A fundamental aspect of turbulence theory is related to the identification of realizable phase-space statistical descriptions able to reproduce in some suitable sense the stochastic fluid equations of a turbulent fluid. In particular, a major open issue is whether a purely Markovian statistical description of hydrodynamic turbulence actually can be achieved. Based on the formulation of a \textit{deterministic inverse kinetic theory} (IKT) for the 3D incompressible Navier-Stokes equations, here we claim that such a \textit{Markovian statistical description actually exists}. The approach, which involves the introduction of the \textit{local velocity probability density} for the fluid (local pdf) - rather than the velocity-difference pdf adopted in customary approaches to homogeneous turbulence - relies exclusively on first principles. These include - in particular - the exact validity of the stochastic Navier-Stokes equations, the principle of entropy maximization and a constant H-theorem for the Shannon statistical entropy. As a result, the new approach affords an exact equivalence between Lagrangian and Eulerian formulations which permit local pdf's which are generally non-Maxwellian (i.e., non-Gaussian). The theory developed is quite general and applies in principle even to turbulence regimes which are non-stationary and non-uniform in a statistical sense.
The process of the kinetic energy and kinetic helicity transfer over the spectrum in an incompressible, rapidly rotating turbulent flow is considered. An analogue of the Fjortoft theorem for 3D rapidly rotating turbulence is proposed. It is shown that, similar to 2D turbulence, there are two cascades simultaneously: the inverse cascade of the kinetic energy and the direct cascade of the kinetic helicity, which in the case of 2D turbulence corresponds to the cascade of enstrophy. The proposed scenario is in agreement with our earlier calculations, some recent numerical simulations, and physical…
We report on the observation of surface gravity wave turbulence at scales larger than the forcing ones in a large basin. In addition to the downscale transfer usually reported in gravity wave turbulence, an upscale transfer is observed, interpreted as the inverse cascade of weak turbulence theory. A steady state is achieved when the inverse cascade reaches a scale in between the forcing wavelength and the basin size, but far from the latter. This inverse cascade saturation, which depends on the wave steepness, is probably due to the emergence of nonlinear dissipative structures such as sharp-c…
A closure for the effective relaxation time of the Boltzmann-BGK kinetic equation for fluid turbulence is presented, based on a double-averaging procedure over both kinetic and turbulent fluctuations. The resulting effective relaxation time appears to agree with values obtained via a renormalization group treatment of the Navier-Stokes equation only at low values of $k/T$, the ratio of turbulent kinetic energy to fluid temperature. For $k/T>0.1$ the kinetic treatment delivers a significantly longer effective relaxation time.
We perform experiments to study the inverse cascade regime of gravity wave turbulence on the surface of a fluid. Surface waves are forced at an intermediate scale corresponding to the gravity-capillary wavelength. In response to this forcing, waves at larger scales are observed. The spectrum of their amplitudes exhibits a frequency-power law at high enough forcing. Both observations are ascribed to the upscale wave action transfers of gravity wave turbulence. The spectrum exponent is close to the value predicted by the weak turbulence theory. The spectrum amplitude is found to scale linearly w…
The cascade of energy in turbulent flows, i.e., the transfer of kinetic energy from large to small flow scales or vice versa (backward cascade), is the cornerstone of most theories and models of turbulence since the 1940s. Yet, understanding the spatial organisation of kinetic energy transfer remains an outstanding challenge in fluid mechanics. Here, we unveil the three-dimensional structure of the energy cascade across the shear-dominated scales using numerical data of homogeneous shear turbulence. We show that the characteristic flow structure associated with the energy transfer is a vortex …
The wave turbulence equation is an effective kinetic equation that describes the dynamics of wave spectrum in weakly nonlinear and dispersive media. Such a kinetic model has been derived by physicists in the sixties, though the well-posedness theory remains open, due to the complexity of resonant interaction kernels. In this paper, we provide a global unique radial strong solution, the first such a result, to the wave turbulence equation for capillary waves.
Magnetized turbulence is ubiquitous in many astrophysical and terrestrial systems but no complete, uncontested theory even in the simplest form, magnetohydrodynamics (MHD), exists. Many theories and phenomenologies focus on the joint (kinetic and magnetic) energy fluxes and spectra. We highlight the importance of treating kinetic and magnetic energies separately to shed light on MHD turbulence dynamics. We conduct an implicit large eddy simulation of subsonic, super-Alfvénic MHD turbulence and analyze the scale-wise energy transfer over time. Our key finding is that the kinetic energy spectrum…
For the first time, the non-equilibrium time-relaxation kinetic model (NTRKM) is proposed for compressible turbulence modeling on unresolved grids. Within the non-equilibrium time-relaxation framework, NTRKM is extended in the form of modified Bhatnagar-Gross-Krook model. Based on the first-order Chapman-Enskog expansion, NTRKM connects with the six-variable macroscopic governing equations. The first five governing equations correspond to the conservative laws in mass, momentum and total energy, while the sixth equation governs the evolution of unresolved turbulence kinetic energy Kutke. The u…
A systematic study of the influence of the viscous effect on both the spectra and the nonlinear fluxes of conserved as well as non conserved quantities in Navier-Stokes turbulence is proposed. This analysis is used to estimate the helicity dissipation scale which is shown to coincide with the energy dissipation scale. However, it is shown using the decomposition of helicity into eigen modes of the curl operator, that viscous effects have to be taken into account for wave vector smaller than the Kolomogorov wave number in the evolution of these eigen components of the helicity.
In hydrodynamic turbulence, the kinetic energy injected at large scales cascades to the inertial range, leading to a constant kinetic energy flux. In contrast, in magnetohydrodynamic (MHD) turbulence, a fraction of kinetic energy is transferred to the magnetic energy. Consequently, for the same kinetic energy injection rate, the kinetic energy flux in MHD turbulence is reduced compared to its hydrodynamic counterpart. This leads to relative weakening of the nonlinear term ($\la | ({\bf u}\cdot \nabla) {\bf u} | \ra$, where ${\bf u}$ is the velocity field) and turbulent drag, but strengthening …
A mean-field approach (filtering out subgrid scales) is applied to the Boltzmann equation in order to derive a subgrid turbulence model based on kinetic theory. It is demonstrated that the only Smagorinsky type model which survives in the hydrodynamic limit on the viscosity time scale is the so-called tensor-diffusivity model. Scaling of the filter-width with Reynolds number and Knudsen number is established. This sets the first rigorous step in deriving turbulence models from kinetic theory.
Using direct numerical simulation of hydrodynamic turbulence with helicity forcing applied at all scales, a near-maximum helical turbulent state is obtained, with an inverse energy cascade at scales larger than the energy forcing scale and a forward helicity cascade at scales smaller than the energy forcing scale. In contrast to previous studies using decimated triads, our simulations contain all possible triads. By computing the shell-to-shell energy fluxes, we show that the inverse energy cascade results from weakly non-local interactions among homochiral triads. Varying the helicity injecti…
We report the generation of large coherent vortices via inverse energy cascade in Faraday wave driven turbulence. The motion of floaters in the Faraday waves is three dimensional but its horizontal velocity fluctuations show unexpected similarity with two-dimensional turbulence. The inverse cascade is detected by measuring frequency spectra of the Lagrangian velocity, and it is confirmed by computing the third moment of the horizontal velocity fluctuations. This is observed in deep water in a broad range of wavelengths. The results broaden the scope of recent findings on Faraday waves in thin …
We study the statistics of free-surface turbulence at large Reynolds numbers produced by direct numerical simulations in a fluid layer at different thickness with fixed characteristic forcing scale. We observe the production of a transient inverse cascade, with a duration which depends on the thickness of the layer, followed by a transition to three-dimensional turbulence initially produced close to the bottom, no-slip boundary. By switching off the forcing, we study the decaying turbulent regime and we find that it cannot be described by an exponential law. Our results show that boundary cond…
Extending the statistical approach proposed in a parallel paper \cite% {Tessarotto2008-aa}, purpose of this work is to propose a stochastic inverse kinetic theory for small-scale hydrodynamic turbulence based on the introduction of a suitable \textit{local phase-space probability density function} (pdf). In particular, we pose the problem of the construction of Fokker-Planck kinetic models of hydrodynamic turbulence. The approach here adopted is based on the so-called IKT approach (inverse kinetic theory), developed by Ellero et al. (2004-2008) which permits an exact phase-space description of…
In this paper, we review the recent developments in the field of buoyancy-driven turbulence. Scaling and numerical arguments show that the stably-stratified turbulence with moderate stratification has kinetic energy spectrum $E_u(k) \sim k^{-11/5}$ and the kinetic energy flux $Π_u(k) \sim k^{-4/5}$, which is called Bolgiano-Obukhov scaling. The energy flux for the Rayleigh-Bénard convection (RBC) however is approximately constant in the inertial range that results in Kolmorogorv's spectrum ($E_u(k) \sim k^{-5/3}$) for the kinetic energy. The phenomenology of RBC should apply to other flows whe…
The present work considers systems whose dynamics are governed by the nonlinear interactions among groups of 6 nonlinear waves, such as those described by the unforced quintic nonlinear Schrödinger equation. Specific parameter regimes in which ensemble-averaged dynamics of such systems with finite size are accurately described by a wave kinetic equation, as used in wave turbulence theory, are theoretically predicted. In addition, the underlying reasons that the wave kinetic equation may be a poor predictor of wave dynamics outside these regimes are also discussed. These theoretical predictions…
We prove that inter-scale transfer of kinetic energy in compressible turbulence is dominated by local interactions. In particular, our results preclude direct transfer of kinetic energy from large-scales directly to dissipation scales, such as into shocks, in high Reynolds number turbulence as is commonly believed. Our assumptions on the scaling of structure functions are weak and enjoy compelling empirical support. Under a stronger assumption on pressure dilatation co-spectrum, we show that mean kinetic and internal energy budgets statistically decouple beyond a transitional "conversion" rang…
Scalings of the streamwise velocity energy spectra in turbulent boundary layers were considered in Part 1. A spectral decomposition analysis provided a means to separate out attached and non-attached eddy contributions and was used to generate three spectral sub-components, one of which is a close representation of the spectral signature induced by self-similar, wall-attached turbulence. Since sub-components of the streamwise turbulence intensity $\overline{u^2}$ follow from an integration of the velocity energy spectra, we here focus on the scaling of the former. Wall-normal profiles and Reyn…
We analyze velocity fluctuations inside coherent vortices generated as a result of the inverse cascade in the two-dimensional ($2d$) turbulence in a finite box. As we demonstrated in \cite{16KL}, the universal velocity profile, established in \cite{14LBFKL}, corresponds to the passive regime of flow fluctuations. The property enables one to calculate correlation functions of the velocity fluctuations in the universal region. We present results of the calculations that demonstrate a non-trivial scaling of the structure function. In addition the calculations reveal strong anisotropy of the struc…
We present an overview of recent works on the statistical description of turbulent flows in terms of probability density functions (PDFs) in the framework of the Lundgren-Monin-Novikov (LMN) hierarchy. Within this framework, evolution equations for the PDFs are derived from the basic equations of fluid motion. The closure problem arises either in terms of a coupling to multi-point PDFs or in terms of conditional averages entering the evolution equations as unknown functions. We mainly focus on the latter case and use data from direct numerical simulations (DNS) to specify the unclosed terms. A…
The physical nature of compressible turbulence is of fundamental importance in a variety of astrophysical settings. We present the first direct evidence that mean kinetic energy cascades conservatively beyond a transitional "conversion" scale-range despite not being an invariant of the compressible flow dynamics. We use high-resolution three-dimensional simulations of compressible hydrodynamic turbulence on $512^3$ and $1024^3$ grids. We probe regimes of forced steady-state isothermal flows and of unforced decaying ideal gas flows. The key quantity we measure is pressure dilatation cospectrum,…
The decay of kinetic helicity is studied in numerical models of forced turbulence using either an externally imposed forcing function as an inhomogeneous term in the equations or, alternatively, a term linear in the velocity giving rise to a linear instability. The externally imposed forcing function injects energy at the largest scales, giving rise to a turbulent inertial range with nearly constant energy flux while for linearly forced turbulence the spectral energy is maximum near the dissipation wavenumber. Kinetic helicity is injected once a statistically steady state is reached, but it is…
We describe results from particle-in-cell simulations of driven turbulence in collisionless, magnetized, relativistic pair plasma. This physical regime provides a simple setting for investigating the basic properties of kinetic turbulence and is relevant for high-energy astrophysical systems such as pulsar wind nebulae and astrophysical jets. In this paper, we investigate the statistics of turbulent fluctuations in simulations on lattices of up to $1024^3$ cells and containing up to $2 \times 10^{11}$ particles. Due to the absence of a cooling mechanism in our simulations, turbulent energy dis…
Properties of the turbulent cascade of kinetic energy are studied using direct numerical simulations of three-dimensional hydrodynamic decaying turbulence with a moderate Reynolds number and the initial Mach number $M=1$. Compressible and incompressible versions of the Karman-Howarth-Monin (KHM) and low-pass filtering/coarse-graining approaches are compared. In the simulation the total energy is well conserved; the scale dependent KHM and coarse-grained energy equations are also well conserved; the two approaches show similar results, the system does not have an inertial range for the cascade …
We discuss structure and geometrical characteristics of coherent vortices appearing as a result of the inverse cascade in the two-dimensional turbulence in a finite box. We demonstrate that the universal velocity profile, established previously, corresponds to the passive regime of flow fluctuations. We find the vortex core radius and the vortex size and argue that an amount of the vortices generated in the box depends on the system parameters.
Rotating turbulence is an example of a three-dimensional system in which an inverse cascade of energy, from the small to the large scales, can be formed. While usually understood as a byproduct of the typical bidimensionalization of rotating flows, the role of the three-dimensional modes is not completely comprehended yet. In order to shed light on this issue, we performed direct numerical simulations of rotating turbulence where the 2D modes falling in the plane perpendicular to rotation are removed from the dynamical evolution. Our results show that while the two-dimensional modes are key to…
The interplay between waves and eddies in stably stratified rotating flows is investigated by means of world-class direct numerical simulations using up to $3072^3$ grid points. Strikingly, we find that the shift from vortex to wave dominated dynamics occurs at a wavenumber $k_R$ which does not depend on Reynolds number, suggesting that partition of energy between wave and vortical modes is not sensitive to the development of turbulence at the smaller scales. We also show that $k_R$ is comparable to the wavenumber at which exchanges between kinetic and potential modes stabilize at close to equ…
We use a coarse-graining approach to prove that inter-scale transfer of kinetic energy in compressible turbulence is dominated by local interactions. Locality here means that interactions between disparate scales decay at least as fast as a power-law function of the scale-disparity ratio. In particular, our results preclude transfer of kinetic energy from large-scales directly to dissipation scales, such as into shocks, in the limit of high Reynolds number turbulence as is commonly believed. The results hold in broad generality, at any Mach number, for any equation of state, and without the re…
Following the exact decomposition in eigenstates of helicity for the Navier-Stokes equations in Fourier space [F. Waleffe, Phys. Fluids A 4, 350 (1992)] we introduce a modified version of helical shell models for turbulence with non-local triadic interactions. By using both an analytical argument and numerical simulation, we show that there exists a class of models, with a specific helical structure, that exhibits a statistically stable inverse energy cascade, in close analogy with that predicted for the Navier-Stokes equations restricted to the same helical interactions. We further support th…
In the article correct method for the kinetic Boltzmann equation asymptotic solution is formulated, the Hilbert's and Enskog's methods are discussed. The equations system of multicomponent non-equilibrium gas dynamics is derived, that corresponds to the first order in the approximate (asymptotic) method for solution of the system of kinetic Boltzmann equations. It is shown, that the velocity distribution functions of particles, obtained by the proposed method and by Enskog's method, within Enskog's approach, are equivalent up to the infinitesimal first order terms of the asymptotic expansion, …
Here we report the first evidence of the inverse energy cascade in a flow dominated by 3D motions. Experiments are performed in thick fluid layers where turbulence is driven electromagnetically. It is shown that if the free surface of the layer is not perturbed, the top part of the layer behaves as quasi-2D and supports the inverse energy cascade regardless of the layer thickness. Well below the surface the cascade survives even in the presence of strong 3D eddies developing when the layer depth exceeds half the forcing scale. In a bounded flow at low bottom dissipation, the inverse energy cas…
We investigate 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 M = 1, and with moderate Reynolds numbers, R_lambda ~ 100. The turbulent dynamics is analyzed using compressible and incompressible versions of the dynamic spectral transfer (ST) and the Karman-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 question of how nonlinear interactions redistribute the energy of fluctuations across available degrees of freedom is of fundamental importance in the study of turbulence and transport in magnetized weakly collisional plasmas, ranging from space settings to fusion devices. In this letter, we present a theory for the dual cascade found in such plasmas, which predicts a range of new behavior that distinguishes this cascade from that of neutral fluid turbulence. These phenomena are explained in terms of the constrained nature of spectral transfer in nonlinear gyrokinetics. Accompanying this t…
The nature of solar wind turbulence at large scale is rather well understood in the theoretical framework of magnetohydrodynamics. The situation is quite different at sub-proton scales where the magnetic energy spectrum measured by different spacecrafts does not fit with the classical turbulence predictions: a power law index close to $-8/3$ is generally reported which is far from the predictions of strong and wave turbulence, $-7/3$ and $-5/2$ respectively. This discrepancy is considered as a major problem for solar wind turbulence. Here, we show with a nonlinear diffusion model of weak kinet…
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.
According to the celebrated Bolgiano--Obukhov \citep{Bolgiano_1959,Obukhov_1959} phenomenology for moderately stably stratified turbulence, the energy spectrum in the inertial range shows a dual scaling; the kinetic energy follows (i) $\sim k^{-11/5}$ for $k < k_B$, and (ii) $\sim k^{-5/3}$ for $k > k_B$, where $k_B$ is Bolgiano wavenumber. The $k^{-5/3}$ scaling akin to passive scalar turbulence is a direct consequence of the assumption that buoyancy is insignificant for $k>k_B$. We revisit this assumption, and using constancy of kinetic and potential energy fluxes and simple theoretical anal…
We revisit the problem of how energy transfer through the turbulent cascade operates in compressible hydrodynamic turbulence. In general, there is no conservative compressible cascade since the kinetic and internal energy reservoirs can exchange energy through pressure dilatation. Moreover, statistically stationary turbulence at high Mach number can only be maintained in nearly isothermal gas, i.e., if excess heat produced by shock compression and kinetic energy dissipation is continuously removed from the system. We mimic this process by a linear cooling term in numerical simulations of turbu…
This paper studies the turbulent kinetic energy ($k_\perp$) in 2D isothermal electrostatic interchange-dominated ExB drift turbulence in the scrape-off layer and its relation to particle transport. An evolution equation for the former is analytically derived from the underlying turbulence equations. Evaluating this equation shows that the dominant source for the turbulent kinetic energy is due to interchange drive, while the parallel current loss to the sheath constitutes the main sink. Perpendicular transport of the turbulent kinetic energy seems to play a minor role in the balance equation. …
A two-dimensional generalized cubic nonlinear Schrödinger equation with complex coefficients for the group dispersion and nonlinear terms is used to investigate the evolution of a finite-amplitude localized initial perturbation. It is found that modulation of the latter can lead to side-band formation, wave condensation, collapse, turbulence, and inverse cascade, although not all together nor in that order.
We present numerical studies of compressible, decaying turbulence, with and without magnetic fields, with initial rms Alfven and Mach numbers ranging up to five, and apply the results to the question of the support of star-forming interstellar clouds of molecular gas. We find that, in 1D, magnetized turbulence actually decays faster than unmagnetized turbulence. In all the regimes that we have studied 3D turbulence-super-Alfvenic, supersonic, sub-Alfvenic, and subsonic-the kinetic energy decays as (t-t0)^(-x), with 0.85 < x < 1.2. We compared results from two entirely different algorithms in t…
The genesis, growth and rupture of intracranial aneurysm (IA) are open questions in neurovascular medicine until the present moment. The complexity of aneurysm mechanobiology and pathobiology staggeringly combine intertwining biological and physical processes that are tightly connected. Recently, transition to turbulence in IA blood flow is thought to play a central role in IA growth and rupture as it can be directly linked to endothelial dysfunction. However, the problem of turbulence brings unprecedented complications to the topic. We found turbulence in IA to be of non-Kolmogorov type. For …
We establish a statistical relationship between the inverse energy cascade and the spatial correlations of clustered vortices in two-dimensional quantum turbulence. The Kolmogorov spectrum $k^{-5/3}$ on inertial scales $r$ corresponds to a pair correlation function between the vortices with different signs that decays as a power law with the pair distance given as $r^{-4/3}$. To test these scaling relations, we propose a novel forced and dissipative point vortex model that captures the turbulent dynamics of quantized vortices by the emergent clustering of same-sign vortices. The inverse energy…
Magnetic and kinetic energy in ideal incompressible MHD are not global invariants and, therefore, it had been justified to discuss only the cascade of their sum, total energy. We provide a physical argument based on scale-locality of the cascade, along with compelling evidence that at high Reynolds numbers, magnetic and kinetic energy budgets statistically decouple beyond a transitional "conversion" range. This arises because magnetic field-line stretching is a large-scale process which vanishes on average at intermediate and small scales within the inertial-inductive range, thereby allowing e…
During direct numerical simulation of the isotropic turbulence of surface gravity waves in the framework of Hamiltonian equations formation of the long wave background or condensate was observed. Exponents of the direct cascade spectra at the different levels of an artificial condensate suppression show a tendency to become closer to the prediction of the wave turbulence theory at lower levels of condensate. A simple qualitative explanation of the mechanism of this phenomenon is proposed.
We study two dimensional superfluid turbulence by employing an effective description valid in the limit where the density of superfluid vortices is parametrically small. At sufficiently low temperatures the effective description yields an inverse cascade with Kolmogorov energy spectrum $E(k) \sim k^{-5/3}$. Denoting the number of vortices as a function of time by $N(t)$, we find that the vortex annihilation rate scales like $\dot N \sim N^{5/3}$ in states with an inverse cascade and $\dot N \sim N^2$ for laminar flow.
Finite-temperature quantum turbulence is often described in terms of two immiscible fluids that can flow with a non-zero mean relative velocity. Such out-of-equilibrium state is known as counterflow superfluid turbulence. We report here the emergence of a counterflow-induced inverse energy cascade in three-dimensional superfluid flows by performing extensive numerical simulations of the Hall-Vinen-Bekarevich-Khalatnikov model. As the intensity of the mean counterflow is increased, an abrupt transition, from a fully three-dimensional turbulent flow to a quasi two-dimensional system exhibiting a…
Compression of turbulent plasma can amplify the turbulent kinetic energy, if the compression is fast compared to the viscous dissipation time of the turbulent eddies. A sudden viscous dissipation mechanism is demonstrated, whereby this amplified turbulent kinetic energy is rapidly converted into thermal energy, suggesting a new paradigm for fast ignition inertial fusion.
Turbulence develops in any stressed flow when the scales of the forcing are much larger than those of the dissipation. In neutral fluids, it consists of chaotic motions in physical space but with a universal energy spectrum in Fourier space. Intermittency (non-Gaussian statistics of fluctuations) is another general property and it is related to the presence of coherent structures. Space plasmas are turbulent as well. Here, we focus on the kinetic plasma scales, which are not yet well understood. We address the following fundamental questions: (1) Do the turbulent fluctuations at kinetic scales…
We report observation of an inverse energy cascade in second sound acoustic turbulence in He II. Its onset occurs above a critical driving energy and it is accompanied by giant waves that constitute an acoustic analogue of the rogue waves that occasionally appear on the surface of the ocean. The theory of the phenomenon is developed and shown to be in good agreement with the experiments.
We present results from particle-in-cell simulations of driven turbulence in magnetized, collisionless, and relativistic pair plasma. We find that fluctuations are consistent with the classical $k_\perp^{-5/3}$ magnetic energy spectrum at fluid scales and a steeper $k_\perp^{-4}$ spectrum at sub-Larmor scales, where $k_\perp$ is the wavevector perpendicular to the mean field. We demonstrate the development of a non-thermal, power-law particle energy distribution, $f(E) \sim E^{-α}$, with index $α$ that decreases with increasing magnetization and increases with increasing system size (relative …
The turbulence of superfluid helium is investigated numerically at finite temperature. Direct numerical simulations are performed with a "truncated HVBK" model, which combines the continuous description of the Hall-Vinen-Bekeravich-Khalatnikov equations with the additional constraint that this continuous description cannot extend beyond a quantum length scale associated with the mean spacing between individual superfluid vortices. A good agreement is found with experimental measurements of the vortex density. Besides, by varying the turbulence intensity only, it is observed that the inter-vort…
Three-dimensional (3D) turbulence is characterized by a dual forward cascade of both kinetic energy and helicity, a second inviscid flow invariant, from the integral scale of motion to the viscous dissipative scale. In helical flows, however, such as strongly rotating flows with broken mirror symmetry, an inverse energy cascade can be observed analogous to that of two-dimensional turbulence (2D) where a second positive-definite flow invariant, enstrophy, unlike helicity in 3D, effectively blocks the forward cascade of energy. In the spectral-helical decomposition of the Navier-Stokes equation …
HEPIA, University of Applied Sciences and Arts of Western Switzerland（西方瑞士应用艺术大学 HEPIA）；Department of Computer Science, University of Geneva（日内瓦大学计算机科学系）
