

Although the mean flow features of the turbulent jet in counterflow have been studied in the past, the large-scale dynamics of this flow configuration remain unexplored. The present work presents the modal analysis, through proper orthogonal decomposition (POD), of large eddy simulations (LESs) of counterflowing jets at different jet-to-counterflow velocity ratios $(\alpha =2.2,3.4,5.1)$ reported in detail by Rovira, Engvall, and Duwig [Phys. Fluids 32, 045102 (2000)]. In the present study, a qualitative investigation of the three-dimensional (3D) turbulent structure of this jet configuration is performed by vortex identification. Additionally, a simplified description of the origin and development of these coherent structures is presented. Planar two-dimensional (2D) POD results for the case with $\alpha =3.4$ are directly compared and found to be in close agreement with the results available literature. In this case, over an equal time interval, temporal and spatial resolutions are observed to have a minor effect on mode energy content. All three cases are also analyzed with 3D POD and the evolution of the peak mode frequency with $\alpha$ is studied. Additionally, by employing a wavelet transform, the intermittent behavior of the fundamental mode dynamics is evidenced for the first time. Finally, the jet in counterflow case with $\alpha =5.1$ is analyzed with a 3D spectral POD. Varying jet penetration, precession, and a stretching and contracting motion are found to be the most dominant modes.

The mixture, or suspension balance, model is the most frequently used to describe shear-induced particle migration in Newtonian fluids. The model suggests that neutrally buoyant particles migrate only if the effective stress tensor of the solid phase is nonuniform. In moderately dense suspensions, where direct particle contacts and interparticle forces are negligible, this tensor originates from the velocity fluctuations of the particles. Using Buyevich's constitutive equation, we show that the time required by these fluctuations to induce significant particle migration exceeds considerably the timescale of the process, obtained experimentally. In particular, the ratio between these two timescales is proportional to the reciprocal of the Reynolds number; hence, for vanishingly small values of the Reynolds number (the case on which this work focuses), particle velocity fluctuations cannot be responsible for particle migration. We conclude that, if direct particle contacts and interparticle forces are absent, particle migration must have another driver. In the literature, it has been suggested that this is the lubrication forces between the particles. On this assumption, Morris and Boulay advanced a closure for the solid effective stress tensor. This closure seems to predict well the migration process, but as discussed by P. R. Nott, E. Guazzelli, and O. Pouliquen, The suspension balance model revisited, Phys. Fluids 23, 043304 (2011), it presents some conceptual issues. We investigate this matter and show that lubrication forces can induce particle migration, and the tensor quantifying their effect can be closed by Morris and Boulay's equation; however, this tensor is not part of the effective stress tensor of the solid phase.

Fiber orientation in oscillatory shearing flow was studied both experimentally and numerically. Optical measurements were made using a custom flow cell containing rigid, noncolloidal fibers suspended at high concentration in a Newtonian fluid. Simulations that account for hydrodynamic drag and excluded volume predict fiber alignment in the vorticity direction for some conditions, in agreement with the measurements. Vorticity alignment was found to be a complex function of strain amplitude and fiber concentration, confinement, and aspect ratio.

Polymer-induced drag reduction is bounded by an asymptotic limit of maximum drag reduction (MDR). For decades, researchers have presumed that MDR reflects the convergence to an ultimate flow state that is not further changed by polymers. Our simulation shows that, as drag reduction converges to its invariant limit, the underlying dynamics continues to evolve with no sign of convergence. The stage of asymptotic drag reduction is not represented by any single flow state, but encompasses states with varying dynamical patterns, all of which are partially sustained by polymer elasticity.

The Maxey–Riley equation describes the motion of a spherical particle suspended in a spatially nonuniform, time-dependent flow, and finds applications in a wide range of flow situations. We reexamine the hydrodynamics underlying the Maxey–Riley equation to find additional inertial forces associated with second gradients of the background flow velocity, not accounted for in the original framework. These forces amplify inertial Faxén terms threefold, while also contributing advective terms that are quadratic in fluid velocity and may exceed Faxén forces in some flows. We present a more comprehensive form of the Maxey–Riley equation that includes these contributions, and discuss its implications for particle dynamics in flows with curvature.

The dynamic response of an encapsulated bubble to an acoustic disturbance in a wall restricted flow is investigated in the context of axial symmetry, when the viscous forces of the surrounding liquid are accounted for. The Galerkin finite element methodology is employed and the elliptic mesh generation technique is used for updating the mesh. The bubble is accelerated towards the wall as a result of the secondary Bjerknes forces and consequently the translational velocity gradually increases in a nearly quadratic fashion as the bubble approaches the wall. Proximity to the wall affects the resonance frequency that is seen to be reduced as the initial distance between the bubble and the wall decreases, as long as the sound amplitude remains below a threshold value that is determined by the onset of parametric shape mode excitation. While the microbubble remains far from the wall an overpressure develops in the upstream region that causes flattening and bending of the shell. However, shell elasticity coupled with viscous shell stresses prevents jet formation. Thus the bubble remains spherical during the expansion phase of the pulsation and deforms mainly in the compressive phase, during which most of the translation takes place due to the reduced added mass effect. As it approaches the wall the maximum overpressure is moved to the downstream pole region and this generates an excess of viscous shell stresses during compression that balance compressive elastic stresses. As a result the latter are attenuated in the downstream region of the shell, in comparison with the bulk of the shell where they are balanced solely by the cross membrane pressure drop, leading to a gradually more pronounced prolate bubble shape. Viscous drag due to the surrounding liquid develops mainly in the bulk of the shell where it is balanced by viscous shell stresses in the tangential stress balance. Over a period of the pulsation it counteracts the Bjerknes force that accelerates the bubble, via a force balance that is almost instantaneously established due to the relatively large shell viscosity. This is in marked difference with the case of rising gas bubbles that acquire oblate shapes as a result of the balance between buoyancy and pressure drag. In the case of coated microbubbles the drag coefficient is seen to obey a law previously obtained for no-slip interfaces for large radial and relatively small translational Reynolds numbers.

The dynamic response of an encapsulated bubble subject to an acoustic disturbance in a wall restricted flow is investigated, when the viscous forces of the surrounding liquid are accounted for. The Galerkin finite element methodology is employed and the elliptic mesh generation technique is used for updating the mesh. As the bubble accelerates towards the wall, the dominant force balance is between Bjerknes forces and the viscous drag that develops. In this process a prolate shape is acquired by the bubble, due to excessive compression at the equator region. When the bubble reaches the wall lubrication pressure develops in the near wall region that resists further approach. As long as the sound amplitude remains below a threshold value determined by the onset of parametric shape mode excitation saturated, or “trapped,” pulsations are performed around a certain small distance from the wall. The balance between Bjerknes attraction and the lubrication pressure that arises due to shell bending along the flattened shell portion that faces the wall generates an oblate shape. Elongation is now observed along the equatorial plane where a local liquid overpressure is established generating large tensile strain. The time-averaged deflection of the microbubble at the pole that lies close to the wall is determined by the bending and stretching resistances of the shell in the manner described by Reissner's linear law for a static compressive load on an elastic shell, corrected for the effect of surface tension. The oscillatory part of the bubble motion in that same region, the contact region, follows the forcing frequency and consists of a pressure driven and a shear flow in the form of a Stokes layer where a significant amount of instantaneous wall shear is generated. The thickness of the film that occupies the Stokes layer is on the order of a few tenths of nm and is determined by the balance between liquid and shell tangential viscous stresses. The steady streaming effect on the wall shear is absent owing to the negligible phase difference between the volume and center of mass pulsations.

Colloidal particles hold promise for mobilizing and removing trapped immiscible fluids from porous media, with implications for key energy and water applications. Most studies focus on accomplishing this goal using particles that can localize at the immiscible fluid interface. Therefore, researchers typically seek to optimize the surface activity of particles, as well as their ability to freely move through a pore space with minimal deposition onto the surrounding solid matrix. Here, we demonstrate that deposition can, surprisingly, promote mobilization of a trapped fluid from a porous medium without requiring any surface activity. Using confocal microscopy, we directly visualize both colloidal particles and trapped immiscible fluid within a transparent, three-dimensional porous medium. We find that as nonsurface active particles deposit on the solid matrix, increasing amounts of trapped fluid become mobilized. We unravel the underlying physics by analyzing the extent of deposition, as well as the geometry of trapped fluid droplets, at the pore scale: deposition increases the viscous stresses on trapped droplets, overcoming the influence of capillarity that keeps them trapped. Given an initial distribution of trapped fluid, this analysis enables us to predict the extent of fluid mobilized through colloidal deposition. Taken together, our work reveals a new way by which colloids can be harnessed to mobilize trapped fluid from a porous medium.

The dynamics of sediment creep under the stress of a porous flow, a situation ubiquitous in the environment, remains scarcely studied. To initiate such effort, experiments of a submerged quasi-two-dimensional sediment layer creeping downslope were performed, varying the setup tilt and a porous flow under the two respective thresholds for yielding. Logarithmic decay rates of the deformation are observed, with the rate increasing with both control parameters. A new dimensionless parameter, $P^{*}$, accounting for the mean porous flow intensity and the distance to the yield stress, is proposed and allows a collapse of all the deformation results on a single curve. Two distinct creep regimes are identified and correspond to a weak but systematic change of the mean void size as $P^{*}$ increases.

It is known that scale invariance is broken in the developed hydrodynamic turbulence due to intermittency, substantiating the complexity of turbulent flows. Here we challenge the concept of broken scale invariance by establishing a hidden self-similarity in intermittent turbulence. Using a simplified (shell) model, we derive a nonlinear spatiotemporal scaling symmetry of inviscid equations, which are reformulated in terms of intrinsic times introduced at different scales of motion. Numerical analysis persuasively confirms that this symmetry is restored in a statistical sense within the inertial interval. At the end, we discuss the implications of this result for real turbulence problems.

Direct numerical simulations of forced homogeneous rotating stratified turbulence are carried out with the same Rossby number and different Froude numbers. We investigated the effects of different stratification on energy transfers across scales and kinetic-potential energy exchange in Fourier space in the inverse energy cascade range. When the stratification is weak, almost all the kinetic energy flux in the inertial range comes from two-dimensional and three-dimensional (2D-3D) coupling interactions and 2D dynamics dominates at very large scales, which are similar to those in the purely rotating case. However, compared with the purely rotating case, the inverse cascade is weakened through the kinetic-potential energy exchange induced by 3D wave-vortical interactions. The total kinetic-potential energy exchange is found to oscillate at later times, which is produced by 2D inertia-gravity waves with fixed wave numbers. When the stratification is strong, the distributions of decomposed kinetic fluxes are different from those in purely rotating case. The magnitude of 2D-3D coupling energy flux becomes small and 3D-mode energy flux is important near the forcing scales. Besides, homo- and heterochiral energy fluxes are different in the inverse cascade. The kinetic-potential energy exchange under strong stratification mainly comes from 3D modes and wave-vortical interactions. Strengths of stratification negligibly affect properties of locality of the kinetic energy cascade, which is infrared local and ultraviolet nonlocal.

The three-layer Saffman-Taylor problem introduces two coupled moving interfaces separating the three fluids. A very recent weakly nonlinear analysis of this problem in a radial Hele-Shaw cell setup has shown that the morphologies of the emerging fingering patterns strongly depend on the initial thickness of the intermediate layer connecting the two interfaces. Here we go beyond the weakly nonlinear regime and explore full nonlinear interfacial dynamics using a spectrally accurate boundary integral method. We quantify the nonlinear instability of both interfaces as the relevant physical parameters (e.g., viscosities and surface tensions) are varied and show that our nonlinear computations are in good agreement with the experimental observations and the weakly nonlinear analysis. Nonlinear simulations reveal that due to the existence of a second interface, the classical highly branched morphologies are replaced by less unstable structures in which finger-tip-splitting and finger competition phenomena are evidently restrained as the initial annulus's thickness is reduced. In addition, these patterns develop fingers with a series of low-amplitude bumps at their tips, associated with the enhanced growth of high-frequency modes promoted by the increasing coupling strength of interfaces.

Many aquatic microorganisms are attached to solid surfaces while creating feeding flows that bring prey particles to them. To explore the effects of surface proximity and orientation of the flow-generating force, we analyze the low-Reynolds-number flow due to a point force above a plane no-slip surface. The presence of the surface reduces the feeding flow relative to the unbounded situation. We show that the reduction of the flow rate through a circular clearance disk perpendicular to the force and centered at its position is twice as large when the force is perpendicular to the surface as when it is parallel. When the force is perpendicular to the surface, the flow forms a toroidal eddy with closed streamlines, and the resulting flow recirculation may lead to refiltration of water that has already been cleared for prey. We prove that due to the nature of the far-field flow, the shortest recirculation time along a streamline through a circular clearance disk is inversely proportional to the flow rate to the power four. Finally, we discuss the biological advantages and disadvantages of perpendicular and parallel force orientation and the effects of prey diffusion and ambient flow, and we argue that recirculation is irrelevant in the typical perpendicular feeding flow since the recirculation time is long compared to the biologically relevant timescales.