A two-fluid model is used to study the effect of point particles on the Rayleigh-Bénard stability threshold in a laterally unbounded cell. Equal particles are steadily and uniformly introduced at the top plate at their terminal velocity with a fixed temperature. Both velocity and temperature are allowed to vary while, falling, the particles interact with the fluid. This interaction is modulated by the ratio of the particle density and heat capacity to those of the fluid. Particles are found to have a stabilizing effect, which increases with their concentration and density up to several orders of magnitude above the single-phase stability threshold. This result is primarily a consequence of the particle mechanical, rather than thermal, coupling with the fluid. The particle initial temperature has a strong effect on the undisturbed temperature distribution in the cell, which is a significant factor for the stability of the system. The addition of particles greatly increases the dimension of the parameter space necessary to characterize the flow.

The interaction between shear-driven turbulence and stratification is a key process in a wide array of geophysical flows with spatiotemporal scales that span many orders of magnitude. A quick numerical model prediction based on external parameters of stratified boundary layers could greatly benefit the understanding of the interaction between velocity and scalar flux at varying scales. For these reasons, here we use the resolvent framework [McKeon and Sharma, J. Fluid Mech., 658 (2010)] to investigate the effects of an active scalar on incompressible wall-bounded turbulence. We obtain the state of the flow system by applying the linear resolvent operator to the nonlinear terms in the governing Navier-Stokes equations with the Boussinesq approximation. This extends the formulation to include the scalar advection equation with the scalar component acting in the wall-normal direction in the momentum equations [Dawson, Saxton-Fox and McKeon, AIAA Fluid Dyn. Conf. 4042 (2018)]. We use the mean velocity profiles from a direct numerical simulation (DNS) of a stably stratified turbulent channel flow at varying friction Richardson number ${\mathrm{Ri}}_{\tau }$. The results obtained from the resolvent analysis are compared to the premultiplied energy spectra, autocorrelation coefficient, and the energy budget terms obtained from the DNS. It is shown that despite using only a very limited range of representative scales, the resolvent model is able to reproduce the balance of energy budget terms as well as provide meaningful insight into coherent structures occurring in the flow. Computation of the leading resolvent models, despite considering a limited range of scales, reproduces the balance of energy budget terms, provides meaningful predictions of coherent structures in the flow, and is more cost-effective than performing full-scale simulations. This quick model can provide a further understanding of stratified flows with only information about the mean profile and prior knowledge of energetic scales of motion in the neutrally buoyant boundary layers.

We numerically simulate the von Kármán swirling flow driven by viscous stirring with a pair of inversely rotating smooth disks at moderate Reynolds numbers well beyond the first Hopf bifurcation. Despite the time-independent driving mechanism, quantities such as the kinetic energy and its dissipation rate fluctuate quasiperiodically with a period longer than the disk rotation period. We employ the toroidal-poloidal and boundary-bulk decompositions to explain the quasiperiodic fluctuations, which are always observed in the examined Reynolds-number range, and a nontrivial relation between the energy input and dissipation rates. The toroidal-poloidal decomposition of the energy reveals that the quasiperiodic fluctuations originate from the exchange of the two energy components; the growth of the toroidal energy $E^{\text{tor}}$ leads to the growth of the poloidal energy $E^{\text{pol}}$ due to the centrifugal instability, whereas the growth of $E^{\text{pol}}$ leads to the decay of $E^{\text{tor}}$ due to the angular momentum transfer. The boundary-bulk decomposition distinguishes the qualitatively different dynamics coexisting in the system, which explains the nontrivial energy cycle.

The paper describes experiments on a sinusoidally pitching NACA 0012 hydrofoil with reduced frequency $0.16\le k\le 2.51$ and angle of attack amplitude $6^{\circ }\le {\alpha }_m\le {34}^{\circ }$. It extends the chord Reynolds number range with respect to earlier studies to $\text{Re}=5.9\times {10}^4,1.2\times {10}^5,1.9\times {10}^5,\text{and}2.4\times {10}^5$. Lift, drag, and moment are directly measured and compared with predictions from linear inviscid theory, while wake flowfields are visualized by phase-locked particle image velocimetry. Three vortex shedding regimes, i.e., the undulating wake, the reverse von Kármán vortex street, and the leading-edge vortex, are identified from the phase-averaged vorticity fields at different $k$ and ${\alpha }_m$. The nonlinear effect on statistical features of the force and moment responses gradually increases with ${\alpha }_m$. The viscous effect leads to relatively large deviations of the measured responses from the linear inviscid models at low $k$. With increasing Re the measured values gradually approach those predicted by the models. Moreover, linear inviscid theory cannot capture the ${\alpha }_m$-dependent behavior of the drag and moment phase lags ${\psi }_d$ and ${\psi }_m$, respectively, resulting in a larger deviation from the measured values. A linear variation of ${\psi }_m$ with ${\alpha }_m$ is found at $k$ and Re for which the reverse von Kármán vortex street dominates. Within the trailing-edge shedding regimes of the undulating wake and the reverse von Kármán vortex street, the force and moment responses are largely insensitive to the wake pattern at varied ${\alpha }_m$. However, in the leading-edge vortex regime, at low $k$ and large ${\alpha }_m$, the flow remains no longer attached and the time-dependent pitching moment is found to be strongly affected by the leading-edge vortex over the wing.

Reduction in contact time and area between the rebounding droplet and the solid surface has attracted great attention due to the potential applications in many fields, such as self-cleaning and anti-icing. In this paper, we provide an alternative strategy for designing a functional surface, craterlike structure, with which the interaction parameter (the integration of contact area over time) can be reduced by over $75\%$. Systematic investigations on the parameters of craterlike structure, including its diameter, depth, and landing location, have been conducted by a particle-based numerical method, many-body dissipative particle dynamics. This work could be helpful for the design and preparation technology of functional surfaces.

Drying of droplets on inclined substrates is relevant to applications such as spray coating, ink-jet printing, and crime-scene reconstruction. Recent experiments have shown that steeper substrate inclination can significantly slow droplet evaporation due to faster droplet depinning. Motivated by these experiments, we develop a lubrication-theory-based model to study the effect of substrate inclination on the evaporation of two-dimensional pure-solvent and particle-laden droplets on smooth and rough inclined substrates. A system of partial differential equations describing the time evolution of the droplet thickness and the colloidal particle concentration is derived and then solved with a finite-difference method. The contact-line motion is described with a disjoining-pressure/precursor-film approach, and the well-known one-sided model is used to describe solvent evaporation. Our results indicate that on smooth substrates steeper inclination speeds up evaporation due to larger deformation of the droplet interface, which leads to a smaller droplet thickness. On rough substrates, the effect of substrate inclination on evaporation depends on the Bond number (Bo). At lower $\mathrm{Bo}$, steeper substrate inclination slows evaporation due to faster droplet depinning, which leads to a larger droplet thickness. At higher $\mathrm{Bo}$, the droplet does not pin due to stronger gravitational forces, and steeper substrate inclination speeds up evaporation, similar to smooth substrates. When colloidal particles are present, the resulting final particle deposition patterns are strongly dependent on the initial conditions ($\mathrm{Bo}$, inclination angle, initial particle concentration, wettability) rather than being a function of only substrate inclination. Our model predictions qualitatively agree with previous experimental work and disentangle the effects of evaporation, substrate inclination, and surface roughness.

Interfacial instabilities play a major role in breakup events in turbulent multiphase flow. Their role has been clearly identified for two-fluid atomization, and is of paramount importance in spray formation. In planar geometries, Kelvin-Helmholtz instabilities are the main mechanism of creation of a two-phase mixing layer, and information such as wavelengths and frequencies is available in the literature. In cylindrical geometries, the instabilities quickly become three-dimensional and thorough characterization is lacking, despite a wide range of applications using coaxial atomization. We conduct an experimental study of how the interfacial instabilities of a liquid jet surrounded by a turbulent gas co-flow accelerate and develop, before break-up and spray formation. We use high-speed shadowgraphy over a wide range of gas Reynolds numbers to compute the velocity of interfacial perturbations, using Lagrangian tracking, followed by a Eulerian conditioning to obtain local statistics. We identified two regimes of the gradient of the longitudinal mean velocity as a function of the gas Reynolds number: a quadratic scaling at low gas Reynolds numbers and a linear scaling at higher gas Reynolds number. In contrast, the transverse velocity gradients show a linear scaling with gas Reynolds number throughout the studied range.

This work extends the framework of the partially averaged Navier-Stokes (PANS) equations to variable-density flow, i.e., multimaterial and/or compressible mixing problems with density variations and production of turbulence kinetic energy by both shear and buoyancy mechanisms. The proposed methodology is utilized to derive the PANS BHR-LEVM closure. This includes a priori testing to analyze and develop guidelines toward the efficient selection of the parameters controlling the physical resolution and, consequently, the range of resolved scales of PANS. Two archetypal test-cases involving transient turbulence, hydrodynamic instabilities, and coherent structures are used to illustrate the accuracy and potential of the method: the Taylor-Green vortex at Reynolds number $\mathrm{Re}=3000$, and the Rayleigh-Taylor flow at Atwood number 0.5 and ${\left(\mathrm{Re}\right)}_{max}\approx 500$. These representative problems, for which turbulence is generated by shear and buoyancy processes, constitute the initial validation space of the new model, and their results are comprehensively discussed in two subsequent studies. The computations indicate that PANS can accurately predict the selected flow problems, resolving only a fraction of the scales of large-eddy simulation and direct numerical simulation strategies. The results also reiterate that the physical resolution of the PANS model must guarantee that the key instabilities and coherent structures of the flow are resolved. The remaining scales can be modeled through an adequate turbulence scale-dependent closure.

In this paper, we present a simplified theoretical model based on the method of images that predicts the direction of the microjet produced after the implosion of a cavitation bubble created in a corner of a free interface and rigid wall. Our theoretical predictions have been verified by means of a thorough experimental study in which the distances of the pulsed-laser cavitation bubble to the wall and the free surface are varied in a systematic manner. In addition, we extend the predictions to arbitrary values of the corner angle, $\pi /\left(2n\right)$ with $n$ a natural number. The present analytical solution might be a hint to a practical design for preventing cavitation-induced damage.

The shear instability of stratified fluids is a well-studied problem in transition to turbulence. In temperate lakes, early springs typically lead to a weak thermal stratification involving water both above and below the temperature at which the density maximum occurs. This implies that mixing of two parcels with the same density, but different temperature, can lead to the creation of denser fluid, a phenomenon known as cabbeling. We report on simulations of shear instability in the cabbeling regime. We find that the initial stages of instability are dominated by shear instability, yielding billows. However, these billows are systematically located below the centerline of the shear layer. Three-dimensionalization occurs through Rayleigh-Taylor-like instabilities, and cabbeling efficiency is greatly increased in the fully three-dimensionalized state. By contrasting with initial states that have the same density profile, but a temperature well outside of the cabbeling regime, we demonstrate that the fully three-dimensional state of the density field is fundamentally different in the cabbeling regime.

Planar hydraulic jump at small inclinations of a narrow rectangular conduit is investigated by means of extensive experiments and theoretical analysis. Both upslope and downslope flows are considered for “natural” jumps formed solely by viscous shear without any geometrical obstruction. The effect of increasing conduit tilt from $-ve$ (upslope) to $+ve$ (downslope) is similar to increasing liquid flow rate. Additional intricacies are noted when flow downstream of the jump approaches the conduit ceiling. In particular, upslope flow exhibits unique instabilities and undergoes a hysteretic excursion to regain the initial stable state. The hydrodynamic states observed for different flow rate and conduit inclination are consolidated as a phase diagram that identifies the natural jump regime bounded by supercritical flow, subcritical flow, and full bore flow throughout the conduit and also demonstrates the existence of multiple hydrodynamic states for a certain range of operating conditions. This study reports jump induced hysteretic flow in sloping conduits. Apart from experiments, the classical shallow water theory is reformulated by incorporating the effect of turbulent viscosity and lateral averaging along the conduit width to account for sidewall effects. Additionally, mass and momentum balance across the jump is used to identify the domain of the natural jump in horizontal conduits. The theoretical predictions are in close agreement with experimental results. This is an analysis of the turbulent natural jump in slightly deviated narrow conduits.

It is shown how the variable density model that governs the Rayleigh-Taylor instability for the miscible mixing of two incompressible fluids can be transformed into a diffusive version of the inhomogeneous, incompressible Navier-Stokes equations forced by gradients of the composition density $\rho$ of the mixing layer. This demonstrates how buoyancy-driven flows drive and enhance Navier-Stokes turbulence. The role of the potential vorticity $q=\mathit{\omega }·\nabla \rho$ is also discussed.

A polyatomic gas with slow relaxation of the internal modes in contact with a solid boundary is considered. In a previous paper [K. Aoki et al., Phys. Rev. E 102, 023104 (2020)], the two-temperature Navier-Stokes system, i.e., a set of compressible Navier-Stokes equations with the translational and internal temperatures, was derived from the ellipsoidal-statistical (ES) model of the Boltzmann equation for a polyatomic gas under the assumption that the Knudsen number is small and the ratio of the collisional mean free time to the relaxation time of the internal modes is as small as the Knudsen number. In the present study, the appropriate boundary conditions for the two-temperature Navier-Stokes system are derived by the analysis of the Knudsen layer on the basis of the ES model for a polyatomic gas and the Maxwell-type diffuse-specular reflection condition on the boundary. The resulting boundary conditions, which are of the type of slip boundary conditions, are summarized, together with the two-temperature Navier-Stokes equations, in a form that is applicable to practical applications immediately.

The transport of liquid and of small rigid spherical particles in a high-Prandtl-number ($\text{Pr}=68$) thermocapillary liquid bridge under zero gravity is studied by highly resolved numerical simulations when the flow arises as an azimuthally traveling hydrothermal wave with azimuthal wave number one. The Langrangian transport of fluid elements reveals the coexistence of regular and chaotic streamlines in the frame of reference rotating with the wave. The structure of the KAM (Kolmogorov-Arnold-Moser) tori is unraveled for several Reynolds numbers for which the flow is periodic in time and space. Based on the streamline topology the segregation of small rigid spherical particles of a dilute suspension into particle accumulation structures (PASs) is studied, based on the steric finite-particle-size effect when the particles moves close to the free surface. It is shown that the intricate KAM structures have their counterparts in a multitude of different attractors for the particle motion. Examples of PASs are provided, and their dependence on particle size, particle-to-fluid density ratio, and Reynolds number are discussed. A large parametric study reveals the most probable combinations of particle size and density ratio which lead to particle clustering.

This paper investigates the variety of dynamics displayed by two identical interwoven helical vortices for different values of their helical pitch. We present simplified approaches aimed at understanding their nonlinear time evolution: in order of increasing complexity, we use models of nonlinear interaction of two point-vortex alleys, of two vortex-ring filament alleys, and of two inviscid helical filaments. Each of these inviscid models leads to a dynamical system of few degrees of freedom that can be analyzed in terms of orbits in a phase space structured by elliptical and hyperbolic points. At low pitch, the basic state with the two helical vortices in symmetric configuration is an unstable equilibrium, and it corresponds to hyperbolic points in the phase space. An initial perturbation induces different types of dynamics depending on its direction and amplitude. Features observed for increasing helical pitches in direct numerical simulations or in experiments are gradually understood as the model complexity is increased. At small pitch, leapfrog cycles are triggered by axial or azimuthal displacements of the vortices, while radial perturbations trigger overtaking; for both regimes, a periodic change in the interwaving order of the vortices occurs. Above a critical pitch value, small-amplitude perturbations trigger a new regime called fluttering, mainly characterized by a periodic evolution of the vortex radii without a change of the interwaving order; large-amplitude displacements then still allow for leapfrog dynamics far from equilibrium. The amplitudes of the radial excursions of the vortices induced by small perturbations are characterized over the whole range of helical pitches, up to the linear stabilization threshold. Mimicking viscous effects in the point-vortex alley model sheds some light on how dissipation causes overtaking to turn into leapfrog (the reverse is not observed).

The present Letter addresses the resuspension of microscopic glass particles from a monolayer bed into a turbulent gas flow. With an intermediate surface coverage, here set to about $10\%$ of the field of view, we report two distinct detachment mechanisms. At relatively low flow velocities, few loosely adhering particles move on the wall to eventually collide with neighboring particles resulting in a clustered resuspension. At higher fluid velocities, mostly individual particles resuspend due to their interaction with the turbulent flow. The resuspension curve, showing the remaining particle fraction as a function of the flow velocity, exhibits a strong bimodal character.

Following recent evidence that the vortices in decaying two-dimensional turbulence can be classified into small mobile and large quasistationary, this paper examines the evidence that the latter might be considered a crystal whose formation embodies the inverse cascade of energy towards larger scales. Several diagnostics of order are applied to the ostensibly disordered large vortices. It is shown that their geometric arrangement is substantially more regular than random, that they move more slowly than could be expected from simple mean-field arguments, and that their energy is significantly lower than in a random reorganization of the same vortices. This is traced to screening of long-range interactions by the preferential association of vortices of opposite sign and it is argued that this is due to the mutual capture of corotating vortices, in a mechanism closer to tidal disruption than to electrostatic screening. Finally, the possible relation of these stochastic crystals to fixed points of the dynamical system representation of the turbulence flow is briefly examined.

The generation of large-scale flows by stochastically excited internal gravity waves remains largely unexplored despite numerous applications in geophysical and astrophysical contexts. Here, we investigate this problem experimentally in a cylindrical annulus geometry. Our working fluid is made of two layers. In the top, fresh water layer, turbulence is generated by 12 jets with an oscillating flow rate. Those turbulent fluctuations impinge the interface with the bottom, linearly stratified, salt water layer, where they excite internal gravity waves which propagate, damp viscously, and generate a mean azimuthal flow. The jet structure, wave spectra, and mean-flow properties are addressed using particle image velocimetry. Our measurements validate quantitatively the transfer of momentum from the waves to the mean flow through the wave associated Reynolds stress, as previously validated for a monochromatic forcing. In addition, wave energy decays through time, likely because of the mixing at the interface between the two layers, and the driven mean flow accordingly decreases and eventually vanishes. This has up to now prevented the observation of quasibiennial-oscillation-like reversals in our system.

We investigate the onset and evolution of zonal flows in a growing convective layer when a stably stratified fluid with a composition gradient is cooled from above. This configuration allows the study of zonal flows for a wide range of values of the Rayleigh number and aspect ratio of the convection zone within a given simulation. We perform a series of two-dimensional (2D) simulations using the Boussinesq approximation with aspect ratio of the computational domain between 1 and 5 and Prandtl number (Pr) $\mathrm{Pr}=0.1$, 0.5, 1, and 7. For simulations with aspect ratio of one we find that zonal flows appear when the aspect ratio of the convective layer is smaller than 2, and the evolution of the system depends on the Prandtl number. For $\mathrm{Pr}\le 1$, the fluid experiences bursts of convective transport with negligible convective transport between bursts. The magnitude and frequency of the bursts are smaller at low Pr, which suggests that the bursting regime is stronger in a narrow range around $\mathrm{Pr}=1$ as observed in previous studies of thermal convection. For $\mathrm{Pr}=7$, the structure of the flow consists of tilted convective plumes, and the convective transport is sustained at all times. In wider domains, the aspect ratio of the convective zone is always much larger than 2, and zonal flows do not appear. These results confirm and extend to fluids with stable composition gradients previous findings on thermal convection. The fact that zonal flows can be avoided by using computational domains with large aspect ratios opens up the possibility of 2D studies of convective overshoot, layer formation, and transport properties across diffusive interfaces.