For turbulent boundary-layer flow under a uniform freestream speed $U_{\infty }$ over a plate of length $L$, covered with uniform roughness of nominal sand-grain scale $k_s$, the physical behaviors underlying two distinguished limits at large ${\text{Re}}_L\equiv U_{\infty }L/\nu$ are explored: the fully rough wall flow where $k_s/L$ is fixed and the long-plate limit where ${\text{Re}}_k\equiv U_{\infty }{k}_s/\nu$ is fixed. For the fully rough limit it is shown that not only is the drag coefficient $C_D$ independent of ${\text{Re}}_L$ but that a universal skin-friction coefficient $C_f$ and normalized boundary-layer thickness $\delta /k_s$ can be found that depends only on $k_s/x$, where $x$ is the downstream distance. In the long-plate limit, it is shown that the flow becomes asymptotically smooth at huge ${\text{Re}}_L$ at a rate that depends on ${\text{Re}}_k$. Comparisons with wind-tunnel and field data are made.

An energy spectrum is preliminarily characterized by its mean and standard deviation. In this study, we derive exact expressions for the means and bandwidths of space-time energy spectra at fixed frequencies. The mean wave numbers are used to determine the phase velocities that bridge from temporal spectra to space-time spectra. The bandwidths are used to measure the well-known spectral broadening. We show that phase velocities alone are insufficient to determine the bandwidths of energy spectra. As a result, the cross-spectral method predicts narrower bandwidths of energy spectra. Therefore, in addition to phase velocities, amplitudes are used to rescale the space-time energy spectra, leading to the correct bandwidths. Existing data from direct numerical simulations of turbulent channel flows validate the rescaling approach.

We use two-dimensional numerical simulations to study dense suspensions of non-Brownian hard particles using the Critical Load Model (CLM) under constant confining pressures. At constant packing fraction this simple model shows shear thickening as the tangential forces get activated upon increased shear stresses. By parameterizing a simple binary system of frictional and nonfrictional particles of different proportions we show that the jamming packing fraction, at which the viscosity diverges, is controlled by the fraction of frictional contacts. The viscosity of dense suspensions can thereby be expressed as a function of the fraction of frictional contacts as well as the packing fraction of solid particles. In addition, we show that there exists a simple relationship between the fraction of frictional contacts and the two control parameters (under confining pressure): the viscous number $J$ and the ratio between the repulsive barrier force and confining pressure. Under confining pressures the viscosity curves are found to depend on the shear protocol, with the possibility of yielding negative dynamic compressibility, an analog to the discontinous shear thickening found at high but constant packing fractions for the same system.

We demonstrate experimentally that clogging in a silo correlates with some features of the particle velocities in the outlet proximities. This finding, that links the formation of clogs with a kinematic property of the system, is obtained by looking at the effect that the position of the lateral walls of the silo has on the flow and clogging behavior. Surprisingly, the avalanche size depends nonmonotonically on the distance of the outlet from the lateral walls. Apart from evidencing the relevance of a parameter that has been traditionally overlooked in bottleneck flow, this nonmonotonicity supposes a benchmark with which to explore the correlation of clogging probability with different variables within the system. Among these, we find that the velocity of the particles above the outlet and their fluctuations seem to be behind the nonmonotonicity in the avalanche size versus wall distance curve.

We study fully compressible convection in the context of plane-parallel, polytropically stratified atmospheres. We perform a suite of two- (2D) and three-dimensional (3D) simulations in which we vary the initial superadiabaticity ($\epsilon$) and the Rayleigh number (Ra) while fixing the initial density stratification, aspect ratio, and Prandtl number. The evolved heat transport, quantified by the Nusselt number (Nu), follows scaling relationships similar to those found in the well-studied, incompressible Rayleigh-Bénard problem. This scaling holds up in both 2D and 3D and is not appreciably affected by the magnitude of $\epsilon$.

We measure the Marangoni elasticity of a flowing soap film to be 22 mN/m irrespective of its width, thickness, flow speed, or the bulk soap concentration. We perform this measurement by generating an oblique shock in the soap film and measuring the shock angle, flow speed, and thickness. We postulate that the elasticity is constant because the film surface is crowded with soap molecules. Our method allows nondestructive measurement of flowing soap film elasticity and the value 22 mN/m is likely applicable to other similarly constructed flowing soap films.

In this work, we examine the influence of viscosity on breakup and coalescence of a swarm of large drops in a wall-bounded turbulent flow. We consider several values of surface tension and a wide range of drops to fluid viscosity ratios $\lambda ={\eta }_d/{\eta }_c$ (with ${\eta }_d$ the viscosity of the drops and ${\eta }_c$ the viscosity of the carrier fluid), from $\lambda =0.01$ to $\lambda =100$, while we maintain the same density for drops and carrier fluids. Drops can coalesce and break following a complex dynamics that is primarily controlled by the interplay between turbulence fluctuations (measured by Reynolds number, ${\text{Re}}_{\tau }$), surface tension (measured by Weber number, $\text{We}$), and $\lambda$. We use direct numerical simulation of turbulence coupled with a phase field method to describe the drops dynamics. We consider three different values of $\text{We}$ (which is the inverse of the surface tension): $\text{We}=0.75$, 1.5, and 3. For each value of $\text{We}$, we assume five values of $\lambda$: $\lambda =0.01$, 0.1, 1, 10, and 100. We observe a consistent action of increasing $\lambda$, which, especially for the larger Weber numbers, decreases significantly the breakup rate of the drops. Qualitatively, an increase of drop viscosity decreases the breakup rate, very much like an increase of surface tension does. The mechanism by which drop viscosity acts is a modulation of turbulence fluctuations inside the drop, which reduces the work surface tension has to do to preserve drop integrity. We believe that this may give important indications in many industrial applications to control drop coalescence and fragmentation via the ratio of drop to fluid viscosity.

This paper describes a study of the self-sustaining process in wall turbulence. The study is based on a second order statistical state dynamics model of Couette flow in which the state variables are the streamwise mean flow (first cumulant) and perturbation covariance (second cumulant). This statistical state dynamics model is closed by either setting the third cumulant to zero or by replacing it with a stochastic parametrization. Statistical state dynamics models with this form are referred to as S3T models. S3T models have been shown to self-sustain turbulence with a mean flow and second order perturbation structure similar to that obtained by direct numerical simulation of the equations of motion. The use of a statistical state dynamics model to study the physical mechanisms underlying turbulence has important advantages over the traditional approach of studying the dynamics of individual realizations of turbulence. One advantage is that the analytical structure of S3T statistical state dynamics models isolates the interaction between the mean flow and the perturbation components of the turbulence. Isolation of the interaction between these components reveals how this interaction underlies both the maintenance of the turbulence variance by transfer of energy from the externally driven flow to the perturbation components as well as the enforcement of the observed statistical mean turbulent state by feedback regulation between the mean and perturbation fields. Another advantage of studying turbulence using statistical state dynamics models of S3T form is that the analytical structure of S3T turbulence can be completely characterized. For example, the perturbation component of turbulence in the S3T system is demonstrably maintained by a parametric perturbation growth mechanism in which fluctuation of the mean flow maintains the perturbation field which in turn maintains the mean flow fluctuations in a synergistic interaction. Furthermore, the equilibrium statistical state of S3T turbulence can be demonstrated to be enforced by feedback regulation in which transient growth of the perturbations episodically suppresses streak growth, preventing runaway parametric growth of the perturbation component. Using S3T to isolate the parametric growth and feedback regulation mechanisms allows a detailed characterization of the dynamics of the self-sustaining process in S3T turbulence with compelling implications for advancing understanding of wall turbulence.

Ever since the discovery of Quincke rotation (spontaneous rotation of a particle in fluid under a dc electric field) more than 100 years ago [G. Quincke, Ann. Phys. (Leipzig) 295, 417 (1896)], the strength of the dc field has been the only external parameter to actively tune the rotation speed. In this paper we theoretically propose an optically tunable Quincke rotor exploiting the photoconductivity of a semiconducting nanometer-thin oblate spheroid. A full analysis of the instability of the Quincke rotation reveals that, unlike a prolate spheroid, no bistability is possible in such a dynamical system. In addition, the required material property and the strength of the dc electric field needed to realize the rotation are also elucidated. It is also predicted that light can be used to tune the spinning speed or simply turn on and off the Quincke rotation very effectively.

The flow in a rapidly rotating cylinder is studied numerically. The cylinder is split in half, and the rapid rotation in the two halves is modulated harmonically with a small amplitude. We consider modulation frequencies ranging from zero to twice the background rotation frequency, so that the system supports inertial waves. The split in the cylinder at midheight provides a localized perturbation from which inertial wave beams emanate, but so too do the corners where the endwalls and the sidewall meet. There is no discontinuity in the boundary condition at these corners, but the thin modulated endwall and sidewall boundary layers meet at the corners, and this leads to a localized perturbation to the rapid background rotation. This interaction produces inertial wave beams that over wide parameter regimes are more intense than those from the split at the cylinder midheight. Due to finite viscosity and nonlinear flow conditions, the wave beams produce intricate patterns formed by constructive and destructive interference as they self-intersect and reflect off cylinder boundaries and the axis. These patterns are very sensitive to the modulation frequency. Additionally, a phase difference between the modulations of the two cylinder halves was imposed. The phase difference impacts the symmetries of the system and its response to the modulations. In particular, some low-order Kelvin modes are driven resonantly, and their selection depends not only on the frequency but also on the phase of the differential modulation.

Oblique impact of drops onto a solid or liquid surface is frequently observed in nature. Most studies on drop impact and splashing, however, focus on perpendicular impact. Here we study oblique impact of $100\mu \text{m}$ drops onto a deep liquid pool, where we quantify the splashing threshold, maximum cavity dimensions and cavity collapse by high-speed imaging above and below the water surface. Gravity can be neglected in these experiments. Three different impact regimes are identified: smooth deposition onto the pool, splashing in the direction of impact only, and splashing in all directions. We provide scaling arguments that delineate these regimes by accounting for the drop impact angle and Weber number. The angle of the axis of the cavity created below the water surface follows the impact angle of the drop irrespectively of the Weber number, while the cavity depth and its displacement with respect to the impact position do depend on the Weber number. Weber number dependency of both the cavity depth and displacement is modeled using an energy argument.

The bathtub vortex has been found to autonomously arise owing to instability of a symmetric flow in a rectangular vessel when water is drained. We consider a model flow through a vessel with a rectangular horizontal cross section and a drain hole at the center of the bottom to investigate the physical mechanism for generation of swirling fluid motion like the bathtub vortex and the sequential transitions of the flow by numerical simulations and the linear stability analyses. The water surface is assumed to be flat even after instability. If the flow becomes unstable under this assumption, it assures that the surface deformation is irrelevant to the instability. It is emphasized that our interest is not limited to the real bathtub vortex but directed to occurrence of a large vortex in a flow having two reflectional symmetries. The configuration of the vessel has the double plane symmetry (DPS), which allows the flow have the same DPS at small Reynolds numbers. It is found that the instabilities and hence transitions occur accompanying symmetry-breaking of the flow field. Namely, the DPS flow experiences instability to yield vortical motion above a critical Reynolds number, losing the DPS but retaining the $\pi$-rotational (twofold rotational) symmetry around the center axis. The vortical flow also becomes unstable at a higher Reynolds number, makes a transition, and loses the $\pi$-rotational symmetry, but still keeps the time-translation symmetry, i.e., steadiness. The steadiness is broken at an even higher Reynolds number, owing to instability caused by an oscillatory mode of disturbance. The first and second transitions of the flow are identified as pitchfork bifurcations, and the third transition is identified as a Hopf bifurcation.

We aim at studying gasodynamic vortex cooling in an analytically solvable, thermodynamically consistent model that can explain limitations on the cooling efficiency. To this end, we study an angular plus radial flow between two (coaxial) rotating permeable cylinders. Full account is taken of compressibility, viscosity, and heat conductivity. For a weak inward radial flow the model qualitatively describes the vortex cooling effect, in terms of both temperature and the decrease of the stagnation enthalpy, seen in short uniflow vortex (Ranque) tubes. The cooling does not result from external work and its efficiency is defined as the ratio of the lowest temperature reached adiabatically (for the given pressure gradient) to the lowest temperature actually reached. We show that for the vortex cooling the efficiency is strictly smaller than 1, but in another configuration with an outward radial flow, we find that the efficiency can be larger than 1. This is related to both the geometry and the finite heat conductivity.

A method is presented for deriving random velocity gradient tensors given a source tensor. These synthetic tensors are constrained to lie within mathematical bounds of the non-normality of the source tensor, but we do not impose direct constraints upon scalar quantities typically derived from the velocity gradient tensor and studied in fluid mechanics. Hence, it becomes possible to ask hypotheses of data at a point regarding the statistical significance of these scalar quantities. Having presented our method and the associated mathematical concepts, we apply it to homogeneous, isotropic turbulence to test the utility of the approach for a case where the behavior of the tensor is understood well. We show that, as well as the concentration of data along the Vieillefosse tail, actual turbulence is also preferentially located in the quadrant where there is both excess enstrophy $\left(\text{Q}>0\right)$ and excess enstrophy production $\left(\text{R}<0\right)$. We also examine the topology implied by the strain eigenvalues and find that for the statistically significant results there is a particularly strong relative preference for the formation of disklike structures in the $(\text{Q}<0,\text{R}<0)$ quadrant. With the method shown to be useful for a turbulence that is already understood well, it should be of even greater utility for studying complex flows seen in industry and the environment.

This paper investigates the linear instability of compound liquid threads in the presence of surfactant. The limitation of the one-dimensional approximation in previous work [Craster, Matar, and Papageorgiou, Phys. Fluids 15, 3409 (2003)] is removed; hence the radial dependence of the axial velocity can be taken into account. Therefore both the stretching and the squeezing modes can be investigated. The disturbance growth rate is reduced with an increase of the dimensionless surface-tension gradient (whether in the stretching or squeezing mode). For the parameter range investigated, it is found that the squeezing mode is much more sensitive to the Marangoni effect than the stretching mode. The disturbance axial velocity and disturbance surfactant concentration for a typical case is investigated. It is found that the disturbance axial velocity is close to uniform in the stretching mode when the dimensionless surface-tension gradient and the wave number are small. In contrast, for wave numbers close to cutoff, or a large dimensionless surface-tension gradient, or in the squeezing mode, the disturbance axial velocity is not uniform. Analytical relations between growth rate and wave number valid in the long-wave limit are derived. In the stretching mode, the flow moves from an extension-dominated regime to a shear-dominated regime when ${\beta }_1+R\sigma {\beta }_2$ increases through $1+R\sigma$, where ${\beta }_1$ and ${\beta }_2$ are the dimensionless surface-tension gradient of the inner and outer interface, respectively, $R$ is the radius ratio, and $\sigma$ is the surface tension ratio. In the squeezing mode, whatever the values of ${\beta }_1$ and ${\beta }_2$, the flow is always in the shear-dominated regime. The expressions of the leading-order axial perturbation velocity in the long-wave limit are derived and they explain the applicability of one-dimensional models. It is found that the leading-order axial velocity in the extension-dominated regime is always uniform and one-dimensional models work well in this regime. For the shear-dominated regime, the leading-order axial velocity can be either nonuniform or close to uniform, depending on the ratio between the dimensionless surfactant diffusivity $d_1$ and the Laplace number $\mathrm{La}$: when $d_1\gg \mathrm{La}$ the velocity profile is close to uniform and one-dimensional models work well; otherwise the velocity profile is nonuniform and one-dimensional models fail.

Ventilated cavitation occurs as a complicated problem if the free surface is close to the cavity boundary around a high-speed underwater vehicle. The present study investigate the cavitating flow around a blunt axisymmetric body very near the free surface. A typical experiment is conducted by using a launching system with a split Hopkinson pressure bar device, and a numerical scheme is established based on large eddy simulation and volume-of-fluid methods. Unsteady behavior, including air entrainment and shedding of the cloud cavity, is observed, and high consistency is achieved between numerical and experimental results. Distinctions of evolution features between the cavities on the upper and lower sides are presented and analyzed. First, strong entrainment of noncondensable air occurs and changes the fluid property inside the cavity, which makes the cavity larger. Moreover, given the small distance between the vehicle and the free surface, the re-entrant jet generated in the upper part is thin and cannot completely cut off the main cavity, which causes the upper part of the cavity to remain approximately unchanged after the growth stage without the occurrence of the shedding phenomenon. Finally, the evolution of vortex structures is also discussed by comparisons with the motions of the air entrainment, re-entrant jet, and shedding cavity.

We study viscous fingering formation in radial Hele-Shaw cell geometry considering the combined action of capillary and inertial effects for arbitrary values of viscosity and density ratios. We tackle the problem by employing a perturbative mode-coupling approach and focus our attention on weakly nonlinear stages of the dynamics. If inertial effects are neglected, our theoretical results indicate that the shape of the resulting interfacial patterns is significantly affected by changes in the viscosity ratio. Under such conditions, the growing fingers tend to proliferate through a repeated ramification process (e.g., by finger bifurcation, quadrifurcation, etc.) as the capillary number is increased. Nevertheless, we find that this scenario is dramatically altered when inertia is taken into account. When inertia is relevant, the conventional finger splitting morphologies are replaced by three-lobed structures, characterized by the occurrence of sidebranching phenomena. We verify that slightly different types of sidebranched patterns arise, presenting either wide or sharp fingertips, for a range of capillary numbers and density ratios.

Direct numerical simulation of fully developed, internally heated channel flows with isothermal walls is performed using the low-Mach-number approximation of Navier-Stokes equation to investigate the influence of temperature-dependent properties on turbulent scalar statistics. Different constitutive relations for density $\rho$, viscosity $\mu$, and thermal conductivity $\lambda$ as a function of temperature are prescribed in order to characterize the turbulent scalar statistics. It is shown that the dominant effect caused by property variations on scalar statistics can be parameterized by two nondimensional parameters, namely the semilocal Reynolds number ${\text{Re}}_{\tau }^{★}\equiv {\text{Re}}_{\tau }\sqrt{(\overline{\rho }/{\rho }_w)}/(\overline{\mu }/{\mu }_w)$ (the bar and subscript $w$ denote Reynolds averaging and wall value respectively, while ${\text{Re}}_{\tau }$ is the friction Reynolds number based on wall values), and the local Prandtl number ${\text{Pr}}^{★}={\text{Pr}}_w\left(\overline{\mu }/{\mu }_w\right)/\left(\overline{\lambda }/{\lambda }_w\right)$ (${\text{Pr}}_w$ is the molecular Prandtl number based on wall values). Near-wall gradients in ${\text{Re}}_{\tau }^{★}$ modulate the turbulent heat flux generation mechanism because of structural changes in turbulence. However, the influence of these modulations on the inner scaling of turbulent heat conductivity normalized by local mean viscosity is shown to be weak. Using this observation, a temperature transformation is derived that is invariant of ${\text{Re}}_{\tau }^{★}$ variations and only exhibits a ${\text{Pr}}^{★}$-dependent shift.

In this paper we analyze the active and hibernating turbulence in drag-reducing plane Couette flows using direct numerical simulations of the viscoelastic finitely extensible nonlinear elastic model with the Peterlin approximation fluids. The polymer-turbulence interactions are studied from an energetic standpoint for a range of Weissenberg numbers (from 2 up to 30), fixing the Reynolds number based on the plate velocities at 4000, the viscosity ratio at 0.9, and the maximum polymer molecule extensibility at 100. The qualitative picture that emerges from this investigation is a cyclic mechanism of energy exchange between the polymers and turbulence that drives the flow through an oscillatory behavior.

Viscous heating is investigated using high-resolution direct numerical simulations. Scaling relations are derived and verified for different values of the Reynolds and Prandtl numbers. The scaling of the heat fluctuations is shown to depend on Lagrangian correlation times and on the scaling of dissipation-rate fluctuations. The convergence of the temperature spectrum to asymptotic scaling is observed to be slow, due to the broadband character of the temperature production spectrum and the slow convergence of the dissipation-rate spectrum to its asymptotic form.