Effects of forcing in three dimensional turbulent flows

We present the results of a numerical investigation of three-dimensional homogeneous and isotropic turbulence, stirred by a random forcing with a power law spectrum, $E_f(k)\sim k^{3-y}$. Numerical simulations are performed at different resolutions up to $512^3$. We show that at varying the spectrum slope $y$, small-scale turbulent fluctuations change from a {\it forcing independent} to a {\it forcing dominated} statistics. We argue that the critical value separating the two behaviours, in three dimensions, is $y_c=4$. When the statistics is forcing dominated, for $y<y_c$, we find dimensional scaling, i.e. intermittency is vanishingly small. On the other hand, for $y>y_c$, we find the same anomalous scaling measured in flows forced only at large scales. We connect these results with the issue of {\it universality} in turbulent flows.Comment: 4 pages, 4 figure

Isotropy vs anisotropy in small-scale turbulence

The decay of large-scale anisotropies in small-scale turbulent flow is investigated. By introducing two different kinds of estimators we discuss the relation between the presence of a hierarchy for the isotropic and the anisotropic scaling exponents and the persistence of anisotropies. Direct measurements from a channel flow numerical simulation are presented.Comment: 7 pages, 2 figure

Multiscale properties of Large Eddy Simulations: correlations between resolved-scale velocity-field increments and subgrid-scale quantities

We provide analytical and numerical results concerning multi-scale correlations between the resolved velocity field and the subgrid-scale (SGS) stress-tensor in large eddy simulations (LES). Following previous studies for Navier-Stokes equations (NSE), we derive the exact hierarchy of LES equations governing the spatio-temporal evolution of velocity structure functions of any order. The aim is to assess the influence of the sub-grid model on the inertial range intermittency. We provide a series of predictions, within the multifractal theory, for the scaling of correlation involving the SGS stress and we compare them against numerical results from high-resolution Smagorinsky LES and from a-priori filtered data generated from direct numerical simulations (DNS). We find that LES data generally agree very well with filtered DNS results and with the multifractal prediction for all leading terms in the balance equations. Discrepancies are measured for some of the subleading terms involving cross-correlation between resolved velocity increments and the SGS tensor or the SGS energy transfer, suggesting that there must be room to improve the SGS modelisation to further extend the inertial range properties for any fixed LES resolution.Comment: Journal of Turbulence (2018

Inverse velocity statistics in two dimensional turbulence

We present a numerical study of two-dimensional turbulent flows in the enstrophy cascade regime, with different large-scale forcings and energy sinks. In particular, we study the statistics of more-than-differentiable velocity fluctuations by means of two recently introduced sets of statistical estimators, namely {\it inverse statistics} and {\it second order differences}. We show that the 2D turbulent velocity field, $\bm u$, cannot be simply characterized by its spectrum behavior, $E(k) \propto k^{-\alpha}$. There exists a whole set of exponents associated to the non-trivial smooth fluctuations of the velocity field at all scales. We also present a numerical investigation of the temporal properties of $\bm u$ measured in different spatial locations.Comment: 9 pages, 12 figure

Intermittency in Turbulence: computing the scaling exponents in shell models

We discuss a stochastic closure for the equation of motion satisfied by multi-scale correlation functions in the framework of shell models of turbulence. We give a systematic procedure to calculate the anomalous scaling exponents of structure functions by using the exact constraints imposed by the equation of motion. We present an explicit calculation for fifth order scaling exponent at varying the free parameter entering in the non-linear term of the model. The same method applied to the case of shell models for Kraichnan passive scalar provides a connection between the concept of zero-modes and time-dependent cascade processes.Comment: 12 pages, 5 eps figure

Lyapunov exponents of heavy particles in turbulence

Lyapunov exponents of heavy particles and tracers advected by homogeneous and isotropic turbulent flows are investigated by means of direct numerical simulations. For large values of the Stokes number, the main effect of inertia is to reduce the chaoticity with respect to fluid tracers. Conversely, for small inertia, a counter-intuitive increase of the first Lyapunov exponent is observed. The flow intermittency is found to induce a Reynolds number dependency for the statistics of the finite time Lyapunov exponents of tracers. Such intermittency effects are found to persist at increasing inertia.Comment: 4 pages, 4 figure

Fully developed turbulence and the multifractal conjecture

We review the Parisi-Frisch MultiFractal formalism for Navier--Stokes turbulence with particular emphasis on the issue of statistical fluctuations of the dissipative scale. We do it for both Eulerian and Lagrangian Turbulence. We also show new results concerning the application of the formalism to the case of Shell Models for turbulence. The latter case will allow us to discuss the issue of Reynolds number dependence and the role played by vorticity and vortex filaments in real turbulent flows.Comment: Special Issue dedicated to E. Brezin and G. Paris

New Exact Betchov-like Relation for the Helicity Flux in Homogeneous Turbulence

In homogeneous and isotropic turbulence, the relative contributions of different physical mechanisms to the energy cascade can be quantified by an exact decomposition of the energy flux (P. Johnson, Phys. Rev. Lett., 124, 104501 (2020), J. Fluid Mech. 922, A3(2021)). We extend the formalism to the transfer of kinetic helicity across scales, important in the presence of large-scale mirror breaking mechanisms, to identify physical processes resulting in helicity transfer and quantify their contributions to the mean flux in the inertial range. All subfluxes transfer helicity from large to small scales. About 50% of the mean flux is due to the scale-local vortex flattening and vortex twisting. We derive a new exact relation between these effects, similar to the Betchov relation for the energy flux, revealing that the mean contribution of the former is three times larger than that of the latter. Multi-scale effects account for the remaining 50% of the mean flux, with approximate equipartition between multi-scale vortex flattening, twisting and entangling

Anisotropy in large eddy simulations determined from SO(3) symmetry group

The issue of small-scale anisotropy in the context of eddy-viscosity-type subgrid-scale models is discussed in the present work. Recent developments in turbulence research suggest that anisotropy from large spatial scales is felt far into the inertial subrange of turbulence. This is of particular importance for subgrid-scale models of large eddy simulations. To address this issue, we present solutions of the random-phase Kolmogorov flow at moderate Reynolds numbers using direct numerical simulations and large eddy simulations with four subgrid-scale models: the Smagorinsky, the dynamic, the dynamic Clark, and the tensor-diffusivity models. The degree of anisotropy at different scales is analysed by decomposing the structure function into their irreducible representation of the SO(3) symmetry group. The results suggest that the dynamic model and the dynamic Clark model reproduce the statistical behaviour reasonably well, even in the anisotropic sectors at small length scales

Evidences of Bolgiano scaling in 3D Rayleigh-Benard convection

We present new results from high-resolution high-statistics direct numerical simulations of a tri-dimensional convective cell. We test the fundamental physical picture of the presence of both a Bolgiano-like and a Kolmogorov-like regime. We find that the dimensional predictions for these two distinct regimes (characterized respectively by an active and passive role of the temperature field) are consistent with our measurements.Comment: 4 pages, 3 figure