Turbulence is a mechanism leading to energy dissipation, however it also accumulates energy by spreading it over a range of scales. This valuable energy reservoir is known as the inertial interval. The broader this interval is, the more energy is stored and an interesting question is whether it is possible to efficiently use this energy. Recent advances in the understanding of turbulence rely on the trajectory-based or Lagrangian description of the flow. Here we show how to extract energy from the inertial interval of two-dimensional turbulence by taking advantage of its fine Lagrangian structure. A floating object in wave-driven turbulence can exploit the fluid erratic motion to fuel either directional propulsion or rotation. The shape of the object controls its ability to become a vehicle or a rotor that can tap the energy of correlated bundles of fluid trajectories. These findings offer methods of creating self-propelled devices or turbines utilizing the energy of turbulence.

A resonance between a long wave and a short wave occurs if the phase velocity of the long wave matches the group velocity of the short wave. Rogue waves modeled as special breathers (pulsating modes) can arise from these resonant interactions. This scenario is investigated for internal waves in a density stratified fluid. We examine the properties of these rogue waves, such as the polarity, amplitude and robustness, and show that these depend critically on the specific density stratification and the choice of the participating modes. Three examples, namely, a two-layered fluid, a stratified fluid with constant buoyancy frequency, and a case of variable buoyancy frequency are examined. We show that both elevation and depression rogue waves are possible, and the maximum displacements need not be confined to a fixed ratio of the background plane wave. Furthermore, there is no constraint on the signs of nonlinearity and dispersion, nor any depth requirement on the fluid. All these features contrast sharply with those of a wave packet evolving on water of finite depth governed by the nonlinear Schrödinger equation. The amplitude of these internal rogue waves generally increases when the density variation in the layered or stratified fluid is smaller. For the case of constant buoyancy frequency, critical wave numbers give rise to nonlinear evolution dynamics for “long wave-short wave resonance,” and also separate the focusing and defocusing regimes for narrow-band wave packets of the nonlinear Schrödinger equation. Numerical simulations are performed by using baseband modes as initial conditions to assess the robustness of these rogue waves in relation to the modulation instability of a background plane wave.

We consider sedimentation of a rigid helical filament in a viscous fluid under gravity. In the Stokes limit, the drag forces and torques on the filament are approximated within the resistive-force theory. We develop an analytic approximation to the exact equations of motion that works well in the limit of a sufficiently large number of turns in the helix (larger than two, typically). For a wide range of initial conditions, our approximation predicts that the center of the helix itself follows a helical path with the symmetry axis of the trajectory being parallel to the direction of gravity. The radius and the pitch of the trajectory scale as nontrivial powers of the number of turns in the original helix. For the initial conditions corresponding to an almost horizontal orientation of the helix, we predict trajectories that are either attracted towards the horizontal orientation, in which case the helix sediments in a straight line along the direction of gravity, or trajectories that form a helical-like path with many temporal frequencies involved. Our results provide insight into the sedimentation of chiral objects and might be used to develop new techniques for their spatial separation.

It is known that turbulent energy is rapidly transferred in the direction of the rotation axis in a rotating system, in comparison with the nonrotating case. In this study, this phenomenon is investigated as a problem of energy diffusion expressed by the Reynolds averaged Navier-Stokes (RANS) model. The conventional gradient-diffusion approximation for the turbulent energy flux cannot account for the enhanced energy transport observed in rotating inhomogeneous turbulence. In experiments, inhomogeneity of turbulence is modeled with an oscillating grid, leading to the turbulent energy falling off away from the grid. To adequately describe the phenomenon, we propose a new model for the energy flux due to the pressure associated with the rotational motion of a fluid. The model of the energy flux is expressed to be proportional to the turbulent helicity, which is the statistically averaged value of the inner product of the velocity and vorticity fluctuations. This property is closely related to the group velocity of inertial waves in a rapidly rotating fluid. The validity of the model is assessed using a direct numerical simulation of inhomogeneous turbulence under rotation where the flow configuration is similar to the oscillating-gird turbulence. It is shown that most of the turbulent energy transport enhanced by the system rotation is attributed to the pressure diffusion term. The spatial distribution of the energy flux due to the pressure related to the system rotation is similar to that of the turbulent helicity with negative coefficient. Hence, the new model which is proportional to the turbulent helicity is able to qualitatively account for the enhanced energy flux due to the system rotation. Finally, the helical Rossby number is proposed to estimate the relative importance of the energy flux enhanced by the turbulent helicity and the rotation, in comparison to the conventional gradient-diffusion approximation.

We compare the rheology of two kinds of non-Brownian suspensions. One is made of spherical monodisperse polystyrene particles $(80\mu \text{m}$ in diameter), and the other is made of faceted sugar particles (average size, $100\mu \text{m})$, both suspended in a Newtonian silicon oil. We perform shear reversal experiments on both suspensions for several particle volume fractions, $\varphi$, and several shear stresses, $\tau$. The two suspensions behave in a quite different fashion. For the faceted particle suspensions (FPSs), a large shear thinning is observed, while it is much more moderate for the spherical polystyrene particle suspensions (SPSs). Another striking difference lies in the value of the jamming packing fraction, ${\varphi }_m$, which is much lower for FPSs than for SPSs. Despite these differences, we will show that shear reversal experiments make it possible to obtain a universal scaling that holds for both FPSs and SPSs. In this scaling, the difference between the steady viscosity and the viscosity at the minimum that follows the shear reversal, normalized by the steady viscosity, is shown to depend only on the ratio $\varphi /{\varphi }_m\left(\tau \right)$. The collapse of all the data suggests that concentrated non-Brownian suspensions behave in a universal way regardless of the mechanisms responsible for flow hindering (rotation frustration or sliding friction).

Recent studies have shown that entrainment effectively describes the behavior of natural and forced separating flows developing behind bluff bodies, potentially paving the way to new, scalable separation control strategies. In this perspective, we propose a new interpretative framework for separated flows, based on mass entrainment. The cornerstone of the approach is an original model of the mean flow, representing it as a stationary vortex scaling with the mean recirculation length. We test our model on a set of mean separated topologies, obtained by forcing the flow over a descending ramp with a rack of synthetic jets. Our results show that both the circulation of the vortex and its characteristic size scale simply with the intensity of the backflow (the amount of mass going through the recirculation region). This suggests that the vortex model captures the essential functioning of mean mass entrainment, and that it could be used to model and/or predict the mean properties of separated flows. In addition, we use the vortex model to show that the backflow (an integral quantity) can be estimated from a single wall-pressure measurement (a pointwise quantity). This finding encourages further efforts toward industrially deployable control systems based on mass entrainment.

The leading-edge vortex (LEV) is a universal and robust lift enhancement mechanism in biological flapping and autorotating flight. It is characterized by comparatively low Reynolds number and large angle of attack leading to separated three-dimensional flow, which has long precluded analytical approach to this problem. Here we propose a reduced-order analytical model, which is capable of delivering a fast closed-form estimate of the LEV strength and position for a revolving wing at arbitrary angle of attack. It is postulated that equilibrium state of the vortex is primarily maintained by the competing effects of vorticity production at the leading edge and its three-dimensional transport in the presence of spanwise flow and downwash. The results of the model are found consistent with the LEV strength and centroid coordinates measured previously in experiments, as well as determined from numerical solution of the Navier-Stokes equations, in a wide range of the Reynolds number. The agreement is good not only for rectangular wings, but also for bio-inspired shapes of fruit fly, bumblebee, and hawkmoth. Hence, the model offers a simple, versatile, and reliable tool for practical estimation of the LEV parameters.

The coexistence of multiple turbulent states was reported in several recent studies in different flows. We present in this work that multiple turbulent states also exist for thermal convection in two-dimensional tilted cells with large aspect ratios $\left(\mathrm{\Gamma }=\mathrm{width}/\mathrm{height}\right)$ through direct numerical simulations for the Rayleigh number $\text{Ra}={10}^7$ and the Prandtl number $\text{Pr}=0.71$. The considered $\mathrm{\Gamma }$ ranges from 1 to 16. The tilt angle $\beta$ varies from $0^{\circ }$ to ${180}^{\circ }$. Multiple states are identified for small $\beta$ with $\mathrm{\Gamma }\ge 2$, where the different flow states are reflected in different numbers of convection rolls. The corresponding Nu is generally higher for the flow state with more convection rolls. Moreover, flow mode transitions between different roll states are observed for large $\mathrm{\Gamma }\ge 8$ when $\beta$ is larger than a critical value. The effect of cell tilting on Nu and Re is also investigated. It is found that for $\mathrm{\Gamma }\le 4$, Nu first increases with increasing $\beta$ and then declines after reaching its local maximum. However, Nu generally decreases monotonically with increasing $\beta$ for $\mathrm{\Gamma }=8$, 12, and 16. This indicates that the idea to enhance heat transfer by tilting the cell can be realized only for relatively small $\mathrm{\Gamma }$ for the present system. It is also found that the previous finding that Re decreases monotonically with increasing $\beta$ for large $\beta$ with $\mathrm{\Gamma }=1$ does not hold for large-$\mathrm{\Gamma }$ cases.

It has recently been shown that critical points in the skin friction field of wall turbulence exist and negative streamwise skin friction events occur. Further analysis of the critical points at the wall using direct numerical simulation data of turbulent pipe flow is presented here. After identifying and characterizing features of the “no-slip” critical points in a turbulent pipe flow, conditional averages of the flow are presented to reveal the magnitude and extent of the fluctuations in the flow around these extreme events. It is found that the velocity and skin friction fields near critical points resemble the three-dimensional U separation proposed by Perry and Chong [J. Fluid Mech. 173, 207 (1986)].

The paper presents phenomenology of interaction and penetration of liquid-liquid material interfaces initiated by shock-driven collapse of single and multiple microbubbles situated near the material interface. Previous experimental studies have established such a generic setting as relevant for the investigation of sonoporation, i.e., the perforation of live cells by microbubble collapses. We consider a planar or spherical, single- or dual-layer, material interface between a gelatin material and water. A single or several ideal-gas microbubbles are positioned near the interface. Bubble collapse is initiated by a shock wave with a pressure profile specific to laser generation and is flat when hitting the gas-water interface. The interfacial acoustic impedance match singles out the collapse-induced re-entrant jet as main event. High-resolution sharp-interface numerical methods are employed to ensure that wave dynamics, hydrodynamics, and interface transporting are accurately resolved. Bubble configurations are varied between single and double and between attached and with standoff distance. Parameters varied are shock-wave peak pressure and viscosity ratio between single and double layers of gelatin and the surrounding water. For inertia-dominated cases, two regimes are observed, the first characterized by linear growth of the penetration depth and the second by a $t^{2/3}$ scaling. The latter range is affected by viscosity which reduces penetration speed. The results show that process parameters, in particular shock overpressure, control not only penetration depth but also the size of the interface perforation, indicating means to steer processes in biomedical applications.

An implementation of the Macheret-Fridman (MF) dissociation model for the direct simulation Monte Carlo (DSMC) method is developed in this work. The model maintains the fundamental physical assumptions of the MF model, i.e., that high-energy collisions resulting in dissociation can be described by classical mechanics and are close to the impulsive limit, but also eliminates additional approximations of the MF model by using Monte Carlo sampling. Recent quasiclassical trajectory (QCT) calculations of ${\mathrm{N}}_2$, ${\mathrm{O}}_2$, and NO dissociation reactions and experimental measurements are used to validate the model. In general, the reaction rate constants and average vibrational energy removed at thermal equilibrium and nonequilibrium conditions are in good agreement with the QCT and experimental values. The discrepancies in the absolute values of thermal equilibrium rate constants found in some cases are shown to be caused by the underprediction of collision rates with the variable hard sphere model rather than by the MF model itself. QCT-calibrated collision rates combined with the MF dissociation model for the ${\mathrm{N}}_2+\mathrm{O}$ colliding pair are shown to yield a very good agreement between the computed thermal equilibrium dissociation rates and the QCT results. The model is also evaluated by simulating shock tube experiments with oxygen. The present study suggests the possibility of using the model as the standard dissociation reaction model for nonequilibrium flows.

Simulations are performed of a surfactant-laden drop that is stretched by an imposed uniaxial extension flow at infinity with flow focusing provided by two transverse, coaxial, annular baffles placed symmetrically to either side of the drop. The geometry is axisymmetric, with additional symmetry in the transverse plane that contains the drop center. Under suitable conditions, the drop can enter a mode of drop breakup referred to as tipstreaming, in which a thin elongated filament or thread is emitted from the drop ends and which subsequently breaks up into small droplets via capillary instability. The influence that flow focusing has on the conditions required for tipstreaming and on quantities such as the thread radius are investigated by study of sample simulations and the extent of flow focusing is varied by changing the inner or aperture radius of the annular baffles. The surfactant is soluble and bulk-interface surfactant exchange is in the mixed-kinetic or finite-Biot-number regime. The boundary-integral method is used for the underlying two-phase Stokes flow solver, combined with a finite-difference scheme for evolution of adsorbed surfactant on the interface. The dynamics of dissolved bulk phase surfactant is resolved by a large-bulk-Péclet-number asymptotic approach. Results on the conditions for tipstreaming in the simulations are compared to separate experimental results on conditions for tipstreaming in a microfluidic flow-focusing device.

Richtmyer-Meshkov instability of an inverse-chevron air/${\mathrm{SF}}_6$ interface subjected to a weak shock wave is experimentally studied. The inverse-chevron interface is a typical configuration that possesses multimode features and sharp corners. Using the soap film technique, five inverse-chevron interfaces with different initial vertex angles are generated to highlight the effects of initial amplitude-wavelength ratio on flow characteristics. A high-speed Schlieren system is used to observe the postshock flow field. After shock impact, a vortex pair is derived from the upstream interface, and the scale of the vortex pair is sensitive to the initial amplitude-wavelength ratio. The width growth in the linear phase is measured and compared with the classical impulsive model and a modified model considering a velocity reduction factor, and the latter is proven to be effective for moderate to large initial amplitudes. The linear growth rate is also a nonmonotone function of the amplitude-wavelength ratio. Further comparison with our previous work illustrates that the amplitude-wavelength ratio corresponding to the maximum width growth rate is associated with the Atwood number, which is consistent with the previous numerical results. A weakly nonlinear growth is observed at late stages, which deviates from the predictions of most typical nonlinear models. Finally, an empirical model is proposed that provides a satisfactory prediction of width growth in linear and weakly nonlinear stages.

Free-surface flow past a semi-infinite or a finite-length corrugation in an otherwise flat and horizontal open channel is considered. Numerical solutions for the steady flow problem are computed using both a weakly nonlinear and fully nonlinear model. The new solutions are classified in terms of a depth-based Froude number and the four classical flow types (supercritical, subcritical, generalized hydraulic rise, and hydraulic rise) for flow over a small bump. While there is no hydraulic fall solution for semi-infinite topography, we provide strong numerical evidence that such a solution does exist in the case of a finite-length corrugation. Numerical solutions are also found for the other flow types for either semi-infinite or finite-length corrugation. For subcritical flow over a semi-infinite corrugation, the free-surface profile is found to be quasiperiodic downstream.

Variable-density mixing occurs in the ocean and atmosphere, inertial confinement fusion capsules, stars, and many industrial processes. Our team studies mixing at the laboratory scale, with the goal of extending our understanding to larger and smaller length scales and into multiphysics regimes that include such physics as chemical and thermonuclear reactions and high-energy density plasmas. I will provide examples of studies from Los Alamos in variable-density mixing in multiple regimes, including shock-driven mixing, subsonic mixing, and high-energy density (HED) plasma mixing. In all cases, the density differences of the mixing fluids are at least double, making the mixing well outside regimes covered by the Boussinesq approximation. In these flows, we have discovered time-dependent mixing phenomena, asymmetries in mixing and distribution of turbulent kinetic energy, and interscale energy transfer driven by the mean flow that moves energy from small to large scales via eddy stretching. We have improved our physical understanding by implementing diagnostics such as particle image velocimetry and planar laser-induced fluorescence in challenging, shock-driven flow regimes. Our experimental studies and physical understanding benefit from collaborations with colleagues studying turbulence modeling and performing validation simulations, and these collaborations push us to further improve our experimental platforms and diagnostics.

Changes in bulk rheology of suspensions with the particle concentration are well documented, ranging from normal stress differences to shear-thinning and shear-thickening behaviors. However, relatively little is known about the impact this bulk rheology can have on the interfacial dynamics of free-surface, particle-laden flows. Recently, it has been demonstrated that particles suspended in liquid may cause viscous fingering by modifying the local rheology near the fluid-fluid interface, when a mixture of noncolloidal particles and viscous oil displaces air inside a Hele-Shaw cell. As the same flow configuration sans particles is inherently stable to viscous fingering, the simplicity of the baseline flow renders this a perfect model problem to study to gain insight into the coupling between the bulk rheology and fluid-fluid interface. To that end, we first summarize the recent experimental findings of this particle-induced viscous fingering, which highlights the effect of the particle volume fraction and the particle diameter relative to the gap size on the emergent finger geometries. We also present experimental measurements of the critical viscosity gradient at the fingering onset, as well as the surprising time-independent finger growth regime for sufficiently large volume fractions. These results—both old and new—together highlight the similarities as well as important differences between fingering in suspensions versus pure liquid, suggesting a direction for continued research at the intersection between suspension rheology and interfacial dynamics.

Some of the most interesting structures observed in hydrodynamics are best understood as singularities of the equations of fluid mechanics. Examples are drop formation in free-surface flow, shock waves in compressible gas flow, or vortices in potential flow. These examples show that singularities are characteristic for the tendency of the hydrodynamic equations to develop small-scale features spontaneously, starting from smooth initial conditions. As a result, new structures are created, which form the building blocks of more complicated flows. The mathematical structure of singularities is self-similar, and their characteristics are fixed by universal properties. We review recent developments in this field through the lens of one of the great scientific challenges of today: understanding the structure of turbulence.

For centuries, bubbles have fascinated artists, engineers, and scientists alike. In spite of century-long research on them, new and often surprising bubble phenomena, features, and applications keep popping up. In this paper I sketch my personal scientific bubble journey, starting with single-bubble sonoluminescence, continuing with sound emission and scattering of bubbles, cavitation, snapping shrimp, impact events, air entrainment, and surface micro- and nanobubbles, and finally arriving at effective force models for bubbles and dispersed bubbly two-phase flow. In particular, I also cover various applications of bubbles, namely, in ultrasound diagnostics, drug and gene delivery, piezoacoustic inkjet printing, immersion lithography, sonochemistry, electrolysis, catalysis, acoustic marine geophysical survey, and bubble drag reduction for naval vessels, and show how these applications crossed my way. I also try to show that good and interesting fundamental science and relevant applications are not a contradiction, but mutually stimulate each other in both directions.

A liquid foam, a dense assembly of gas bubbles in a surfactant solution, is a deformable porous material. As classically observed in divided systems, electrokinetic transport can be induced, for example, when an electric field is applied from either side of the foam sample. We determine here the liquid fraction profile obtained when a foam is submitted to an electro-osmotic flow, when the surfactant induces so-called rigid or mobile interfaces. We show that the main governing equation for the liquid fraction repartition in space and time is diffusivelike and similar to the one describing pressure-induced drainage only. The electric field however significantly affects the general profile by modifying the boundary conditions. A capillary number that compares electro-osmotic stress and capillary pressure in the foam geometry is introduced and characterizes the magnitude of electrically induced flow in a macroscopic foam. In particular, the ability of a foam to capture liquid from a reservoir is quantitatively estimated.

Acoustic waves are omnipresent in modern life and are well described by the linearized equations of fluid dynamics. Once generated, linear acoustic waves carry and collect information about their source and the environment through which they propagate, and this information may be retrieved by analyzing recordings of these waves. Because of this, acoustics is the primary means for imaging and remote sensing in otherwise opaque environments, such as the Earth's oceans and crust and the interior of the human body. For these information-retrieval tasks, acoustic fields are nearly always interrogated within their recorded frequency range or bandwidth. However, this frequency-range restriction is not general; acoustic fields may also carry hidden information at frequencies outside their bandwidth that can be revealed by analyzing the quadratic products of a pair of complex frequency-domain field amplitudes having different frequencies. The two unique quadratic field products, known as the frequency-difference and frequency-sum autoproducts, can be utilized for remote sensing at the difference and sum of the two constituent frequencies, respectively, even if these difference and sum frequencies lie outside the recorded field's bandwidth. Despite some fundamental limitations, forming and analyzing the autoproducts enables a variety of acoustic remote sensing applications that were long thought to be impossible. In particular, analysis of the frequency-difference autoproduct allows the detrimental effects of sparse-array recordings, random scattering, and other unknown source-to-receiver propagation effects to be suppressed when the recorded acoustic field has sufficient bandwidth. Examples and applications from laboratory and ocean propagation experiments are provided that involve frequencies from a few Hertz to more than 100 kHz and propagation distances from tens of centimeters to more than 100 km.