In the present work we show how the subgrid-scale (SGS) energy transfer among resolved scales in large eddy simulations (LESs) can be used to evaluate unknown constants in SGS models and derive new models. The essence of the method is that for a given LES velocity field energy transfers among resolved scales can be computed without reference to a particular SGS model and then used to estimate the total SGS energy transfer for an unknown, full velocity field. The total transfer becomes a physical constraint on any proposed SGS model and can be used to obtain and update model constants at each time step in actual LES, allowing self-contained simulations. The method is evaluated by implementing it in LESs of high Reynolds number isotropic turbulence and for several classical SGS modeling expressions. It is shown that the performance of models depends not only on their ability to capture the total SGS dissipation (which is enforced by the method) but also by distribution of the SGS dissipation among scales of motion (which is enforced by a model). However, the main conclusion is that a broad class of modeling expressions that only qualitatively approximate the SGS dissipation distribution among scales perform very well in LESs as long us the total dissipation constraint is satisfied. We also discuss the relation of the method to the well-known dynamic modeling procedure.

We simultaneously measure both spinning and tumbling components of rotation for long near-neutrally buoyant fibers in homogeneous and isotropic turbulence. The lengths and diameters of the measured fibers extend to several orders of the Kolmogorov length of the surrounding turbulent flow. Our measurements show that the variance of the spinning rate follows a $-4/3$ power-law scaling with the fiber diameter $\left(d\right)$ and is always larger than the variance of the tumbling rate. This behavior surprisingly resembles that observed previously for sub-Kolmogorov fibers. These observations suggest that long fibers preferentially align with vortex filaments that can be as long as the integral length of turbulence. We compute the Lagrangian timescale and the distribution of both tumbling and spinning that supports this outlook. Our measurements also allow us to quantify the importance of the Coriolis term on the rotational dynamics of fibers in turbulent flows.

The article explores the various mechanisms by which a rotating magnetic field causes to rotate a magnetic fluid contained in a cylinder (the so-called spin-up of ferrofluids). It is shown first that the generally accepted theory of spin diffusion cannot explain this phenomenon due to the extremely low spin viscosity ${\eta }^{\prime }$: Our calculations give ${\eta }^{\prime }\sim {10}^{-14}\mathrm{g}\mathrm{cm}/\mathrm{s}$ which is 11 orders of magnitude less than the most optimistic estimates. Then we develop a theory linking the rotation of a free surface layer to the shape of the meniscus. The latter, equally as the strength and frequency of the rotating field, determines both the direction and the magnitude of the fluid velocity. However, the magnetic torque created on the curved surface of the liquid captures only a thin subsurface layer and does not cause rotation in the volume. As for the volumetric flow, we associate it with the release of heat in microvortices that arise around rotating magnetic particles. In a vertical cylinder, such heating forms a parabolic temperature profile, which makes the magnetization of the fluid spatially inhomogeneous. As shown, this is sufficient to induce an observable bulk flow of the ferrofluid. The influence of natural convection on this spin-up flow is also investigated. In conclusion, it is shown that the stress tensor of a magnetic fluid can always be brought to a symmetric form.

To realize high Reynolds number turbulent flow in a numerical simulation, an artificial energy input is required. In this study, we propose a deterministic forcing method and a stochastic forcing method to maintain the mean turbulence kinetic energy (TKE) and helicity at ideal values. The proposed forcing methods control both the mean TKE and helicity by introducing two tuning parameters: $\alpha$ and $\beta$, where $\alpha$ is the helicity injection rate and $\beta$ is the convergence of target statistical quantities to ideal values. We carried out 24 direct numerical simulations to investigate the effects of the forcing methods, including the tuning parameters, on turbulence. When we controlled the forcing term based on the proposed methods, the temporal correlation between the TKE and energy dissipation rate was artificially suppressed in the deterministic forcing method, and for higher $\beta$ in the stochastic forcing method. No differences were found between the proposed deterministic and stochastic forcing methods in terms of one- and two-point statistics. There are also some common characteristics between the energy and helicity dissipation rates, including the normalized mean energy and helicity dissipation rates, scale-by-scale budgets, and stretched exponential form of probability density functions. The numerical results support the joint cascade scenario of energy and helicity.

The unexpectedly low cavitation inception threshold of water is widely attributed to the presence of cavitation nuclei either in the bulk water or attached to immersed surfaces. Being compressible, such objects are expected to respond to modest tensile stresses. Surprisingly, a large corpus of experiments shows that micro- and nanobubbles attached to planar smooth surfaces are unresponsive to tensile stresses, seemingly ruling out their ability to serve as cavitation nuclei. Here, using optical microscopy we show that, although these surface micro- and nanobubbles are not directly responsive to tensile stresses induced by a nearby cavitation bubble, strong short-lived shear flows induced by cavitation jetting cause tethers to extend from the surface micro- and nanobubbles and lead to the pinch-off of daughter bubbles. Our results show a unique and previously unanticipated mechanism for the generation of cavitation nuclei.

We investigate the behavior of large particles in a transitional swirling flow in a closed vessel, focusing on both their transport and flow sampling. We conduct a Lagrangian study of slightly buoyant particles, considering three particle diameters, keeping the fluid's density and velocity magnitude constant and varying the Reynolds number by changes of the fluid's viscosity. The literature lacks study of material particles in such flows, where chaos and bursts of turbulence can exist, despite applications in industrial and natural situations. One striking result is that particles beyond a certain size, between 10 and 18 mm, are subject to a strong trapping in the vicinity of the islands of the laminar flow, while large particles below this threshold sample the flow homogeneously, independently of the Reynolds number. The exploration of the flow by the large particles is widely different from the preferential sampling in fully developed turbulent conditions, in terms of characteristic times associated with motions escaping the regions and dimensions of the sampled regions. While the particle mean velocity is found to be independent of both the fluid's viscosity and particle size, the fluctuation magnitude strongly increases with decreasing flow viscosity and is marginally affected by size. We also characterize the intensity of the trapping through probability density functions of the particle positions, a measure of the dimensions of the sampled regions, and particle position autocorrelation functions as an attempt to quantify residence times. A qualitative origin for the trapping existence criterion based on a shear-induced lift force is proposed, as an argument for its sole dependence on particle size.

The jet in crossflow, or a transverse jet, eventually undergoes a linear transition from convectively to absolutely/globally unstable as the crossflow to jet velocity ratio increases. This flow field, however, has an extremely complex dynamics. Hence, determining this transition location is not a trivial task. It has long been known that this transition is associated with the upstream shear layer connected to the near field Kelvin-Helmholtz vortex ring, but it was only recently that the most unstable global mode and wave maker were located there as well. These findings led to the realization that an inviscid and planar linear stability analysis of the local velocity profile extracted from the jet in the crossflow upstream shear layer was strongly correlated with its transition to absolute/global instability. It is shown in this paper that such an analysis can be turned into an accurate predictive tool with the use of a viscous (instead of inviscid) and round (instead of planar) mixing layer. In other words, replacing an inviscid analysis of a planar mixing layer with counterflow by a viscous analysis of a round coaxial jet with outer nozzle suction leads to an accurate prediction of the jet in crossflow convective to an absolute instability transition.

We investigate the properties of the scale dependence and cross-scale transfer of kinetic energy in compressible three-dimensional hydrodynamic turbulence by means of two direct numerical simulations of decaying turbulence with initial Mach numbers $M=1/3$ and 1, and with moderate Reynolds numbers, $R_{\lambda }\sim 100$. The turbulent dynamics is analyzed using compressible and incompressible versions of the dynamic spectral transfer (ST) and the Kármán-Howarth-Monin (KHM) equations. We find that the nonlinear coupling leads to a flux of the kinetic energy to small scales where it is dissipated; at the same time, the reversible pressure-dilatation mechanism causes oscillatory exchanges between the kinetic and internal energies with an average zero net energy transfer. While the incompressible KHM and ST equations are not generally valid in the simulations, their compressible counterparts are well satisfied and describe, in a quantitatively similar way, the decay of the kinetic energy on large scales, the cross-scale energy transfer/cascade, the pressure dilatation, and the dissipation. There exists a simple relationship between the KHM and ST results through the inverse proportionality between the wave vector $k$ and the spatial separation length $l$ as $kl\simeq \sqrt{3}$. For a given time, the dissipation and pressure-dilatation terms are strong on large scales in the KHM approach, whereas the ST terms become dominant on small scales; this is due to the complementary cumulative behavior of the two methods. The effect of pressure dilatation is weak when averaged over a period of its oscillations and may lead to a transfer of the kinetic energy from large to small scales without a net exchange between the kinetic and internal energies. Our results suggest that for large-enough systems, there exists an inertial range for the kinetic energy cascade. This transfer is partly due to the classical, nonlinear advection-driven cascade and partly due to the pressure dilatation-induced energy transfer. We also use the ST and KHM approaches to investigate the properties of the internal energy. The dynamic ST and KHM equations for the internal energy are well satisfied in the simulations but behave very differently with respect to the viscous dissipation. We conclude that ST and KHM approaches would better be used for the kinetic and internal energies separately.

Air film stability underneath a drop is crucial for drop contact dynamics upon impact. An unstable film leads to the drop contacting the surface and subsequent spreading or splashing. Apart from previously reported film and kink contact modes, here we present the experimental evidence for a dimple failure mode of an air film, driven by a thin film instability when a drop impacts onto an atomically smooth surface. The dimple failure occurs beyond the inertial-capillary timescale and is initiated when the dimple inverts at the drop's central axis. For the same impact Weber number, the dimple failure observed in low-viscosity drops is absent at a higher viscosity, due to damping of capillary waves.

Flow and transport in coupled channel-matrix systems are ubiquitous to many environmental and engineering applications such as flows in fractured porous media over canopies and in membrane filtration units. The multiscale nature of such systems, where the horizontal length scale is often orders of magnitude larger than the vertical one, allows one to employ vertically averaged descriptions of the system. As a result, two-dimensional transport in the channel and the matrix can be upscaled to a coupled system of transient one-dimensional advection-dispersion equations, where matrix and channel properties can be analytically related to macroscopic transport observables. In this work, we first develop a semianalytical solution based on integral transforms that can be employed to predict macroscopic transport in channel-matrix shear flows in a computationally efficient manner. Then we demonstrate that under appropriate dynamic conditions, the coupled system at the macroscale can be further simplified to a single upscaled one-dimensional advection-dispersion equation, which admits an analytical closed-form solution, thus enabling real-time macroscale concentration estimates in relevant applications.

The stability and overturning of fully three-dimensional internal gravity wave packets is examined for a rotating, uniformly stratified Boussinesq fluid that is stationary in the absence of waves. We derive through perturbation theory an integral expression for the mean flow induced by upward-propagating fully localized wave packets subject to Coriolis forces. This induced Bretherton flow manifests as a dipolelike recirculation about the wave packet in the horizontal plane. We perform numerical simulations of fully localized wave packets with the predicted Bretherton flow superimposed, for a range of initial amplitudes, wave-packet aspect ratios, and relative vertical wave numbers spanning the hydrostatic and nonhydrostatic regimes. Results are compared with predictions based on linear theory of wave breaking due to overturning, convection, self-acceleration, and shear instability. We find that nonhydrostatic wave packets tend to destabilize due to self-acceleration, eventually overturning although the initial amplitude is well below the overturning amplitude predicted by linear theory. Strongly hydrostatic waves, propagating almost entirely in the horizontal, are found not to attain amplitudes sufficient to become shear unstable, overturning instead due to localized steepening of isopycnals. Results are discussed in the broader context of previous studies of one- and two-dimensional wave packets overturning and recent observations of oceanic internal waves.

The physical problem based on a shock-accelerated bubble has long been a fascinating subject in the study of the Richtmyer-Meshkov (RM) instability. In this study the behavior of a shock-accelerated heavy cylindrical bubble under the nonequilibrium conditions of diatomic and polyatomic gases is investigated numerically. For this purpose, a two-dimensional system of unsteady physical conservation laws derived from the Boltzmann-Curtiss kinetic equations is solved by employing an explicit mixed-type modal discontinuous Galerkin method with uniform meshes. For validation, the numerical results are compared with available experimental and computational results, and are found to be in good agreement. The results demonstrate that the effects of different physical properties, including thermal nonequilibrium and bulk viscosity associated with the viscous excess normal stress on diatomic and polyatomic gases, play a significant role in describing the RM instability during the interaction between a planar shock wave and a heavy bubble. The effects of diatomic and polyatomic gases result in a substantial change in the flow morphology with complex wave patterns, vortex creation, vorticity generation, and bubble deformation. In contrast to monatomic gas, the generation of larger rolled-up vortex chains, a different kind of outward jet formation, and a large mixing zone with strong and large expansion are observed in diatomic and polyatomic gases. A detailed study of the effects of diatomic and polyatomic gases is investigated through the vorticity generation, degree of nonequilibrium, the evolution of enstrophy, and dissipation rate. Furthermore, the time variations of the shock trajectories and the interface scales are investigated from the viewpoint of quantitative analysis. Finally, the effects of nonequilibrium parameters, including bulk viscosity and index of inverse power law, are also investigated. The present work can be seen as a supplement to the RM instability research to examine the nonequilibrium effects of diatomic and polyatomic gases on the dynamics of a shock-accelerated heavy cylindrical bubble.

Model form uncertainty arises from physical assumptions made in constructing models either to model physical processes that are not well understood or to reduce the physical complexity. Understanding these uncertainties is important for both quantifying prediction uncertainty and unraveling the source and nature of model errors. Physics-based uncertainty quantification utilizes inherent physical model assumptions to estimate and ascertain the sources of model form uncertainty or error. Compared to data-based approaches, physics-based approaches can be extrapolated beyond available data and go beyond strictly uncertainty estimation. In this work, an implied models approach is developed where the transport equation for the model error is derived by taking the difference between the exact transport equation for a quantity of interest and the transport equation implied by a particular model form. The implied models approach is then specifically applied to the modeling of the Reynolds stresses by the Boussinesq eddy viscosity model. Budgets of the model error transport are analyzed to better understand the sources of error in two-equation Reynolds-averaged Navier-Stokes models focusing on the relative contributions from the Boussinesq hypothesis and the specific form of the eddy viscosity in turbulent channel flow at various friction Reynolds numbers. The results indicate that the errors are largely due to the misalignment of the mean strain rate tensor and the Reynolds stress tensor as well as the high degree of anisotropy near the wall, with errors in the shear component being dominant. An exploration of the $k\text{−}\varepsilon$ and $k\text{−}\omega$ models reveals that both models benefit from error cancellation. In particular, the improved results of the $k\text{−}\omega$ model over the $k\text{−}\varepsilon$ model are shown to be the direct result of this error cancellation. An exploration of the effect of friction Reynolds number on the error budgets reveals that the errors saturate with increasing Reynolds number owing to the relative decrease of anisotropy.

Recent work has used an introduced property, termed granular fluidity (defined as the shear rate divided by the stress ratio), to help quantify and model nonlocal behavior within granular flows. A so-called “microscopic” definition was subsequently proposed which links this granular fluidity to the packing fraction, particle diameter, and the granular temperature. This definition provides a physical basis on which the nature of granular fluidity can be understood. Here we have examined the microscopic definition, first replicating the previously demonstrated behavior using DEM simulations of shear cells and then demonstrating that the relationship's coefficients are dependent on the coefficient of friction, the presence of tangential damping, and the presence of rolling resistance. When the geometry is changed from a shear cell to a cylindrical hopper, the relationship shifts away from the expected response, thus demonstrating that there are geometry dependent effects that are not captured by the original formulation. This shows that granular fluidity is more complex than previously thought and that the current microscopic definition is insufficient.

Inertial particles, i.e., small heavy particles, can inhomogeneously distribute and form clusters even in statistically homogeneous turbulence. When the Reynolds number of turbulence is sufficiently high so that coherent structures with various length and time scales coexist, particles form clusters by the action of the coherent structures when the particle velocity relaxation time is in the inertial-range time scales. In general, thus formed clusters are larger for larger Stokes numbers (the nondimensional relaxation time). We propose a method to objectively describe the particle cluster created by the action of coherent structures in the inertial range. For this purpose, we generalize the sweep-stick mechanism [S. Goto and J. C. Vassilicos, Phys. Rev. Lett. 100, 054503 (2008)] to express two-dimensional sheetlike clusters in terms of the coarse-grained acceleration field of turbulence. The generalized mechanism also predicts the thickness of the clusters, which depends on the particle relaxation time, the magnitude of acceleration gradients, and the lifetime of coherent flow structures. The direct numerical simulations of fully developed turbulence in a periodic cube with the Taylor-length Reynolds number being about 740 support the proposed mechanism.

Inhomogeneous co-flowing fluids inside a microchannel exposed to an acoustic standing wave can lead to the relocation of the fluids. Here we investigate the use of combined acoustic relocation and acoustophoretic migration for the transfer of particles between co-flowing fluids inside a microchannel exposed to a standing pressure half-wave with a pressure nodal plane along the channel center line and antinodal planes along the walls. We show that under the influence of the applied field, particles suspended in a carrier fluid of low acoustic impedance flowing along the channel center are initially dragged toward the walls along with the relocating fluid and later migrate into the target fluid that relocates from the walls to the channel center. We found that the particle motion is initially controlled by the dominant fluid relocation-induced Stokes drag force and later governed by the primary acoustic radiation force as stable fluid configuration is reached. Experimentally we unraveled that depending on the operating parameters—particle size, flow rates, and acoustic energy density—the final locations of the particles at the end of the channel leads to three distinct regimes—complete medium exchange, partial medium exchange, and no medium exchange. Our study reveals that the relocation and migration dynamics of the particles is underpinned by the relevant timescales â advection timescale, acoustophoretic timescale, and the relocation timescale, which in turn govern the different regimes observed. Numerical simulations predicted the complete migration and nonmigration of particles of two different sizes, in agreement with the experimental observations. We also demonstrate the medium exchange and size-based sorting of biological cells, which shows the potential application of the study in biochemical assays.

Statistical quantities in channel (Poiseuille), Couette, and pipe flow, including Reynolds stresses and their budgets, are studied for their dependence on the normalized distance from the wall $y^{+}$ and the friction Reynolds number ${\text{Re}}_{\tau }$. Any quantity $Q$ can be normalized in wall units, based on the friction velocity $u_{\tau }$ and viscosity $\nu$, and it is accepted that the physics of fully developed turbulence in ducts leads to standard results of the type $Q^{+}=f(y^{+},{\text{Re}}_{\tau })$, in which $f(...)$ means “only a function of,” and $f$ is different in different flow types. Good agreement between experiments and simulations is expected. We are interested in stronger properties for $Q$, generalized from those long recognized for the velocity, but not based on first principles. These include the law of the wall $Q^{+}=f\left(y^{+}\right)$; the logarithmic law for velocity; and for the Reynolds-number dependence, the possibility that at a given $y^{+}$ it is proportional to the inverse of ${\text{Re}}_{\tau }$, that is, $Q^{+}(y^{+},{\text{Re}}_{\tau })=f_{\infty }\left(y^{+}\right)+f_{\text{Re}}\left(y^{+}\right)/{\text{Re}}_{\tau }$. This has been proposed before, also on an empirical basis, and recent work by Luchini [Phys. Rev. Lett. 118, 224501 (2017)] for $Q\equiv U$ is of note. The question of whether the profiles are the same in all three flows, in other words, that there is a single function $f_{\infty }$, is still somewhat open. We arrive at different conclusions for different $Q$ quantities. The inverse-${\text{Re}}_{\tau }$ dependence is successful in some cases. Its failure for some of the Reynolds stresses can be interpreted physically by invoking “inactive motion,” following Townsend [The Structure of Turbulent Shear Flow, 2nd ed. (Cambridge University Press, Cambridge, 1976)] and Bradshaw [J. Fluid Mech. 30, 241 (1967)], but that is difficult to capture with any quantitative theory or turbulence model. The case of the boundary layer is studied, and it is argued that a direct generalization of ${\text{Re}}_{\tau }$ is questionable, which would prevent a sound extension from the internal flows.

Various physical principles can be utilized for molecular tagging velocimetry (MTV). In this article, the capabilities and limitations of photoisomerization in MTV are studied. The molecular rotor 9-(2-carboxy-2-cyanovinyl)julolidine (CCVJ) exists in two isomers. Although the $E$ isomer, which is present in the absence of light, yields a fluorescent behavior, the $Z$ isomer is a photoproduct with no detectable luminescence. This regenerative behavior is utilized for MTV. The two time constants define the experimental limitations of the method for tagging and recovery. It is shown that, whereas the tagging time constant is in the range of milliseconds to seconds, the recovery time is in the range of minutes to hours, enabling measurements of slow flow phenomena. A flow in a rectangular channel with a Reynolds number of $9\times {10}^{-3}$ and a Péclet number of 1009 is investigated. Furthermore, the addition of methyl-$\beta$-cyclodextrin (methyl-$\beta$-CD) to the solution increases the fluorescent quantum yield and the isomeric rate constants, supporting the hypothesis of a complex formation with CCVJ. It is shown that photoisomeric MTV is suitable for analyzing slow flow regimes in the liquid phase. The addition of methyl-$\beta$-CD increases the dynamic range of the results. In comparison with existing MTV principles, photoisomerization has the advantage of an intrinsic regenerative behavior. The cost-efficient and simple setup make it an alternative in biological and environmental flow studies.

We study the rheology of suspensions of capsules with a rigid nucleus at negligible and finite flow inertia by means of numerical simulations. The capsule membrane is modeled as a thin Neo-Hookean hyperelastic material and the nucleus as a rigid particle with radius equal to half the radius of the undeformed spherical capsules. The fluid and solid motion are coupled with an immersed boundary method, validated for both the deformable membrane and the rigid nucleus. We examine the effect of the Reynolds number, capillary number, and volume fraction on the macroscopic properties of the suspensions, comparing with the case of capsules without nuclei. To explain the rheological measurables, we examine the mean capsule deformation, the mean orientation with respect to the flow direction, and the stress budget. The results indicate that the relative viscosity decreases with the capillary number, i.e., increasing deformability, and increases with inertia. The presence of a nucleus always reduces the membrane deformation. Capsules align more in the flow direction at higher capillary numbers and at higher volume fractions, where we also see a significant portion of them oriented with their longer deformed axis in the spanwise direction. When increasing inertia, the alignment with the flow decreases while more capsules orient in the spanwise direction. The first normal stress difference increases with the capillary number and it is always less for the nucleated capsules. Finally, the relative viscosity and the first normal stress difference increase with the capsule volume fraction, an effect more pronounced for the first normal stress difference.

For the purpose of turbulence drag reduction, a velocity-temperature coupled control method is proposed based on the velocity boundary layer control and the thermal boundary layer. The spatial evolution of supersonic turbulent boundary layer at a Mach number of 2.25, subject to steady blowing with different velocities and temperatures, is investigated using direct numerical simulations. Noting that the wall is isothermal with nearly adiabatic temperature, it is found that the thickness of boundary layer increases by the control of heated blowing, as do the viscous sublayer and the logarithmic zone. Moreover, drag reduction of 20.1% is achieved by heated wall blowing, higher than that of unheated wall blowing, while drag increases 12.2% by the control of cooled wall blowing. Nevertheless, the control efficiency of heated wall blowing is low due to high energy consumption, which needs further study. The reduction of mean viscous shear stress is mainly responsible for the drag reduction mechanism though there is a substantial increase in Reynolds stresses. Compressible Renard-Deck decomposition of $C_f$ indicates that it is the decrease of the spatial growth term that determines the turbulence drag reduction. The strong Reynolds analogies are still valid in all controlled cases. The average streamwise scale of near-wall streaks reduces by introducing heated blowing. Turbulence amplifications are observed in heated cases while turbulence attenuations are observed in cooled cases.