Experimental results of towing a cylinder through a dense suspension of cornstarch and sucrose-water are presented. Focus is placed on the jamming fronts that exist in such systems. The literature has concentrated on the propagation of the jammed region under pushing, pulling, or shearing conditions independently. How the different fronts interact and if the fronts are symmetric when generated simultaneously has remained unexplored. Investigating this is our main goal. With the current setup, we are able to view a continuous, quasi-two-dimensional field around the cylinder. As such, a way of generating jamming fronts is presented whereby pushing, pulling, and shearing can be examined simultaneously. In agreement with previous studies, the front propagates roughly twice as fast in the longitudinal direction compared to the transverse direction, which is attributed to a single underlying onset strain, regardless of orientation from the cylinder. Although the jamming front shows nearly perfect transverse symmetry, there is clear longitudinal asymmetry. This is evident in the velocity and strain fields, and is also detectable in the front propagation velocity and onset strain.

We elucidate the turbulent structure of supercritical gravity currents by means of highly resolved simulations that employ up to a billion grid points. Three families of hairpin vortices dominate the near-bed and interface layers of the current, with their generation mechanisms dictating their shape, orientation, and number density. The interaction of near-bed and lower-interface hairpins explains the weak inviscid lidlike behavior of the streamwise velocity maximum, while the upper-interface vortices are responsible for the substantially lower entrainment compared to turbulent wall jets.

A number of approximations have been proposed to estimate basic hydrodynamic quantities, in particular, the frequency of a limit cycle. One of these, real zero imaginary frequency (RZIF), calls for linearizing the governing equations about the mean flow and estimating the frequency as the imaginary part of the leading eigenvalue. A further reduction, the self-consistent model (SCM), approximates the mean flow as well, as resulting only from the nonlinear interaction of the leading eigenmode with itself. Both RZIF and SCM have proven dramatically successful for the archetypal case of the wake of a circular cylinder. Here, the SCM is applied to thermosolutal convection, for which a supercritical Hopf bifurcation gives rise to branches of standing waves and traveling waves. The SCM is solved by means of a full Newton method coupling the approximate mean flow and leading eigenmode. Although the RZIF property is verified for the traveling waves, the SCM reproduces the nonlinear frequency only very near the onset of the bifurcation and for another isolated parameter value. Thus, the nonlinear interaction arising from the leading mode is insufficient to reproduce the nonlinear mean field and frequency.

Particle-laden pipe flows exhibit a gradual laminar-turbulent transition, beyond a critical volume fraction ($\varphi$). While classical transition behavior is characterized by the presence of turbulent puffs, this intermittent nature is absent for particle-induced transition. For small pipe-to-particle diameter ratios ($D/d$) even dilute systems exhibit this particle-induced transition behavior. In this study we use neutrally buoyant particles with a $D/d$ of 5.7, which represents a “sweet spot,” allowing the use of particle image velocimetry to study this particular phenomenon. The average velocity profile gradually changes from a parabola (laminar flow) to a blunted velocity profile for increasing Reynolds number. The instantaneous velocity profiles fluctuate around this profile. These velocity fluctuations, described by $u_x-rms$ and $u_r-rms$, gradually increase for increasing Reynolds number, as do the Reynolds stresses. For low ${\text{Re}}_s$, the velocity fluctuations increase proportional to the bulk velocity, which can be explained by a simple model based on the finite size of the particles. The velocity fields show the presence of elongated streamwise structures. The largest length scales are found in the transition region, where average integral length scales up to $5D$ are found. The structures decrease in length when the flow has fully transitioned to a turbulent state.

We use theory and direct numerical simulations (DNSs) coupled with point particles to explore the average vertical velocities and spatial distributions of inertial particles settling in a wall-bounded turbulent flow. The theory is based on the exact phase-space equation for the probability density function describing particle positions and velocities. This allows us to identify the distinct physical mechanisms governing the particle transport, which we then examine using the DNS data and relate them to the well-known preferential sweeping mechanism in homogeneous isotropic turbulence. When the average vertical particle mass flux is zero, the averaged vertical particle velocity is zero away from the wall due to the particles preferentially sampling regions where the fluid velocity is positive, which balances with the downward Stokes settling velocity. When the average mass flux is negative, the combined effects of turbulence and particle inertia lead to average vertical particle velocities that can significantly exceed the Stokes settling velocity by as much as ten times. Sufficiently far from the wall, the enhanced vertical velocities are due to the preferential sweeping mechanism. However, as the particles approach the wall, the contribution from the preferential sweeping mechanism becomes small, and a downward contribution from the turbophoretic velocity dominates the behavior. Close to the wall, the particle concentration grows dramatically, and the behavior is directly related to the behavior of the mechanisms governing the particle settling velocity. Finally, our results highlight how the Rouse model of particle concentration is to be modified for particles with finite inertia by identifying particular mechanisms missing from that model due to its assumption of vanishing inertia.

Streaks in the buffer layer of wall-bounded turbulence are tracked in time to study their life cycle. Spatially and temporally resolved direct numerical simulation data are used to analyze the strong wall-parallel movements conditioned to low-speed streamwise flow. The analysis of the streaks shows that there is a clear distinction between wall-attached and detached streaks, and that the wall-attached streaks can be further categorized into streaks that are contained in the buffer layer and the ones that reach the outer region. The results reveal that streaks are born in the buffer layer, coalescing with each other to create larger streaks that are still attached to the wall. Once the streak becomes large enough, it starts to meander due to the large streamwise-to-wall-normal aspect ratio, and consequently the elongation in the streamwise direction, which makes it more difficult for the streak to be oriented strictly in the streamwise direction. While the continuous interaction of the streaks allows the superstructure to span extremely long temporal and length scales, individual streak components are relatively small and short-lived. Tall-attached streaks eventually split into wall-attached and wall-detached components. These wall-detached streaks have a strong wall-normal velocity away from the wall, similar to ejections or bursts observed in the literature. Conditionally averaging the flow fields to these split events show that the detached streak has not only a larger wall-normal velocity compared to the wall-attached counterpart, it also has a larger (less negative) streamwise velocity, similar to the velocity field at the tip of a vortex cluster.

Although a suction vortex is the one of the most common vortices appearing in our everyday life, its internal structure has not been fully understood yet. One of the few things that we understand is that the radius of the core results from the competition between the diffusion of the vorticity due to the kinematic viscosity and the transportation of the vorticity due to the inward flow. To understand the structure of the suction vortex, we investigated a suction vortex produced in liquid helium. In the normal fluid phase, liquid helium behaves as a viscous fluid. In contrast, in the superfluid phase, a quantum vortex line carries all the microscopic circulation, and the suction vortex can be understood as a complex of quantized vortex lines. We generated a superfluid suction vortex with a cryogenic turbine and measured its circulation with a pulsed first sound circulation meter, and also measured the vorticity by the second sound attenuation technique. The experimental results indicate that the quantized vortex lines accumulated in the narrow region around the axis of symmetry due to an inward flow, the core structure of which cannot be described by a simple bundle of fully polarized quantized vortex lines.

The formation of drops of a complex fluid, for instance including dissolved polymers and/or solid particles, has practical implications in several industrial and biophysical processes. In this Letter, we experimentally investigate the generation of drops of a viscoelastic suspension, made of non-Brownian spherical particles dispersed in a dilute polymer solution. Using high-speed imaging, we characterize the different stages of the detachment. Our experiments show that the particles primarily affect the initial Newtonian necking by increasing the fluid viscosity. In the viscoelastic regime, particles do not affect the thinning until the onset of the blistering instability, which they accelerate. We find that the transition from one regime to another, which corresponds to the coil-stretch transition of the polymer chains, strongly depends on the particle content. Considering that the presence of rigid particles increases the deformation of the liquid phase, we propose an expression for the local strain rate in the suspension, which rationalizes our experimental results. This method could enable the precise measurement of local stresses in particulate suspensions.

In this paper we investigate whether the features of the nonequilibrium cascade, which have been identified in recent studies using high-fidelity tools, can be captured in the case of the classical dissipation scaling by turbulence closures based on the statistical description of freely decaying isotropic turbulence. Numerical results obtained using the eddy damped quasinormal Markovian (EDQNM) model over a very large range of Reynolds numbers (from $R{e}_{\lambda }=50$ up to $R{e}_{\lambda }={10}^6$) are analyzed to perform an extensive investigation of the scaling region identified as inertial range in Kolmogorov's theory. It is observed that EDQNM results are in agreement with the results of Lundgren's matched asymptotic expansion approach to the Kármán-Howarth equation. Both predict that the Kolmogorov inertial range equilibrium is never obtained irrespective of Reynolds number. Equilibrium is reached in the vicinity of the Taylor length $\lambda$ (which depends on viscosity) as Reynolds number tends to infinity and there is a gradual departure from equilibrium as the length scale moves away from $\lambda$, in particular towards scales larger than $\lambda$ all the way to the integral length scale.

We analyze the Prandtl number (Pr) dependence of spectra and fluxes of kinetic energy, as well as the energy injection rates and dissipation rates, of turbulent thermal convection using numerical data. As expected, for a flow with $\mathrm{Pr}⪅1$, the inertial-range kinetic-energy flux is constant, and the kinetic-energy spectrum is Kolmogorov-like ($k^{-5/3}$). More importantly, we show that the amplitudes of the kinetic-energy fluxes and spectra and those of structure functions increase with the decrease of Pr, thus exhibiting stronger nonlinearity for flows with small Prandtl numbers. Consistent with these observations, both the kinetic-energy injection rates and the dissipation rates increase with the decrease of Pr. Our results are in agreement with earlier studies that report the Reynolds number to be a decreasing function of Prandtl number in turbulent convection. On the other hand, the tail of the probability distributions of the local heat flux grows with the increase of Pr, indicating increased fluctuations in the local heat flux with Pr.

Thermocapillary-driven convection around an air bubble immersed in a liquid matrix under a heated wall is experimentally investigated under gravitational conditions. This work explores the thermocapillary convective flow behavior under conditions beyond the steady state towards turbulent flow. The phenomenon is basically studied through the visualization of the fluid flow and its structure around the interface of an injected air bubble subjected to an upward temperature gradient. The flow is qualitatively categorized according to the transient behavior of the thermocapillary vortex boundary contour around the bubble using the shadowgraph technique. The volatility of the low-viscosity silicone oil as test fluid restricts the maximum flow temperature to $53{}^{\circ }\mathrm{C}$ to avoid the formation of disruptive vapor bubbles. However, the introduction of experiments under excess pressure conditions facilitates studying the impact of higher flow driving temperature gradients while greatly reducing the distortion effect. Both periodic and nonperiodic oscillations of the liquid flow around the bubble have been observed. Also, symmetric and nonsymmetric periodic fluid flow oscillations were recorded depending on different interfacial boundary conditions due to the bubble volumes and the applied temperature gradient. These periodic oscillations were distinguished from the nonperiodic ones through the behavior of the thermocapillary vortex boundary contour. The values of the transitional Marangoni number ${\mathrm{Mg}}_{\mathrm{tran}}$, where the liquid flow evolves into a nonperiodic state, could be achieved at different bubble aspect ratios $r_B/z_B$. Four different nonperiodic flow modes surrounding the bubble periphery have been identified within the nonperiodic flow regime. Our study reveals, that under appropriate conditions, a surface-tension-driven (thermocapillary) flow can become turbulent.

Kinetic energy transfer in compressible homogeneous anisotropic turbulence is studied by numerical simulations of forced anisotropic turbulence (FAT) in a periodic box and homogeneous shear turbulence (HST) at different turbulent Mach numbers $M_t$ and different Taylor Reynolds numbers ${\mathrm{Re}}_{\lambda }$. In both FAT and HST, the subgrid-scale (SGS) kinetic energy flux is dominated by the streamwise component at large scales, and tends to be isotropic at small scales. As the turbulent Mach number increases, the compressibility slightly enhances the anisotropy of SGS kinetic energy flux and viscous dissipation. The redistribution of kinetic energy from the streamwise direction to two transverse directions by pressure-strain mainly occurs at large length scales. The kinetic energy transferred from the streamwise component through the pressure-strain is shared unequally by the other two components in HST, which is different from the situation of FAT. In FAT, as the Taylor Reynolds number increases, the total SGS kinetic energy flux and its positive and negative components tend to a Reynolds number asymptotic state at small scales for ${\mathrm{Re}}_{\lambda }\ge 105$. In HST, the positive vertical SGS flux of kinetic energy is significantly enhanced by compression motions, causing the vertical SGS flux component to be larger than the streamwise component at small scales. The interscale energy transfer of the solenoidal mode and dilatational mode is studied by employing Helmholtz decomposition. The dilatational kinetic energy of FAT is nearly isotropic, but that of HST is significantly anisotropic. In HST, the dilatational mode obtains energy not only from the solenoidal mode through nonlinear advection, but also from mean shear by the dilatational production. As the turbulent Mach number increases, the nonlinear advection of HST increases first and then decreases. The dilatational production of HST increases monotonically with the turbulent Mach number, providing the main source of kinetic energy to the dilatational mode at high turbulent Mach number $M_t\ge 0.46$.

We present a numerical study on the motion of a rigid cylinder promoted by its interaction with an incoming flow when the cylinder is restricted to move along the arc of a circle and thus has only one degree of freedom. The analysis also includes the description of the flow around the cylinder, which is influenced by the motion of the cylinder. The Reynolds number, based on the diameter of the cylinder and the far-away incoming flow velocity, is 180. It is considered that the diameter of the circle is three times the diameter of the cylinder and that the ratio of the cylinder to fluid densities is 1.6. The mass and momentum conservation equations in two dimensions are solved in a Cartesian grid, and the presence and motion of the cylinder are resolved using the immersed boundary method. The motion of the cylinder and the flow are two-way coupled in the sense that the aerodynamic forces that drive the displacement of the cylinder result from the fluid-solid interaction, and in turn, the flow around the cylinder is modified by its motion. We analyze the initial transient dynamics and long-time behavior for two different cases. The present results illustrate that the motion of the cylinder and the torque are quasiperiodic with cycles composed of three oscillations with different amplitudes. The stagnation point and the boundary layers are displaced periodically around the rim of the cylinder according to the incoming direction of its relative velocity with respect to the fluid. The upper and lower separation points undergo similar periodic angular displacements. This effect is superposed to the alternating vortex shedding mechanism that occurs in fixed cylinders. Two rows of alternating vortices similar to von Karman vortex street are formed downstream of the cylinder, but their centers are farther apart from the symmetry line than those generated in the wake of a fixed cylinder; this effect is closely related to the coupling between the oscillatory motion of the cylinder and the vortex shedding process. The pressure field and the instantaneous streamlines are also presented and related to the dynamical features of the cylinder motion. It is found that the pressure is the dominant effect on the dynamics of the cylinder and its magnitude and the direction of the total force on the cylinder is related to the motion of the cylinder and the genesis and emission of vortices.

In this paper, we present an experimental study of weakly nonlinear interaction of axisymmetric internal gravity waves in a resonant cavity, supported by theoretical considerations. Contrary to plane waves in Cartesian coordinates, for which self-interacting terms are null in a linear stratification, the nonlinear self-interaction of an internal wave mode in axisymmetric geometry is found to be efficient at producing super-harmonics, i.e., waves whose frequencies are integer multiples of the excitation frequency. Due to the range of frequencies tested in our experiments, the first harmonic frequency is below the cutoff imposed by the stratification so the lowest harmonic created can always propagate. The study shows that the super-harmonic wave field is a sum of standing waves satisfying both the dispersion relation for internal waves and the boundary conditions imposed by the cavity walls, while conserving the axisymmetry.

Direct microscopic visualization experiments are reported to quantify the diffusiophoretic migration of oil droplets in high-salinity solutions ($c>0.7$ mol/L). Contrary to usual results in the low-salinity limit, we find negligible enhancement in the droplet migration under electrolyte gradients at high salinity. Rationalization of this observation suggests nonelectrolyte gradients as possible alternatives to effectively drive diffusiophoresis beyond the low-salinity limit. In particular, micelle gradients of the zwitterionic surfactant clearly enhance droplet migration into dead-end channels at high salinity. Characterization of such migration—proceeding down the gradient—indicates repulsive interaction between micelles and droplets, which may involve various micelle dynamics at different salinity conditions. Furthermore, we identify a synergistic effect from simultaneous electrolyte and micelle gradients to further enhance droplet migration. These findings, together with the robustness of our experimental system, contribute knowledge or enable more studies to understand and design colloid migration in varieties of systems at elevated salinity.

Using direct numerical simulation, we study the behavior of the maximal Lyapunov exponent in thin-layer turbulence, where one dimension of the system is constrained geometrically. Such systems are known to exhibit transitions from fully three-dimensional turbulence through a mixed two- and three-dimensional phenomenology state and then onto fully two-dimensional dynamics. We find a discontinuous jump in the Lyapunov exponent at this second transition, implying the predictability of such systems can change dramatically. Such transitions are seen in a number of different turbulent systems, for example, those undergoing strong rotation; hence these results may be relevant for the predictability of complicated real world flows. The Lyapunov exponent is found to provide a particularly clear measure of the transition to two-dimensional dynamics. Finally, the application of these results to atmospheric predictability with regard to high-resolution modeling is examined.

In this paper, the turbulence fields generated by a group of modified fractal grids, referred to as the rectangular fractal grids (RFGs), are documented and discussed. The experiments were carried out using hot-wire anemometry in three facilities at Imperial College London and the Laboratory of Fluid Mechanics in Lille, France. Due to the large Reynolds number of the resulting turbulence, several data processing methods for turbulence properties are carefully evaluated. Two spectral models were adopted, respectively, to correct the large and small wave-number ranges of the measured spectrum. After the technical discussion, the measurement results are presented in terms of one-point statistics, length scales, homogeneity, isotropy, and dissipation. The main conclusions are twofold. First, the location of maximum turbulence intensity $x_{\text{peak}}$ is shown to be independent of the inlet Reynolds number but dependent on the ratio between the lengths of the largest grid bars in the transverse and vertical directions. This is crucial to the production of prescribed features of turbulent flows in laboratory. Second, these RFG-generated turbulent flows are shown to be quasihomogeneous in the decay region for $x/x_{\text{peak}}>1.5$, but the isotropy is poorer than that of the previous studied fractal square grid-generated turbulence. In the beginning of the decay region, a decreasing pattern of the integral length scale $L_u$ and Taylor microscale $\lambda$ was observed, yet the ratio $L_u/\lambda$ remained roughly constant along the centerline, so $C_{\epsilon }\sim {\text{Re}}_{\lambda }^{-1}$, complying with the nonequilibrium scaling relation reported in previous studies for various turbulent flows.

We use the background method to find an upper bound on the nondimensional temperature dissipation, $〈{‖\mathbf{\nabla }T‖}_2^2〉$, for Rayleigh-Bénard convection with the temperature of one boundary modulated in time. The resulting bound depends on characteristics of the temperature modulation profile, $f\left(t\right)$, including the nondimensional parameter $\omega$, which is defined as the supremum of $|f^{\prime }\left(t\right)|$. It is found that the resulting bound on $〈{‖\mathbf{\nabla }T‖}_2^2〉$ grows like $\sqrt{\omega }$ for $\omega \gg \mathrm{Ra}$, with $\mathrm{Ra}$ fixed, and like $\sqrt{\mathrm{Ra}}$ for $\mathrm{Ra}\gg \omega$, with $\omega$ fixed. Asymptotically, the bound for large $\mathrm{Ra}$ has the same leading order behavior as the nonmodulated case, with modulation effects appearing only at $O\left({\mathrm{Ra}}^{-1/2}\right)$.

The transport of energy in a moving fluid with a simply connected free surface is analyzed, taking into account the contribution of surface tension. This is done by following a “control volume” with arbitrary, specified velocity, independent of the flow velocity, and determining the rates of energy passing through the boundaries, as well as the energy dissipation in the bulk. In particular, a simple conservation equation for the surface area is given, which clearly shows the contribution of the Laplace pressure at the free surface and the tangential surface tension forces at its boundary. It emerges as the mechanical conservation law for the surface energy in its general form. For a static control volume, all contributions from surface tension disappear, except that the pressure has to be modified by the Laplace contribution.

A growing body of work on the dynamics of eukaryotic flagella has noted that their oscillation frequencies are sufficiently high that the viscous penetration depth of unsteady Stokes flow is comparable to the scales over which flagella synchronize. Incorporating these effects into theories of synchronization requires an understanding of the global unsteady flows around oscillating bodies. Yet, there has been no precise experimental test on the microscale of the most basic aspects of such unsteady Stokes flow: the orbits of passive tracers and the position-dependent phase lag between the oscillating response of the fluid at a distant point and that of the driving particle. Here, we report the first such direct Lagrangian measurement of this unsteady flow. The method uses an array of 30 submicron tracer particles positioned by a time-shared optical trap at a range of distances and angular positions with respect to a larger, central particle, which is then driven by an oscillating optical trap at frequencies up to 400 Hz. In this microscale regime, the tracer dynamics is considerably simplified by the smallness of both inertial effects on particle motion and finite-frequency corrections to the Stokes drag law. The tracers are found to display elliptical Lissajous figures whose orientation and geometry are in agreement with a low-frequency expansion of the underlying dynamics, and the experimental phase shift between motion parallel and orthogonal to the oscillation axis exhibits a predicted scaling form in distance and angle. Possible implications of these results for synchronization dynamics are discussed.