Turbulent Flows Are Not Uniformly Multifractal.

Understanding turbulence rests delicately on the conflict between Kolmogorov's 1941 theory of nonintermittent, space-filling energy dissipation characterized by a unique scaling exponent and the overwhelming evidence to the contrary of intermittency, multiscaling, and multifractality. Strangely, multifractality is not typically envisioned as a local flow property, variations in which might be clues exposing inroads into the fundamental unsolved issues of anomalous dissipation and finite time blowup. We present a simple construction of local multifractality and find that much of the dissipation field remains surprisingly monofractal à la Kolmogorov.

Turbulent route to two-dimensional soft crystals.

We investigate the effect of a two-dimensional, incompressible, turbulent flow on soft granular particles and show the emergence of a crystalline phase due to the interplay of Stokesian drag and short-range interparticle interactions. We quantify this phase through the bond order parameter and local density fluctuations and find a sharp transition between the crystalline and noncrystalline phases as a function of the Stokes number. Furthermore, the nature of preferential concentration, characterized by the correlation dimension, is significantly different from that of particle-laden flows in the absence of repulsive potentials.

Dynamic scaling in rotating turbulence: A shell model study.

We investigate the scaling form of appropriate timescales extracted from time-dependent correlation functions in rotating turbulent flows. In particular, we obtain precise estimates of the dynamic exponents z_{p}, associated with the timescales, and their relation with the more commonly measured equal-time exponents ζ_{p}. These theoretical predictions, obtained by using the multifractal formalism, are validated through extensive numerical simulations of a shell model for such rotating flows.

Editorial: Scaling the Turbulence Edifice (part 2).

This is the second part of a two-part special issue of the Philosophical Transactions of the Royal Society A, which recognizes, and hopefully encourages, the growing convergence of interests amongst mathematicians and physicists to scale the turbulence edifice. This convergence is explained in more detail in the editorial which accompanies the first part (Bec . 2022 , 20210101.

Editorial: Scaling the Turbulence Edifice.

Turbulence is unique in its appeal across physics, mathematics and engineering. And yet a microscopic theory, starting from the basic equations of hydrodynamics, still eludes us. In the last decade or so, new directions at the interface of physics and mathematics have emerged, which strengthens the hope of 'solving' one of the oldest problems in the natural sciences.

Many-Body Chaos in Thermalized Fluids.

Linking thermodynamic variables like temperature T and the measure of chaos, the Lyapunov exponents λ, is a question of fundamental importance in many-body systems. By using nonlinear fluid equations in one and three dimensions, we show that in thermalized flows λ∝sqrt[T], in agreement with results from frustrated spin systems. This suggests an underlying universality and provides evidence for recent conjectures on the thermal scaling of λ.

Anomalous Diffusion and Lévy Walks Distinguish Active from Inertial Turbulence.

Bacterial swarms display intriguing dynamical states like active turbulence. Now, using a hydrodynamic model, we show that such dense active suspensions manifest superdiffusion, via Lévy walks, which masquerades as a crossover from ballistic to diffusive scaling in measurements of mean-squared displacements, and is tied to the emergence of hitherto undetected oscillatory streaks in the flow. Thus, while laying the theoretical framework of an emergent advantageous strategy in the collective behavior of microorganisms, our Letter underlines the essential differences between active and inertial turbulence.

Orientation Dynamics of Sedimenting Anisotropic Particles in Turbulence.

We examine the dynamics of small anisotropic particles (spheroids) sedimenting through homogeneous isotropic turbulence using direct numerical simulations and theory. The gravity-induced inertial torque acting on sub-Kolmogorov spheroids leads to pronouncedly non-Gaussian orientation distributions localized about the broadside-on (to gravity) orientation. Orientation distributions and average settling velocities are obtained over a wide range of spheroid aspect ratios, Stokes, and Froude numbers.

Elastoinertial chains in a two-dimensional turbulent flow.

The interplay of inertia and elasticity is shown to have a significant impact on the transport of filamentary objects, modeled by bead-spring chains, in a two-dimensional turbulent flow. We show how elastic interactions among inertial beads result in a nontrivial sampling of the flow, ranging from entrapment within vortices to preferential sampling of straining regions. This behavior is quantified as a function of inertia and elasticity and is shown to be very different from free, noninteracting heavy particles, as well as inertialess chains [Picardo et al.

Dynamics of a long chain in turbulent flows: impact of vortices.

We show and explain how a long bead-spring chain, immersed in a homogeneous isotropic turbulent flow, preferentially samples vortical flow structures. We begin with an elastic, extensible chain which is stretched out by the flow, up to inertial-range scales. This filamentary object, which is known to preferentially sample the circular coherent vortices of two-dimensional (2D) turbulence, is shown here to also preferentially sample the intense, tubular, vortex filaments of three-dimensional (3D) turbulence.

Statistics of Lagrangian trajectories in a rotating turbulent flow.

We investigate the Lagrangian statistics of three-dimensional rotating turbulent flows through direct numerical simulations. We find that the emergence of coherent vortical structures because of the Coriolis force leads to a suppression of the "flight-crash" events reported by Xu et al. [Proc.

Understanding droplet collisions through a model flow: Insights from a Burgers vortex.

We investigate the role of intense vortical structures, similar to those in a turbulent flow, in enhancing collisions (and coalescences) which lead to the formation of large aggregates in particle-laden flows. By using a Burgers vortex model, we show, in particular, that vortex stretching significantly enhances sharp inhomogeneities in spatial particle densities, related to the rapid ejection of particles from intense vortices. Furthermore our work shows how such spatial clustering leads to an enhancement of collision rates and extreme statistics of collisional velocities.

Preferential Sampling of Elastic Chains in Turbulent Flows.

A string of tracers interacting elastically in a turbulent flow is shown to have a dramatically different behavior when compared to the noninteracting case. In particular, such an elastic chain shows strong preferential sampling of the turbulent flow unlike the usual tracer limit: An elastic chain is trapped in the vortical regions. The degree of preferential sampling and its dependence on the elasticity of the chain is quantified via the Okubo-Weiss parameter.

Inertial spheroids in homogeneous, isotropic turbulence.

We study the rotational dynamics of inertial disks and rods in three-dimensional, homogeneous, isotropic turbulence. In particular, we show how the alignment and the decorrelation timescales of such spheroids depend, critically, on both the level of inertia and the aspect ratio of these particles. These results illustrate the effect of inertia-which leads to a preferential sampling of the local flow geometry-on the statistics of both disks and rods in a turbulent flow.

Light-Cone Spreading of Perturbations and the Butterfly Effect in a Classical Spin Chain.

We find that the effects of a localized perturbation in a chaotic classical many-body system-the classical Heisenberg chain at infinite temperature-spread ballistically with a finite speed even when the local spin dynamics is diffusive. We study two complementary aspects of this butterfly effect: the rapid growth of the perturbation, and its simultaneous ballistic (light-cone) spread, as characterized by the Lyapunov exponents and the butterfly speed, respectively. We connect this to recent studies of the out-of-time-ordered commutators (OTOC), which have been proposed as an indicator of chaos in a quantum system.

Enhanced droplet collision rates and impact velocities in turbulent flows: The effect of poly-dispersity and transient phases.

We compare the collision rates and the typical collisional velocities amongst droplets of different sizes in a poly-disperse suspension advected by two- and three-dimensional turbulent flows. We show that the collision rate is enhanced in the transient phase for droplets for which the size-ratios between the colliding pairs is large as well as obtain precise theoretical estimates of the dependence of the impact velocity of particles-pairs on their relative sizes. These analytical results are validated against data from our direct numerical simulations.

Dynamic multiscaling in magnetohydrodynamic turbulence.

We present a study of the multiscaling of time-dependent velocity and magnetic-field structure functions in homogeneous, isotropic magnetohydrodynamic (MHD) turbulence in three dimensions. We generalize the formalism that has been developed for analogous studies of time-dependent structure functions in fluid turbulence to MHD. By carrying out detailed numerical studies of such time-dependent structure functions in a shell model for three-dimensional MHD turbulence, we obtain both equal-time and dynamic scaling exponents.

Intermittency in fractal Fourier hydrodynamics: Lessons from the Burgers equation.

We present theoretical and numerical results for the one-dimensional stochastically forced Burgers equation decimated on a fractal Fourier set of dimension D. We investigate the robustness of the energy transfer mechanism and of the small-scale statistical fluctuations by changing D. We find that a very small percentage of mode-reduction (D ≲ 1) is enough to destroy most of the characteristics of the original nondecimated equation.

Abrupt growth of large aggregates by correlated coalescences in turbulent flow.

Smoluchowski's coagulation kinetics is here shown to fail when the coalescing species are dilute and transported by a turbulent flow. The intermittent Lagrangian motion involves correlated violent events that lead to an unexpected rapid occurrence of the largest particles. This new phenomena is here quantified in terms of the anomalous scaling of turbulent three-point motion, leading to significant corrections in macroscopic processes that are critically sensitive to the early-stage emergence of large embryonic aggregates, as in planet formation or rain precipitation.

Transition from dissipative to conservative dynamics in equations of hydrodynamics.

We show, by using direct numerical simulations and theory, how, by increasing the order of dissipativity (α) in equations of hydrodynamics, there is a transition from a dissipative to a conservative system. This remarkable result, already conjectured for the asymptotic case α→∞ [U. Frisch et al.

Gravity-driven enhancement of heavy particle clustering in turbulent flow.

Heavy particles suspended in a turbulent flow settle faster than in a still fluid. This effect stems from a preferential sampling of the regions where the fluid flows downward and is quantified here as a function of the level of turbulence, of particle inertia, and of the ratio between gravity and turbulent accelerations. By using analytical methods and detailed, state-of-the-art numerical simulations, settling is shown to induce an effective horizontal two-dimensional dynamics that increases clustering and reduce relative velocities between particles.

Multiscaling in Hall-magnetohydrodynamic turbulence: insights from a shell model.

We show that a shell-model version of the three-dimensional Hall-magnetohydrodynamic (3D Hall-MHD) equations provides a natural theoretical model for investigating the multiscaling behaviors of velocity and magnetic structure functions. We carry out extensive numerical studies of this shell model, obtain the scaling exponents for its structure functions, in both the low-k and high-k power-law ranges of three-dimensional Hall-magnetohydrodynamic, and find that the extended-self-similarity procedure is helpful in extracting the multiscaling nature of structure functions in the high-k regime, which otherwise appears to display simple scaling. Our results shed light on intriguing solar-wind measurements.

Sticky elastic collisions.

The effects of purely elastic collisions on the dynamics of heavy inertial particles are investigated in a three-dimensional random incompressible flow. It is shown that the statistical properties of interparticle separations and relative velocities are strongly influenced by the occurrence of sticky elastic collisions-particle pairs undergo a large number of collisions against each other during a small time interval over which, hence, they remain close to each other. A theoretical framework is provided for describing and quantifying this phenomenon and it is substantiated by numerical simulations.

Real-space manifestations of bottlenecks in turbulence spectra.

An energy-spectrum bottleneck, a bump in the turbulence spectrum between the inertial and dissipation ranges, is shown to occur in the nonturbulent, one-dimensional, hyperviscous Burgers equation and found to be the Fourier-space signature of oscillations in the real-space velocity, which are explained by boundary-layer-expansion techniques. Pseudospectral simulations are used to show that such oscillations occur in velocity correlation functions in one- and three-dimensional hyperviscous hydrodynamical equations that display genuine turbulence.

Turbulence in noninteger dimensions by fractal Fourier decimation.

Fractal decimation reduces the effective dimensionality D of a flow by keeping only a (randomly chosen) set of Fourier modes whose number in a ball of radius k is proportional to k(D) for large k. At the critical dimension D(c)=4/3 there is an equilibrium Gibbs state with a k(-5/3) spectrum, as in V. L'vov et al.