This experimental study investigates the effects of Reynolds number ($5000\le \text{Re}\le 20000$, where $\text{Re}=UH/\nu$) and initial release diameter (2.2 mm $\le D\le$ 9.4 mm) on the scalar power spectra, fractal geometry, and turbulent length scales of high-Schmidt-number passive scalar fields resulting from an isokinetic release in a turbulent boundary layer. The turbulence analysis is based on 12 000 scalar fields collected using the planar laser-induced fluorescence technique for each case at six locations downstream. The scalar integral length scale and scalar Taylor microscale are calculated directly from the fields using the autocorrelation function and variance/gradient of the concentration fluctuation fields. With increasing downstream distance, the Taylor microscale decreases and the integral length scale increases, each to an asymptotic value. This indicates a larger range of scales exists as the scalar becomes more mixed, as one would expect. For locations beyond $x/H\ge 10$ (where $H$ is the flow depth), the self-similarity condition is observed by considering the ratio between the scalar integral length scale and scalar Taylor microscale. Local isotropy is approached as measured by computing the ratio of longitudinal to transverse scalar Taylor microscales, and a change in the growth rate is observed for the fractal dimension computed from a planar section of the interfaces in the concentration fluctuation fields. The spectral slope magnitude in the inertial-convective regime decreases near the source ($x/H<10$) due to the large-scale anisotropy. In the self-similar regime ($x/H\ge 10$), the scaling-exponent is found to be dependent on the initial release diameter. The lower wave-number portion of the inertial-convective regime, where the scales are larger than or closer to the scale of the nozzle diameter, scales close to $k^{-1}$ scaling in agreement with the cascade-bypass situation, and the spectral slope in the upper wave-number portion of the inertial-convective regime is found to be closer to $-5/3$. The viscous-convective scaling behavior deviated significantly from Batchelor's $k^{-1}$ scaling law, clearly disputing the generality of Batchelor's arguments. Intermittency analysis, using computation of the intermittency factor as well as probability density functions of the fluctuating scalar gradient, suggests that the discrepancy between theory and observations for the scaling of the viscous-convective regime can be explained by the high intermittency in the small scales of the scalar fluctuations.

This paper presents how the machine learning (ML) approach combined with a three-dimensional (3D) printing technique facilitates the flow analysis in fluidic devices. A digital light processing 3D printing rapidly prototypes geometrically complex flow devices with low cost. Then a simple but powerful machine learning algorithm, the random forests algorithm, is used to classify the flow images taken from semitransparent 3D printed tubes. In particular, this work focuses on the laminar-turbulent transition process occurring in a 3D wavy tube and a straight tube, which is visualized by dye injection. The ML model automatically classifies experimentally obtained flow images within $\sim 0.01$ second per image only and identifies when and where the flow regime changes with an accuracy greater than 0.95. This work demonstrates a high-throughput and accurate method of flow visualization analysis.

This work uses a nonorthogonal multiple-relaxation-time lattice Boltzmann (LB) method to simulate a water droplet impacting on a hydrophobic plate with a cylindrical pore. The LB method is based on a pseudopotential multiphase model with tunable contact angles. It is first validated against experimental data and then employed to study the dynamics of a water droplet impacting a perforated hydrophobic plate. A comprehensive parametric study is carried out by varying the pore size, plate thickness, and Weber number. Based on these results, a phase diagram is constructed to describe the different regimes of droplet penetration behaviors after impingement on the perforated plate. Three distinctive regimes are found, that is, continuously dripping, totally crossing, and hanging, and the mechanisms behind them are scrutinized through the analysis of pressure and energy balance. The competition between the dynamic pressure and the capillary pressure determines the formation of the liquid jet below the plate. Viscous dissipation hinders the development of liquid fingering. Based on the balance of the droplet dynamic pressure, capillary pressure, and the viscous pressure losses, the boundary between different regimes is established.

Despite being a quantum two-fluid system, superfluid helium-4 (He II) is observed to behave similarly to classical fluids when a flow is generated by mechanical forcing. This similarity has brought up the feasibility of utilizing He II for high Reynolds number classical turbulence research, considering the small kinematic viscosity of He II. However, it has been suggested that the nonclassical dissipation mechanism in He II at small scales may alter its turbulent statistics and intermittency. In this work, we report our study of a nearly homogeneous and isotropic turbulence (HIT) generated by a towed grid in He II. We measure the velocity field using particle tracking velocimetry with solidified deuterium particles as the tracers. By correlating the velocities measured simultaneously on different particle trajectories or at different times along the same particle trajectory, we are able to conduct both Eulerian and Lagrangian flow analyses. Spatial velocity structure functions obtained through the Eulerian analysis show scaling behaviors in the inertial subrange similar to that for classical HIT but with enhanced intermittency. The Lagrangian analysis allows us to examine the flow statistics down to below the dissipation length scale. Interestingly, abnormal deviations from the classical scaling behaviors are observed in this regime. We discuss how these deviations may relate to the motion of quantized vortices in the superfluid component in He II.

Direct numerical simulations of compressible turbulent channel flows are performed for bulk Mach numbers 0.8 and 1.5 and bulk Reynolds numbers in the range of $3000\text{–}34000$. The compressibility effects are well accounted for when using the semilocal scaling, as expected. Compared to incompressible flows at comparable semilocal Reynolds number ${\text{Re}}_{\tau c}^{*}$, the mean velocity profile perfectly collapses after the Trettel and Larsson transformation [Trettel and Larsson, Phys. Fluids 28, 026102 (2016)]. Furthermore, the Reynolds stresses, such as their peak values and locations, follow similar trends as in incompressible cases. In particular, the Reynolds shear stress peak follows the nonuniversal scaling transition predicted by Chen et al. [J. Fluid Mech. 871, R2 (2019)]. Although the streamwise Reynolds stress peak continuously increases with Mach number, this increase becomes smaller as the Reynolds number increases. The streamwise and spanwise velocity spectra reveal that the typical eddy size does not vary with the Mach number when scaled using the local friction velocity and thermodynamic properties. Additionally, the compressibility contribution to the skin friction continuously decreases with Reynolds numbers. These results suggest that incompressible and compressible flows differ little at sufficiently high Reynolds number.

We study experimentally the early stages of integrable turbulence of unidirectional deep water gravity waves. By generating partially coherent waves in a $148\text{−}\mathrm{m}$-long wave flume, we observe the emergence of high-amplitude structures formed by nonlinear focusing, commonly referred to as rogue waves. This work confronts the experiment with two recent results obtained in the framework of the nonlinear Schrödinger equation (NLSE), namely that (i) these structures can be locally fitted by a Peregrine soliton and (ii) their emergence leaves a visible trace on the evolution of statistical parameters such as kurtosis. We show that (i) yields accurate results as long as the wave steepness remains moderate, whereas (ii) is very robust and remains valid beyond the assumption of integrability. Numerical simulations of the NLSE and of the fully nonlinear dynamical equations are also performed to support these results.

The diffuse-interface model (DIM) is a tool for studying interfacial dynamics. In particular, it is used for modeling contact lines, i.e., curves where a liquid, gas, and solid are in simultaneous contact. As well as all other models of contact lines, the DIM implies an additional assumption: that the flow near the liquid-gas interface is isothermal. In this work, this assumption is checked for the four fluids for which all common models of contact lines fail. It is shown that, for two of these fluids (including water), the assumption of isothermality does not hold.

Three-dimensional control is considered in the flow past a backward-facing step (BFS). The BFS flow at Reynolds number $\text{Re}=500$ (defined with the step height and the maximum inlet velocity) is two-dimensional and linearly stable but increasingly receptive to disturbances, with a potential for amplification as the recirculation length increases. We compute optimal spanwise-periodic control (steady wall blowing/suction or wall deformation) for decreasing the recirculation length, based on a second-order sensitivity analysis. Results show that wall-normal velocity control is always more efficient than wall-tangential control. The most efficient spanwise wavelength for the optimal control depends on the location: $\beta =0.6$ on the upper wall and $\beta =1$ on the upstream part of the lower wall. The linear amplification of the optimal control resembles the maximum linear gain, which confirms the link between recirculation length and amplification potential in this flow. Sensitivity predictions for blowing/suction amplitudes up to $O\left({10}^{-3}\right)$ and wall deformation amplitudes up to $O\left({10}^{-2}\right)$ are in good agreement with three-dimensional direct numerical simulations. For larger wall deformation amplitudes, the flow becomes unsteady. This study illustrates how the concept of second-order sensitivity and the associated optimization method allow for a systematic exploration of the best candidates for spanwise-periodic control.

Free-surface flows of viscous liquid down an inclined plane and past cylinders of various cross-sections are investigated theoretically and experimentally. The cylinders are oriented with their axis perpendicular to the plane and are sufficiently tall that they are not overtopped. A lubrication model is applied to derive the steady governing equation for the flow depth, which is integrated numerically and analyzed asymptotically to calculate how the depth of a steady uniform flow is perturbed as it flows past the cylinder. Flows past cylinders that are narrow relative to the depth of the oncoming flow are only slightly perturbed, but for relatively wide cylinders, there forms a pond of nearly stationary fluid upstream of the cylinder and a dry region in which there is no fluid downstream of the cylinder. The structure of the flow in the regime of a relatively wide cylinder depends in detail upon the curvature of the cylinder at the upstream stagnation point. For flows past cylinders with circular and square cross-sections, the maximum flow depth occurs at the upstream stagnation point. Its numerical value may be predicted analytically on the basis of the asymptotic expressions and exhibits different dependencies upon the variables that characterize the motion. In addition, wedge-shaped obstructions are analyzed for which the flow depth increases along the wedge wall and the maximum flow depth occurs away from the upstream stagnation point. The results from new laboratory experiments of flows past circular cylinders are reported and these corroborate the theory, confirming the occurrence of both pond and dry regions. The investigation has direct relevance to the deflection of lava flows by barriers and buildings and the theory is employed to deduce simplified asymptotic expressions of the force exerted on the cylinders.

Numerical simulations are carried out to study the spectra and statistics in chemically reacting compressible homogeneous isotropic turbulence at turbulent Mach number $M_t$ from 0.1 to 1.0 and at Taylor Reynolds number ${\mathrm{Re}}_{\lambda }$ from 54 to 103 with solenoidal forcing. A single-step irreversible Arrhenius-type chemical reaction is implemented to evaluate the influence of chemical reaction on spectra and flow statistics. It is shown that in the situation of isothermal reactions, both the ratio of compressible kinetic energy to solenoidal kinetic energy $K^c/K^s$ and the ratio of compressible dissipation to solenoidal dissipation ${\epsilon }^c/{\epsilon }^s$ exhibit a $M_t^4$ scaling at low turbulent Mach numbers $M_t<0.4$. At $M_t⩾0.4$, $K^c/K^s$ and ${\epsilon }^c/{\epsilon }^s$ exhibit $M_t^2$ and $M_t^5$ scaling behaviors, respectively, and the flow is in strong acoustic equilibrium. The spectra of velocity, pressure, density, and temperature are nearly unaffected by the isothermal chemical reaction. In contrast, heat release in exothermal reactions significantly enhances the spectra of velocity and thermodynamic variables in a wide range of length scales. It is found that the spectra of pressure and compressible velocity satisfy the strong acoustic equilibrium relation at $M_t$ from 0.1 to 0.6, indicating that the acoustic mode dominates over the dynamics of compressible velocity and pressure. In the situation of exothermal reactions, $K^c/K^s$ and ${\epsilon }^c/{\epsilon }^s$ appear to be independent of turbulent Mach number. The normalized root-mean-square values of pressure, density, and temperature exhibit a $M_t^2$ scaling in the isothermal reactions and exhibit a $M_t$ scaling in the exothermal reactions.

We report frozen ice patterns for the water droplets impacting on a cold substrate through high-speed images. These patterns can be manipulated by several physical parameters (the droplet size, falling height, and substrate temperature), and the scaling analysis has a remarkable agreement with the phase diagram. The observed double-concentric toroidal shape is attributed to the correlation between the impacting dynamics and freezing process, as confirmed by the spatiotemporal evolution of the droplet temperature, the identified timescale associated with the morphology and solidification $(t_{\mathrm{inn}}\simeq {\tau }_{\mathrm{sol}})$, and the ice front-advection model. These results for frozen patterns provide insight into the complex interplay of the rapid impacting hydrodynamics, the transient heat transfer, and the intricate solidification process.

Closure models for the turbulent scalar flux are an important source of uncertainty in Reynolds-averaged Navier-Stokes (RANS) simulations of scalar transport. This paper presents an approach to quantify this uncertainty in simulations of complex engineering flows. The approach addresses the uncertainty in modeling the pressure scrambling (PS) effect, which is the primary mechanism balancing the productions in scalar flux dynamics. Inspired by the two classical phenomenological theories of return to isotropy (RI) and isotropization of production (IP), we assume that the most likely directions of the PS term are around a fan-shaped region bounded by the RI and IP directions. Subsequently, we propose a strategy that requires two additional simulations, defining perturbations of the PS directions toward the RI and IP limits. The approach is applied to simulations of forced heat convection in a complex pin-fin array configuration, and shows favorable monotonic properties and bounding behaviors for various quantities of interest (QoIs) relevant to heat transfer. To conclude, the results are analyzed from the perspective of transverse scalar transport in a shear flow; the analysis indicates that the proposed approach is likely to exhibit monotonic behaviors in a wide range of scalar transport problems.

We consider a suspension of solid spheres in a viscoelastic suspending fluid. We use the second-order fluid model to capture the first effects of viscoelasticity in the suspension and a mean-field cell model to express the influence of the solid particles. We create a semianalytical constitutive equation for the whole suspension, a second-order fluid with modified material parameters. We find that, in simple shear, the ratio of first normal stress difference to shear stress is independent of volume fraction, but that the second normal stress difference can change sign as the volume fraction of solids increases. Our model is valid for all flows for which the second-order fluid expansion is applicable.

We report the results of our investigation of a fluid-based driven-dissipative oscillator system consisting of a lattice of millimetric fluid droplets bouncing on a vertically vibrating liquid bath and bound within an annular ring. We characterize the system behavior as it is energized through a progressive increase in the bath's vibrational acceleration. Depending on the number of drops, the onset of motion of the lattice may take the form of either out-of-phase oscillations or a striking solitary wavelike instability. Theoretical modeling demonstrates that these behaviors may be attributed to different bifurcations at the onset of instability. The results presented here demonstrate the potential and utility of the walking droplet system as a platform for investigating wave-mediated, inertial, nonequilibrium particle dynamics at the macroscale.

The influence of the gravity level on the frozen wave instability in finite containers of immiscible liquids is investigated numerically to shed light on the transformation from a supercritical pitchfork bifurcation in normal gravity, which produces stable finite-amplitude waves, to an apparently degenerate bifurcation in weightlessness, leading to large columnar patterns that collide with the container walls. The vibroequilibria effect grows in importance as gravity is reduced and has a symmetry-breaking effect on the bifurcation, selecting frozen waves with the heavier fluid displaced upward along the lateral walls. Three possible growth regimes are identified. With finite gravity, there is an initial gravity-capillary regime with the square-root growth predicted by weakly nonlinear theory, associated with small-amplitude waves. This is followed by a linear growth regime that is dominated by gravity and associated with larger finger-like waves. Lastly, in some cases with reduced gravity, we observe a third regime characterized by the close proximity of the frozen wave crests to the upper wall and an interval of nearly saturated wave amplitude. The defining parameters of the bifurcation diagram are measured and presented as a function of Bond number and, when possible, compared with theoretical predictions. In particular, there is excellent agreement between theory and simulations for the weakly nonlinear cubic (branching) coefficient and reasonable qualitative agreement for the threshold. Differences are attributed to finite-size effects, vibroequilibria, and viscosity.

Foraging and other natural phenomena show superdiffusive transport that are described by Lévy walks. We present a model experimental system, an octanoic acid (OA) drop on aqueous unsaturated OA solutions, for studying Lévy walks in controlled environments. The drop spontaneously moves due to unbalanced Marangoni forces, in a manner that mimics biological propulsion in living systems. The drop motion is shown to be a Lévy walk by demonstrating superdiffusive transport, Lévy-stable distributed step lengths, and power-law decay in the velocity autocorrelation function, with consistent exponents.

In this paper, the liquid sloshing problem in an upright circular tank undergoing an oscillation in a single degree of freedom is considered. A fully nonlinear time-domain harmonic polynomial cell (HPC) method based on overset mesh is developed to delve into the flow physics, and the comparison is made with the weakly nonlinear multimodal theory. Both time-harmonic (or periodic) and transient-type oscillations are considered. For the time-harmonic oscillation, planar and swirling waves (including time-harmonic and periodically modulated swirling waves) occur when the excitation frequency is close to the lowest natural frequency. The swirling direction is dependent on initial conditions. The periodically modulated swirling waves switch back and forth between swirling waves and planar waves. The occurrence of swirling waves results in lateral hydrodynamic force and roll moment on top of in-line force and pitch moment components acting on the tank. The sloshing response in terms of surface elevations contains higher harmonic components, while the hydrodynamic forces and moments on the tank are remarkably linear. A NewWave type of excitation is imposed which represents on average the most probable maximum excitation to be expected for a given sea state, and narrow-banded sloshing responses are observed. This allows application of a designer-wave type of excitation which would excite the most probable maximum response in sloshing. A focused-wave-type excitation is also considered, and an impulselike feature is observed in the in-line force and pitch moment components. The total in-line force and pitch moment are further decomposed into inertial component, which is induced by the acceleration of the external motion, and residual component, which is closely associated with the liquid sloshing. It is found that under a focused-wave-type excitation the inertial component contribution is more dominant, while under a designer-wave-type excitation the residual component dominates instead.

Soft modulated phases have been shown to undergo complex morphological transitions, in which layer remodeling induced by mean and Gaussian curvatures plays a major role. This is the case in smectic films under thermal treatment, where focal conics can be reshaped into conical pyramids and concentric ring structures. We build on earlier research on a smectic-isotropic, two-phase configuration in which diffusive evolution of the interface was driven by curvature, while mass transport was neglected. Here, we explicitly consider evaporation-condensation processes in a smectic phase with mass transport through a coexisting isotropic fluid phase, as well as the hydrodynamic stresses at the interface and the resulting flows. By employing the Coleman-Noll procedure, we derive a phase-field model that accounts for a varying density field coupled to smectic layering of the order parameter. The resulting equations govern the evolution of an interface between a modulated phase and an isotropic fluid phase with distinct densities, and they capture compressibility effects in the interfacial region and topological transitions. We first verify a numerical implementation of the governing equations by examining the dispersion relation for interfacial transverse modes. The inverse decay rate is shown to scale as $Q^2$ ($Q$ is the wave number of the perturbation) due to hydrodynamic effects, instead of the $Q^4$ expected for diffusive decay. Then, by integrating the equations forward in time, we investigate fluid flow on distorted layers and focal conics, and show how interfacial stresses and density contrast significantly determine the structure of the flow and the evolution of the configuration.

In this work we investigate flow topology modifications produced by a swarm of large surfactant-laden droplets released in a turbulent channel flow. Droplets have the same density and viscosity of the carrier fluid, so only surface tension effects are considered. We run one single-phase flow simulation at ${\text{Re}}_{\tau }=\rho u_{\tau }h/\mu =300$ and ten droplet-laden simulations at the same ${\text{Re}}_{\tau }$ with a constant volume fraction $\mathrm{\Phi }\simeq 5.4\%$. For each simulation, we vary the Weber number We (ratio between inertial and surface tension forces) and the elasticity number ${\beta }_s$ (parameter that quantifies the surface tension reduction). We use direct numerical simulations of turbulence coupled with a phase-field method to investigate the role of capillary forces (normal to the interface) and Marangoni forces (tangential to the interface) on turbulence (inside and outside the droplets). As expected, due to the low volume fraction of droplets, we observe minor modifications in the macroscopic flow statistics. However, we observe major modifications of the vorticity at the interface and important changes in the local flow topology. We highlight the role of Marangoni forces in promoting an elongational type of flow in the dispersed phase and at the interface. We provide detailed statistical quantification of these local changes as a function of the Weber number and elasticity number, which may be useful for simplified models.

Particle-laden flow in a vertical channel was simulated using a Reynolds-averaged Navier-Stokes two-fluid model including a Reynolds-stress model (RSM). Two sets of cases varying the overall mass loading were done using particle sizes corresponding to either a large or small Stokes number. Primary and turbulent statistics extracted from counterpart Eulerian-Lagrangian and Eulerian-Eulerian anisotropic-Gaussian simulations were used to inform parameters and closures applied in the RSM. While the behavior at the center of the channel compared well with the other simulations, including the transition from fully developed turbulent flow to relaminarization to cluster-induced turbulence as the mass loading increased, the behavior close to the wall deviated significantly. The primary contributor to this difference was the application of a uniform drag coefficient, which resulted in the RSM overpredicting the fluid-phase turbulent kinetic energy close to the wall. When considering small Stokes particles, the RSM at greater mass loadings reproduced the transient clustering observed in the other models. This was not observed using larger particles.