Sustained and rapid advances in computing have enabled the conduct of direct numerical simulations (DNS) at increasing problem sizes and higher levels of physical realism, which have in turn contributed to many advances in understanding turbulence. However, continuing and future success at the “extreme-scale” level will likely require new algorithms adapted to emerging heterogeneous architectures, and even then, long simulations at extreme problem sizes are probably still too costly. In this paper we first describe the essential elements of an asynchronous parallel algorithm for DNS of incompressible isotropic turbulence, which scales effectively up to $18{432}^3$ resolution (more than 6 trillion grid points) on a world-class IBM-NVIDIA CPU-GPU machine. We then propose a simulation paradigm, built on the idea that, for physical quantities of short timescales, sampling over well-separated snapshots in a long simulation at high resolution can be replaced by sampling over short simulation segments with a high degree of statistical independence evolved from snapshots at modest or even low resolution. The total computational cost is now counted in Kolmogorov timescales instead of large-eddy timescales, leading to tremendous savings at high Reynolds number. This “Multiple Resolution Independent Simulations” (MRIS) approach is validated through a series of comparisons, and subsequently applied to obtain results on fine-scale intermittency, at Taylor-scale Reynolds numbers 390 to 1300, with grid spacing smaller than the Kolmogorov length scale. The results show conclusively that extreme fluctuations of the dissipation rate are usually accompanied by extreme enstrophy, while extreme enstrophy is usually accompanied by less-intense dissipation. Statistics of the locally averaged dissipation and enstrophy suggest these two variables scale together at inertial-range scale sizes (but not in the dissipation range). Finally, brief remarks are made concerning perspectives on likely major challenges in an exascale future, and several other topics of study where the MRIS approach may be useful.

Understanding how turbulence leads to the enhanced irreversible transport of heat and other scalars (such as salt and pollutants) in density-stratified fluids is a fundamental and central problem in geophysical and environmental fluid dynamics. There is a wide range of highly important applications, an important example being the description and parameterization of diapycnal transport in the world's oceans, a key area of uncertainty in climate modeling. Recently, possibly due to the proliferation of data obtained through direct observation, numerical simulation, and laboratory experimentation, there has been an explosion in research activity directed at improving community understanding, modeling, and parametrization of the subtle interplay among energy conversion pathways, turbulence, and irreversible mixing in density-stratified fluids. However, there are still leading-order open questions and areas of profound uncertainty concerning this interesting and important research challenge.

Suspensions are considered from the perspective of development of their bulk fluid mechanics. Suspension mechanics has had a fluid mechanical basis since its inception, as description of the motion of such a mixture requires consideration of the coupling of fluid motions to the surface stresses driving motion on the particles. While it thus sits on a very firm foundation of prior study of the microhydrodynamics, i.e., the microscale forces and motions of the particles and their relation to the properties, the bulk fluid mechanics of suspensions is still in its early stages. This work first outlines the foundations and then proceeds to describe some basic developments from studies exploring the behavior of suspensions as bulk fluids. The focus is on the near-hard-sphere suspension of solid particles in Newtonian liquid, for which a coherent and extensive, though far from complete, understanding of properties and phenomena exists; an overview of the state of understanding of rheology and migration phenomena is provided. This is followed by a consideration of part of the rather limited body of work which explores a central fluid mechanical paradigm of the viscous-inertial balance, i.e., the influence of the bulk Reynolds number $Re$, emphasizing its impact on two flows studied by the author, namely stability of bulk suspensions in pipe and Taylor-Couette (TC) flows. In the TC flow, states not seen in pure fluids under similar conditions are observed. Similarly, elevated Reynolds number flow in bifurcating conduit flows is shown to challenge our ability to predict behavior based on continuum descriptions of the particle phase, indicating directions for productive study.

Understanding multiphase flows is vital to addressing some of our most pressing human needs: clean air, clean water, and the sustainable production of food and energy. This article focuses on a subset of multiphase flows called particle-laden suspensions involving nondeforming particles in a carrier fluid. The hydrodynamic interactions in these flows result in rich multiscale physics, such as clustering and pseudo-turbulence, with important practical implications. Theoretical formulations to represent, explain, and predict these phenomena encounter peculiar challenges that multiphase flows pose for classical statistical mechanics. A critical analysis of existing approaches leads to the identification of key desirable characteristics that a formulation must possess in order to be successful at representing these physical phenomena. The need to build accurate closure models for unclosed terms that arise in statistical theories has motivated the development of particle-resolved direct numerical simulations (PR-DNS) for model-free simulation at the microscale. A critical perspective on outstanding questions and potential limitations of PR-DNS for model development is provided. Selected highlights of recent progress using PR-DNS to discover new multiphase flow physics and develop models are reviewed. Alternative theoretical formulations and extensions to current formulations are outlined as promising future research directions. The article concludes with a summary perspective on the importance of integrating theoretical, modeling, computational, and experimental efforts at different scales.

This paper shows that the wavelength and rate of spatial attenuation of the small ripples accompanying the large waves that form on a liquid film flowing down an inclined plane are dictated by the requirement that their velocity equal the velocity of the large wave. For this purpose numerical simulations of film flow are carried out and validated by comparison with published work. The wavelength and rate of spatial attenuation of the computed capillary waves are shown to equal, to an excellent approximation, the corresponding quantities obtained from an approximate form of the Orr-Sommerfeld equation in which the phase velocity is set equal to the velocity of the large waves. Thus the overall structure of the falling film waves is similar to that encountered in many other problems exhibiting a wave-hierarchical structure, such as waves in dusty or reacting gases, hydraulic jumps, undular bores, and others.

We report experimental evidence of a new merge-split transition (MST) to elastoinertial turbulence (EIT) in Taylor-Couette flows of viscoelastic polymer solutions, caused by merging and splitting of base Taylor vortices when crossed by elastic axial waves (rotating standing waves, RSW). These vortex merging and splitting events are not due to transient behavior, finite aspect ratio, or shear-thinning behavior. They are random in nature and increase in frequency with Re; when superimposed on a RSW flow state they cause abrupt changes in the axial spatial wavelength, leading to the transition from a RSW to the EIT state. We thus identify MST as an inertial feature solely triggered by elasticity and independent of any shear-thinning behavior.

A subcritical route to turbulence via purely quasi-two-dimensional mechanisms, for a quasi-two-dimensional system composed of an isolated exponential boundary layer, is numerically investigated. Exponential boundary layers are highly stable and are expected to form on the walls of liquid metal coolant ducts within magnetic confinement fusion reactors. Subcritical transitions were detected only at weakly subcritical Reynolds numbers (at most $\approx 70$% below critical). Furthermore, the likelihood of transition was very sensitive to both the perturbation structure and initial energy. Only the quasi-two-dimensional Tollmien–Schlichting wave disturbance, attained by either linear or nonlinear optimization, was able to initiate the transition process, by means of the Orr mechanism. The lower initial energy bound sufficient to trigger transition was found to be independent of the domain length. However, longer domains were able to increase the upper energy bound, via the merging of repetitions of the Tollmien–Schlichting wave. This broadens the range of initial energies able to exhibit transitional behavior. Although the eventual relaminarization of all turbulent states was observed, this was also greatly delayed in longer domains. The maximum nonlinear gains achieved were orders of magnitude larger than the maximum linear gains (with the same initial perturbations), regardless if the initial energy was above or below the lower energy bound. Nonlinearity provided a second stage of energy growth by an arching of the conventional Tollmien–Schlichting wave structure. A streamwise independent structure, able to efficiently store perturbation energy, also formed.

Transition prediction is an important aspect of aerodynamic design because of its impact on skin friction and potential coupling with flow separation characteristics. Traditionally, the modeling of transition has relied on correlation-based empirical formulas based on integral quantities such as the shape factor of the boundary layer. However, in many applications of computational fluid dynamics, the shape factor is not straightforwardly available or not well-defined. We propose using the complete velocity profile along with other quantities (e.g., frequency, Reynolds number) to predict the perturbation amplification factor. While this can be achieved with regression models based on a classical fully connected neural network, such a model can be computationally more demanding. We propose a convolutional neural network inspired by the underlying physics as described by the stability equations. Specifically, convolutional layers are first used to extract integral quantities from the velocity profiles, and then fully connected layers are used to map the extracted integral quantities, along with frequency and Reynolds number, to the output (amplification ratio). Numerical tests on classical boundary layers clearly demonstrate the merits of the proposed method. More importantly, we demonstrate that, for Tollmien-Schlichting instabilities in two-dimensional, low-speed boundary layers, the proposed network encodes information in the boundary-layer profiles into an integral quantity that is strongly correlated to a well-known, physically defined parameter—the shape factor.

The structure of turbulent wall-bounded flows is comprised by a complete spectrum of scales. Studies showed that the large-scale structures of the outer layer influence near-wall small-scale structures by several mechanisms, namely, superposition, amplitude and frequency modulation, and distortions by sweeps and ejections. Most analyses focus on one specific aspect of these phenomena, which means that the full interaction scenario is not comprehensively analyzed. In this paper, a method is presented which targets the combined effect of superposition, amplitude modulation, and distortions on the near-wall dynamics. It is validated against synthetic signals to provide a reliable tool for further analysis including the scale separation technique and the detection and elimination of large-scale influences. For the sake of clarity, the proposed method is applied to one-dimensional signals. Besides synthetic data, one-dimensional time-dependent streamwise velocity fluctuations of a near-wall and an outer-layer location extracted from a three-dimensional direct numerical simulation of a turbulent channel flow at ${\text{Re}}_{\tau }\approx 1000$ are analyzed. The paper shows that scale separation by the empirical mode decomposition approach and by conventional spectral filtering yields similar conclusions about the interaction mechanisms. However, the empirical mode decomposition is advantageous since it does not require any a priori knowledge about the analyzed flow and, thus, preprocessing and error sources are reduced. Furthermore, an approach for the investigation of the amplitude modulation is presented. Compared to existing techniques, it is superior in revealing this phenomenon due to a preceding removal of the influences of superposition and distortions and a different approach to determine the near-wall modulation. The near-wall and the outer-layer large-scale amplitudes are determined from the analytical large-scale signals, which are obtained by the Hilbert transform. Unlike conventional methods, this approach reveals the existence of a significant amplitude modulation across the channel half-height.

The two-fluid (ions and electrons) plasma Richtmyer-Meshkov instability of a cylindrical light-heavy density interface is numerically investigated without an initial magnetic field. Varying the Debye length scale, we examine the effects of the coupling between the electron and ion fluids. When the coupling becomes strong, the electrons are restricted to co-move with the ions and the resulting evolution is similar to the hydrodynamic neutral fluid case. The charge separation that occurs between the electrons and ions is responsible for the self-generated electromagnetic fields. We show that the Biermann battery effect dominates the generation of magnetic field when the coupling between the electrons and ions is weak. In addition to the Rayleigh-Taylor stabilization effect during flow deceleration, the interfaces are accelerated by the induced spatiotemporally varying Lorentz force. As a consequence, the perturbations develop into the Rayleigh-Taylor instability, leading to an enhancement of the perturbation amplitude compared with the hydrodynamic case.

Spark plasma discharges induce vortex rings and a hot gas kernel. We develop a model to describe the late stage of the spark-induced flow and the role of the vortex rings in the entrainment of cold ambient gas and the cooling of the hot gas kernel. The model is tested in a plasma-induced flow using density and velocity measurements obtained from simultaneous stereoscopic particle image velocimetry and background oriented schlieren. We show that the spatial distribution of the hot kernel follows the motion of the vortex rings, whose radial expansion increases with the electrical energy deposited during the spark discharge. The vortex ring cooling model establishes that entrainment in the convective cooling regime is induced by the vortex rings and governs the cooling of the hot gas kernel, and the rate of cooling increases with the electrical energy deposited during the spark discharge.

To analyze the influence of a precipitation mineralization reaction between dissolved ${\mathrm{CO}}_2$ and calcium ions on the convective transfer of ${\mathrm{CO}}_2$ toward an aqueous phase, the convective dissolution of ${\mathrm{CO}}_2$ into aqueous solutions of calcium hydroxyde $\left[\mathrm{Ca}{\left(\mathrm{OH}\right)}_2\right]$ and calcium chloride $\left({\mathrm{CaCl}}_2\right)$ of various concentrations is studied experimentally. We show that different precipitation patterns develop in the aqueous solution depending on the nature and concentration of the reactant in the host phase. In the case of $\mathrm{Ca}{\left(\mathrm{OH}\right)}_2$, precipitation coupled to convection leads to vigorous convective mixing in the host phase and sedimentation of solid particles of calcium carbonate $\left({\mathrm{CaCO}}_3\right)$ down to the bulk of the reservoir. Conversely, dissolution of ${\mathrm{CO}}_2$ in buffered ${\mathrm{CaCl}}_2$ solutions leads to a stabilization of the buoyancy-driven convection due to a decrease in density and the adherence of the precipitate to the cell walls.

Reservoir computing is an efficient implementation of a recurrent neural network that can describe the evolution of a dynamical system by supervised machine learning without solving the underlying mathematical equations. In this work, reservoir computing is applied to model the large-scale evolution and the resulting low-order turbulence statistics of a two-dimensional turbulent Rayleigh-Bénard convection flow at a Rayleigh number $\mathrm{Ra}={10}^7$ and a Prandtl number $\mathrm{Pr}=7$ in an extended spatial domain with an aspect ratio of 6. Our data-driven approach, which is based on a long-term direct numerical simulation of the convection flow, comprises a two-step procedure: (1) reduction of the original simulation data by a proper orthogonal decomposition (POD) snapshot analysis and subsequent truncation to the first 150 POD modes which are associated with the largest total energy amplitudes; (2) setup and optimization of a reservoir computing model to describe the dynamical evolution of these 150 degrees of freedom and thus the large-scale evolution of the convection flow. The quality of the prediction of the reservoir computing model is comprehensively tested by a direct comparison of the results of the original direct numerical simulations and the fields that are reconstructed by means of the POD modes. We find a good agreement of the vertical profiles of mean temperature, mean convective heat flux, and root-mean-square temperature fluctuations. In addition, we discuss temperature variance spectra and joint probability density functions of the turbulent vertical velocity component and temperature fluctuation, the latter of which is essential for the turbulent heat transport across the layer. At the core of the model is the reservoir, a very large sparse random network characterized by the spectral radius of the corresponding adjacency matrix and a few further hyperparameters which are varied to investigate the quality of the prediction. Our work demonstrates that the reservoir computing model is capable of modeling the large-scale structure and low-order statistics of turbulent convection, which can open new avenues for modeling mesoscale convection processes in larger circulation models.

We show that when a drop of water is maintained in its Leidenfrost regime, a sound in the form of periodic beats emits from the drop. The process of beat emission involves two distinct frequencies. One component is the frequency of beats itself, and the second is the frequency of sound in every beat which is emitted when one oscillation in the drop occurs. Experiments were performed by placing a drop of water over a concave metallic surface, and the beats of the drop were recorded by fixing a microphone above the drop. A video camera was also fixed above the drop to record its oscillations. Simple analytical techniques like Fourier and wavelet transforms of the audio signals and image processing of the videos of the drop were used to gain insight into the mechanism of the beat emission process. This analysis also helped us in studying the dependence of frequencies, if any, on the radius of the drop and the substrate temperature.

The withdrawal of a liquid or the translation of a liquid slug in a capillary tube leads to the deposition of a thin film on the inner wall. When particles or contaminants are present in the liquid, they deposit and contaminate the tube if the liquid film is sufficiently thick. In this article, we experimentally investigate the condition under which particles are deposited during the air invasion in a capillary tube initially filled with a dilute suspension. We show that the entrainment of particles in the film is controlled by the ratio of the particle and the tube radii and the capillary number associated with the front velocity. We also develop a model which suggests optimal operating conditions to avoid contamination during the withdrawal of a suspension from a tube. This deposition mechanism can also be leveraged in coating processes by controlling the deposition of particles on the inner walls of channels.

Acoustically actuated sessile bubbles can be used as a tool to manipulate microparticles, vesicles, and cells. In this work, using acoustically actuated sessile semicylindrical microbubbles, we demonstrate experimentally that finite-sized microparticles undergo size-sensitive migration and trapping toward specific spatial positions in three dimensions with high reproducibility. The particle trajectories are successfully reproduced by passive advection of the particles in a steady three-dimensional streaming flow field augmented with volume exclusion from the confining boundaries. For different particle sizes, this volume exclusion mechanism leads to three regimes of qualitatively different migratory behavior, suggesting applications for separating, trapping, and sorting of particles in three dimensions.

Heavy particles in turbulent flows have been shown to accumulate in regions of high strain rate or low vorticity, a process otherwise known as preferential concentration. This can be observed in geophysical flows and is inferred to occur in astrophysical environments, often resulting in rapid particle growth, which is critical to physical processes such as rain or planet formation. Here we study the effects of preferential concentration in a two-way coupled system in the context of the particle-driven convective instability. To do so, we use direct numerical simulations and adopt the two-fluid approximation. We focus on a particle size range for which the latter is valid, namely, when the Stokes number is $\lesssim O\left(0.1\right)$. For Stokes number above $\sim 0.01$, we find that the maximum particle concentration enhancement over the mean scales with the rms fluid velocity $u_{\mathrm{rms}}$, the particle stopping time ${\tau }_p$, and the assumed particle diffusivity ${\kappa }_p$ from the two-fluid equations, as $u_{\mathrm{rms}}^2{\tau }_p/{\kappa }_p$. We show that this scaling can be understood from simple arguments of dominant balance. We also show that the typical particle concentration enhancement over the mean scales as ${(u_{\mathrm{rms}}^2{\tau }_p/{\kappa }_p)}^{1/2}$. We finally find that the probability distribution function of the particle concentration enhancement over the mean has an exponential tail whose slope scales as ${(u_{\mathrm{rms}}^2{\tau }_p/{\kappa }_p)}^{-1/2}$. We apply our model to geophysical and astrophysical examples, and discuss its limitations.

A dynamic subgrid-scale (SGS) scalar-flux model, based on the exact rate of production of turbulent scalar fluxes, is proposed. The model is derived from an assumption that the pressure-scalar correlation in the equation for turbulent scalar flux is a vector that is approximately aligned with the scalar flux itself. The formulation then yields a tensor diffusivity which allows nonalignment of the SGS scalar fluxes with respect to the resolved scalar gradient. In contrast to eddy diffusivity models and to general gradient diffusion hypothesis models, for which the diffusivity tensor is symmetric, the present formulation produces an asymmetric diffusion tensor; for theoretical and experimental reasons, that tensor is known to be very asymmetric. The model contains a single coefficient, which is determined dynamically. The model is validated in fully developed turbulent channel flow and in separated and reattaching flow over a backstep.

As predicted by D'yakov [Shock wave stability, Zh. Eksp. Teor. Fiz. 27, 288 (1954)] and Kontorovich [On the shock waves stability, Zh. Eksp. Teor. Fiz. 33, 1525 (1957)], an initially disturbed shock front may exhibit different asymptotic behaviors, depending on the slope of the Rankine-Hugoniot curve. Adiabatic and isolated planar shocks traveling steadily through ideal gases are stable in the sense that any perturbation on the shock front decays in time with the power $t^{-3/2}$ (or $t^{-1/2}$ in the strong-shock limit). While some gases whose equations of state cannot be modeled as a perfect gas, as those governed by van der Waals forces, may induce constant-amplitude oscillations to the shock front in the long-time regime, fully unstable behaviors are seldom to occur due to the unlikely conditions that the equation of state must meet. In this paper, it has been found that unstable conditions might be found when the gas undergoes an endothermic or exothermic transformation behind the shock. In particular, it is reported that constant-amplitude oscillations can occur when the amount of energy release is positively correlated to the shock strength and, if this correlation is sufficiently strong, the shock turns to be fully unstable. The opposite highly damped oscillating regime may occur in negatively correlated configurations. The mathematical description then adds two independent parameters to the regular adiabatic index $\gamma$ and shock Mach number ${\mathcal{M}}_1$, namely, the total energy added/removed and its sensitivity with the shock strength. The formulation in terms of endothermic or exothermic effects is extended but not restricted to include effects associated to ionization, dissociation, thermal radiation, and thermonuclear transformations, so long as the time associated to these effects is a much shorter time than the acoustic time.