The proposed universality of small scale turbulence is investigated for a set of measurements in a cryogenic free jet with a variation of the Reynolds number (Re) from 8500 to 10^6. The traditional analysis of the statistics of velocity increments by means of structure functions or probability density functions is replaced by a new method which is based on the theory of stochastic Markovian processes. It gives access to a more complete characterization by means of joint probabilities of finding velocity increments at several scales. Based on this more precise method our results call in question the concept of universality.
Turbulence is one of the most frequently encountered non-equilibrium phenomena in nature yet characterising the transition that gives rise to it has remained an elusive task. Although in recent studies critical points marking the onset of sustained turbulence have been determined, the physical nature of the transition could not be explained. In extensive experimental and computational studies we show for the example of Couette flow that the onset of turbulence is a second order phase transition and falls into the directed percolation universality class. Consequently the complex laminar-turbule…
We report and discuss case study simulations of the Rayleigh-Taylor instability in the Boussinesq, incompressible regime developed to turbulence. Our main focus is on a statistical analysis of density and velocity fluctuations inside of the already developed and growing in size mixing zone. Novel observations reported in the manuscript concern self-similarity of the velocity and density fluctuations spectra inside of the mixing zone snapshot, independence of the spectra of the horizontal slice level, and universality showing itself in a virtual independence of the internal structure of the mix…
The universality of intermittency in hydrodynamic turbulence is considered based on a recent model for the velocity gradient tensor evolution. Three possible versions of the model are investigated differing in the assumed correlation time-scale and forcing strength. Numerical tests show that the same (universal) anomalous relative scaling exponents are obtained for the three model variants. It is also found that transverse velocity gradients are more intermittent than longitudinal ones, whereas dissipation and enstrophy scale with the same exponents. The results are consistent with the univers…
A hallmark of fluid turbulence theory is the universal power law scaling of the velocity difference statistics between two points in space in the inertial range between the large energy injection scale and the small energy dissipation scale. Even at the highest Reynolds numbers available, laboratory and natural flows such universal power laws have not been convincingly demonstrated. Here we show for the decaying active grid turbulence of the Max Planck Variable Density Turbulence Tunnel that the velocity difference statistics at high Reynolds numbers do not exhibit a power law, but have a univ…
The weak version of universality in turbulence refers to the independence of the scaling exponents of the $n$th order strcuture functions from the statistics of the forcing. The strong version includes universality of the coefficients of the structure functions in the isotropic sector, once normalized by the mean energy flux. We demonstrate that shell models of turbulence exhibit strong universality for both forced and decaying turbulence. The exponents {\em and} the normalized coefficients are time independent in decaying turbulence, forcing independent in forced turbulence, and equal for dec…
The volatile transition from quiescent laminar to strongly fluctuating turbulent dynamics in shear flows remains only poorly understood despite its practical importance and more than a century of intense research. The theoretical understanding of the transition process has been complicated by the lack of a linear instability mechanism and additionally by a catastrophic collapse of turbulence which can occur after extremely long lifetimes. Turbulence close to onset is investigated experimentally in three different geometries: pipe, duct and channel flow. The reverse transition from turbulent to…
Multi-fractal model for dissipation field has been used to provide a detailed structure for the critical exponent σdescribing the scaling form of dissipation εthat appears to exhibit an interesting universality covering radically different hydrodynamic fully developed turbulence (FDT) systems. This result also appears to provide a consistent framework for classification of dissipation field into critical, subcritical and supercritical cases. Some FDT problems that exemplify these cases are discussed.
By taking advantage of laser Doppler velocimetry (LDV), we explore the existence of discrete wave cascades on fluid interfaces excited upon monochromatic excitation. We study viscous liquids of variable capillarity spanning a broad range of frictional stresses. The existence of an inertial regime of weak surface wave turbulence (weak-SWT) has been pointed out as a cascade of discrete modes with amplitudes compatible with universal Kolmogorov`s scaling. The transit from weak to strong surface turbulence has been explored with this tool revealing the importance of inertia over surface forces to …
We examine the onset of turbulence in Waleffe flow -- the planar shear flow between stress-free boundaries driven by a sinusoidal body force. By truncating the wall-normal representation to four modes, we are able to simulate system sizes an order of magnitude larger than any previously simulated, and thereby to attack the question of universality for a planar shear flow. We demonstrate that the equilibrium turbulence fraction increases continuously from zero above a critical Reynolds number and that statistics of the turbulent structures exhibit the power-law scalings of the (2+1)-D directed …
In this paper, the approach for investigation of asymptotic ($Re\to \infty$) scaling exponents of Eulerian structure functions (J. Schumacher et al, New. J. of Physics {\bf 9}, 89 (2007)) is generalized to studies of Lagrangian structure functions in turbulence. The novel "bridging relation" based on the derived expression for the fluctuating, moment-order - dependent dissipation time $τ_{η,n}$ enabled us to calculate scaling exponents ($κ_{n}$) of the moments of Lagrangian velocity differences $S_{n,L}(τ)=\bar{(u(t+τ)-u(t))^{n}}\propto τ^{κ_{n}}$ in a good agreement with experimental and nume…
We systematise the study of dynamic multiscaling of time-dependent structure functions in different models of passive-scalar and fluid turbulence. We show that, by suitably normalising these structure functions, we can eliminate their dependence on the origin of time at which we start our measurements and that these normalised structure functions yield the same linear bridge relations that relate the dynamic-multiscaling and equal-time exponents for statistically steady turbulence. We show analytically, for both the Kraichnan Model of passive-scalar turbulence and its shell model analogue, and…
Nuclear burning plays a key role in a wide range of astrophysical stellar transients, including thermonuclear, pair instability, and core collapse supernovae, as well as kilonovae and collapsars. Turbulence is now understood to also play a key role in these astrophysical transients. Here we demonstrate that turbulent nuclear burning may lead to large enhancements above the uniform background burning rate, since turbulent dissipation gives rise to temperature fluctuations, and in general the nuclear burning rates are highly sensitive to temperature. We derive results for the turbulent enhanceme…
Turbulent flows, ubiquitous in nature and engineering, comprise fluctuations over a wide range of spatial and temporal scales. While flows with fluctuations in thermodynamic variables are much more common, much less is known about these flows than their incompressible counterparts in which thermodynamics is decoupled from hydrodynamics. A critical element in the study of the latter has been the concept of universal scaling laws which provides fundamental as well as practical information about the spatio-temporal behavior of these complex systems. Part of this success is due to the dependence o…
It has long been established that turbulence energy spectra scale on the Kolmogorov (1941) variables over a wide range of Reynolds numbers and in vastly different physical systems, depending only on the dissipation rate, the kinematic viscosity and the wavenumber. On the other hand, the analogous study of structure functions in real space is strongly influenced by the Kolmogorov (1962) refined theory, which introduced a dependence on a large length scale Lext, characteristic of the system size. If such a dependence exists it is surprising that it does not show up in the study of wavenumber spe…
We study the statistical properties of spatially averaged global injected power fluctuations for Taylor-Couette flow of a worm-like micellar gel formed by surfactant CTAT. At sufficiently high Weissenberg numbers (Wi) the shear rate and hence the injected power p(t) at a constant applied stress shows large irregular fluctuations in time. The nature of the probability distribution function (pdf) of p(t) and the power-law decay of its power spectrum are very similar to that observed in recent studies of elastic turbulence for polymer solutions. Remarkably, these non-Gaussian pdfs can be well des…
Using computations of three-dimensional magnetohydrodynamic (MHD) turbulence with a Taylor-Green flow, whose inherent time-independent symmetries are implemented numerically, and in the absence of either a forcing function or an imposed uniform magnetic field, we show that three different inertial ranges for the energy spectrum may emerge for three different initial magnetic fields, the selecting parameter being the ratio of the Alfven to the eddy turnover time. Equivalent computational grids range from 128^3 to 2048^3 points with a unit magnetic Prandtl number and a Taylor Reynolds number of …
We investigate universality of the Eulerian velocity structure functions using velocity fields obtained from the stereoscopic particle image velocimetry (SPIV) technique in experiments and the direct numerical simulations (DNS) of the Navier-Stokes equations. We show that the numerical and experimental velocity structure functions up to order 9 follow a log-universality; we find that they collapse on a universal curve, if we use units that include logarithmic dependence on the Reynolds number. We then investigate the meaning and consequences of such log-universality, and show that it is connec…
Asymptotically large Reynolds number hydrodynamic turbulence is characterized by multi-scaling of moments of velocity increments and spatial derivatives. With decreasing Reynolds number toward $R_λ=R^{tr}_λ\approx 9.0$, the anomalous scaling disappears in favor of the "normal" one and close-to-Gaussian probability densities [Yakhot \& Donzis, {\bf 119}, 044501 (2017)]. The nature of this transition and its universality are subjects of this work. Here we consider Benard convection ( Prandtl number $Pr=1$) between infinite horizontal plates. It is shown that in this system the "competition" betw…
Compressible turbulence shapes the structure of the interstellar medium of our Galaxy and likely plays an important role also during structure formation in the early Universe. The density PDF and the power spectrum of such compressible, supersonic turbulence are the key ingredients for theories of star formation. However, both the PDF and the spectrum are still a matter of debate, because theoretical predictions are limited and simulations of supersonic turbulence require enormous resolutions to capture the inertial-range scaling. To advance our limited knowledge of compressible turbulence, we…
The problem of the interplay between normal and anomalous scaling in turbulent systems stirred by a random forcing with a power law spectrum is addressed. We consider both linear and nonlinear systems. As for the linear case, we study passive scalars advected by a 2d velocity field in the inverse cascade regime. For the nonlinear case, we review a recent investigation of 3d Navier-Stokes turbulence, and we present new quantitative results for shell models of turbulence. We show that to get firm statements is necessary to reach considerably high resolutions due to the presence of unavoidable su…
In these notes we discuss recent developments in the field of non-equilibrium quantum dynamics. Specifically, we consider nearly coherent Bose gases brought far out of equilibrium and study their behaviour in view of connections between universal properties, (quasi-)topological field configurations and turbulent dynamics. We demonstrate that the isolated Bose gas, on its way back to thermal equilibrium, can approach metastable non-equilibrium configurations and spend a long time in their vicinity. In such configurations, which have been termed non-thermal fixed points, the system shows univers…
(Abridged) The small-scale dynamo may play a substantial role in magnetizing the Universe under a large range of conditions, including subsonic turbulence at low Mach numbers, highly supersonic turbulence at high Mach numbers and a large range of magnetic Prandtl numbers Pm, i.e. the ratio of kinetic viscosity to magnetic resistivity. Low Mach numbers may in particular lead to the well-known, incompressible Kolmogorov turbulence, while for high Mach numbers, we are in the highly compressible regime, thus close to Burgers turbulence. In this study, we explore whether in this large range of cond…
The effect of large scales on the statistics and dynamics of turbulent fluctuations is studied using data from high resolution direct numerical simulations. Three different kinds of forcing, and spatial resolutions ranging from 256^3 to 1024^3, are being used. The study is carried out by investigating the nonlinear triadic interactions in Fourier space, transfer functions, structure functions, and probability density functions. Our results show that the large scale flow plays an important role in the development and the statistical properties of the small scale turbulence. The role of helicity…
Traditionally, trends of universal turbulence statistics are presented versus R-lambda, which is the Reynolds number based on Taylor's scale, lambda, and the root-mean-squared (rms) velocity component, u'. Taylor's scale and u', and hence R-lambda, do not have the attribute of universality. The ratio of rms fluid-particle acceleration to rms viscous acceleration is an alternative to R-lambda which has the advantage of being determined by the small scales of turbulence. This ratio, denoted R-a, has the following attributes: it is a Reynolds number, it is composed of statistics of the small scal…
With the aim of determining the statistical properties of relativistic turbulence and unveiling novel and non-classical features, we present the results of direct numerical simulations of driven turbulence in an ultrarelativistic hot plasma using high-order numerical schemes. We study the statistical properties of flows with average Mach number ranging from $\sim 0.4$ to $\sim 1.7$ and with average Lorentz factors up to $\sim 1.7$. We find that flow quantities, such as the energy density or the local Lorentz factor, show large spatial variance even in the subsonic case as compressibility is en…
With the aim of determining the statistical properties of relativistic turbulence and unveiling novel and non-classical features, we resent the results of direct numerical simulations of driven turbulence in an ultrarelativistic hot plasma using high-order numerical schemes. We study the statistical properties of flows with average Mach number ranging from $\sim 0.4$ to $\sim 1.7$ and with average Lorentz factors up to $\sim 1.7$. We find that flow quantities, such as the energy density or the local Lorentz factor, show large spatial variance even in the subsonic case as compressibility is enh…
Invariance properties of physical systems govern their behavior: energy conservation in turbulence drives a wide distribution of energy among modes, observed in geophysical or astrophysical flows. In ideal hydrodynamics, the role of helicity conservation (correlation between velocity and its curl, measuring departures from mirror symmetry) remains unclear since it does not alter the energy spectrum. However, with solid body rotation, significant differences emerge between helical and non-helical flows. We first outline several results, like the energy and helicity spectral distribution and the…
The Rayleigh--Taylor (RT) turbulence is investigated by means of high resolution numerical simulations. The main question addressed here is on whether RT phenomenology can be considered as a manifestation of universality of Navier--Stokes equations with respect to forcing mechanisms. At a theoretical level the situation is far from being firmly established and, indeed, contrasting predictions have been formulated. Our first aim here is to clarify the above controversy through a deep analysis of scaling behavior of relevant statistical observables. The effects of intermittency on the mean field…
The self-similar Richardson cascade admits two logically possible scenarios of small-scale turbulence at high Reynolds numbers. In the first scenario, eddies' population densities vary as a function of eddies' scales. As a result, one or a few eddy types dominate at small scales, and small-scale turbulence lacks diversity. In the second scenario, eddies' population densities are scale-invariant across the inertial range, resulting in small-scale diversity. That is, there are as many types of eddies at the small scales as at the large scales. In this letter, we measure eddies' population densit…
Qian Jian, a Chinese theoretical physicist and fluid dynamicist, devoted the second part of his scientific life to the physical understanding of small-scale turbulence to the exclusion of all else. Qian developed his own statistical theory of small-scale turbulence, based on the Liouville (1853) equation and a perturbation variational approach to non-equilibrium statistical mechanics, which is compatible with the Kolmogorov-Oboukhov energy spectrum. His statistical theory of small-scale turbulence, which appears mathematically and physically valid, successfully led to his contributions to (i) …
Rapidly rotating turbulent flow is characterized by the emergence of columnar structures that are representative of quasi-two dimensional behavior of the flow. It is known that when energy is injected into the fluid at an intermediate scale $L_f$, it cascades towards smaller as well as larger scales. In this paper we analyze the flow in the \textit{inverse cascade} range at a small but fixed Rossby number, {$\mathcal{R}o_f \approx 0.05$}. Several {numerical simulations with} helical and non-helical forcing functions are considered in periodic boxes with unit aspect ratio. In order to resolve t…
The small scales of turbulence in a high-Reynolds-number jet ($Re_λ \approx 350$) are investigated with a \textmu PIV setup to overcome the optical limitations of conventional tomographic PIV setups. With the aim of validating the performances of tomographic long-distance \textmu PIV, analyses are carried out involving statistical aspects of the small scales of turbulence. The technique is assessed and the data are bench-marked to be applied to the analysis of any three dimensional small-scale phenomena in large-scale flow domains.
Jin (Phys. Fluids, vol. 31, 2019, p. 125102) proposed a new turbulence simulation method which shows better performance than other classic turbulence models. It is composed of a small-eddy-dissipation mixing length (SED-ML) model for calculating the reference solution and a parameter extension method for correcting the solution. The mechanism of this method is more deeply analyzed in this study to find out how to develop a turbulence model with a high accuracy and a low computational cost. The turbulent channel flows with Re_tau=821 and 2003 and decaying homogenous and isotropic turbulence are…
We performed high resolution numerical simulations of homogenous and isotropic compressible turbulence, with an average 3D Mach number close to 0.3. We study the statistical properties of intermittency for velocity, density and entropy. For the velocity field, which is the primary quantity that can be compared to the isotropic incompressible case, we find no statistical differences in its behavior in the inertial range due either to the slight compressibility or to the different dissipative mechanism. For the density field, we find evidence of ``front-like'' structures, although no shocks are …
We compute the angular dynamics of a neutrally buoyant nearly spherical particle immersed in an unsteady fluid. We assume that the particle is small, that its translational slip velocity is negligible, and that unsteady and convective inertia are small perturbations. We derive an approximation for the torque on the particle that determines the first inertial corrections to Jeffery's equation. These corrections arise as a consequence of local vortex stretching, and can be substantial in turbulence where local vortex stretching is strong and closely linked to the irreversibility of turbulence.
We introduce transfer learning for nonlinear dynamics, which enables efficient predictions of chaotic dynamics by utilizing a small amount of data. For the Lorenz chaos, by optimizing the transfer rate, we accomplish more accurate inference than the conventional method by an order of magnitude. Moreover, a surprisingly small amount of learning is enough to infer the energy dissipation rate of the Navier-Stokes turbulence because we can, thanks to the small-scale universality of turbulence, transfer a large amount of the knowledge learned from turbulence data at lower Reynolds number.
The Navier-Stokes equation for incompressible liquid is considered in the limit of infinitely large Reynolds number. It is assumed that the flow instability leads to generation of steady-state large-scale pulsations. The excitation and evolution of the small-scale turbulence is investigated. It is shown that the developed small-scale pulsations are intermittent. The maximal amplitude of the vorticity fluctuations is reached along the vortex filaments. Basing on the obtained solution, the pair correlation function in the limit $r\to 0$ is calculated. It is shown that the function obeys the Kolm…
Filaments are ubiquitous in the universe. Recent observations have revealed that stars and star clusters form preferentially along dense filaments. Understanding the formation and properties of filaments is therefore a crucial step in understanding star formation. Here we perform three-dimensional high-resolution magnetohydrodynamical simulations that follow the evolution of molecular clouds and the formation of filaments and stars. We apply a filament detection algorithm and compare simulations with different combinations of physical ingredients: gravity, turbulence, magnetic fields and jet/o…
Three-dimensional miscible Rayleigh--Taylor (RT) turbulence at small Atwood number and at Prandtl number one is investigated by means of high resolution direct numerical simulations of the Boussinesq equations. RT turbulence is a paradigmatic time-dependent turbulent system in which the integral scale grows in time following the evolution of the mixing region. In order to fully characterize the statistical properties of the flow, both temporal and spatial behavior of relevant statistical indicators have been analyzed. Scaling of both global quantities ({\it e.g.}, Rayleigh, Nusselt and Reynold…
We provide evidence that the small-scale statistics of the acceleration of a test particle in high-Reynolds number Lagrangian turbulence is correctly described by Tsallis statistics with entropic index q=3/2. We present theoretical arguments why Tsallis statistics can naturally arise in Lagrangian turbulence and why at the smallest scales q=3/2 is relevant. A generalized Heisenberg-Yaglom formula is derived from the nonextensive model.
This investigation presents evidence of the relation between the dynamics of intense events in small-scale turbulence and the energy cascade. We use the generalised (Hölder) means to track the temporal evolution of intense events of the enstrophy and the dissipation in direct numerical simulations of isotropic turbulence. We show that these events are modulated by large-scale fluctuations, and that their evolution is consistent with a local multiplicative cascade, as hypothesised by a broad class of intermittency models of turbulence.
By means of high-resolution numerical simulations, we compare the statistical properties of homogeneous and isotropic turbulence to those of the Navier-Stokes equation where small-scale vortex filaments are strongly depleted, thanks to a non-linear extra viscosity acting preferentially on high vorticity regions. We show that the presence of such smart small-scale drag can strongly reduce intermittency and non-Gaussian fluctuations. Our results pave the way towards a deeper understanding on the fundamental role of degrees of freedom in turbulence as well as on the impact of (pseudo)coherent str…
We inquire about the properties of 2d Navier-Stokes turbulence simultaneously forced at small and large scales. The background motivation comes by observational results on atmospheric turbulence. We show that the velocity field is amenable to the sum of two auxiliary velocity fields forced at large and small scale and exhibiting a direct-enstrophy and an inverse-energy cascade, respectively. Remarkably, the two auxiliary fields reconcile universal properties of fluxes with positive statistical correlation in the inertial range.
Using experimental longitudinal and transverse velocities data for very high Reynolds number turbulence, we study both anisotropy and asymmetry of turbulence. These both seem to be related to small scale turbulent structures, and to intermittency. We may assume that the large scale velocity shear gives an impact into the small scale turbulence, resulting in non-locality, and related anomalous events.
We study the motion of small inertial particles in stratified turbulence. We derive a simplified model, valid within the Boussinesq approximation, for the dynamics of small particles in presence of a mean linear density profile. By means of extensive direct numerical simulations, we investigate the statistical distribution of particles as a function of the two dimensionless parameters of the problem. We find that vertical confinement of particles is mainly ruled by the degree of stratification, with a weak dependency on the particle properties. Conversely, small scale fractal clustering, typic…
The velocity circulation, a measure of the rotation of a fluid within a closed path, is a fundamental observable in classical and quantum flows. It is indeed a Lagrangian invariant in inviscid classical fluids. In quantum flows, circulation is quantized, taking discrete values that are directly related to the number and the orientation of thin vortex filaments enclosed by the path. By varying the size of such closed loop, the circulation provides a measure of the dependence of the flow structure on the considered scale. Here we consider the scale dependence of circulation statistics in quantum…
We study the growth of small fluctuations of magnetic field in supersonic turbulence, the small-scale dynamo. The growth is due to the fastest turbulent eddies above the resistive scale. We observe that for supersonic turbulence these eddies are effectively incompressible which creates a robust structure of the growth. The eddies are localised below the sonic scale $l_s$ defined as the scale where the typical velocity of the turbulent eddies equals the speed of sound. Thus the flow below $l_s$ is effectively incompressible and the field growth proceeds as in incompressible flow. At large Mach …
