Joint statistics of acceleration and vorticity in fully developed turbulence

We report results from a high resolution numerical study of fluid particles transported by a fully developed turbulent flow. Single particle trajectories were followed for a time range spanning more than three decades, from less than a tenth of the Kolmogorov time-scale up to one large-eddy turnover time. We present results concerning acceleration statistics and the statistics of trapping by vortex filaments conditioned to the local values of vorticity and enstrophy. We distinguish two different behaviors between the joint statistics of vorticity and centripetal acceleration or vorticity and longitudinal acceleration.Comment: 8 pages, 6 figure

Homogeneous and Isotropic Turbulence: a short survey on recent developments

We present a detailed review of some of the most recent developments on Eulerian and Lagrangian turbulence in homogeneous and isotropic statistics. In particular, we review phenomenological and numerical results concerning the issue of universality with respect to the large scale forcing and the viscous dissipative physics. We discuss the state-of-the-art of numerical versus experimental comparisons and we discuss the dicotomy between phenomenology based on coherent structures or on statistical approaches. A detailed discussion of finite Reynolds effects is also presented.Comment: based on the talk presented by R. Benzi at DSFD 2-14. postprint version, published online on 6 July 2015 J. Stat. Phy

Cascades and transitions in turbulent flows

Turbulence is characterized by the non-linear cascades of energy and other inviscid invariants across a huge range of scales, from where they are injected to where they are dissipated. Recently, new experimental, numerical and theoretical works have revealed that many turbulent configurations deviate from the ideal 3D/2D isotropic cases characterized by the presence of a strictly direct/inverse energy cascade, respectively. We review recent works from a unified point of view and we present a classification of all known transfer mechanisms. Beside the classical cases of direct and inverse cascades, the different scenarios include: split cascades to small and large scales simultaneously, multiple/dual cascades of different quantities, bi-directional cascades where direct and inverse transfers of the same invariant coexist in the same scale-range and finally equilibrium states where no cascades are present, including the case when a condensate is formed. We classify all transitions as the control parameters are changed and we analyse when and why different configurations are observed. Our discussion is based on a set of paradigmatic applications: helical turbulence, rotating and/or stratified flows, MHD and passive/active scalars where the transfer properties are altered as one changes the embedding dimensions, the thickness of the domain or other relevant control parameters, as the Reynolds, Rossby, Froude, Peclet, or Alfven numbers. We discuss the presence of anomalous scaling laws in connection with the intermittent nature of the energy dissipation in configuration space. An overview is also provided concerning cascades in other applications such as bounded flows, quantum, relativistic and compressible turbulence, and active matter, together with implications for turbulent modelling. Finally, we present a series of open problems and challenges that future work needs to address.Comment: accepted for publication on Physics Reports 201

Evaluation of DVFS techniques on modern HPC processors and accelerators for energy-aware applications

Energy efficiency is becoming increasingly important for computing systems, in particular for large scale HPC facilities. In this work we evaluate, from an user perspective, the use of Dynamic Voltage and Frequency Scaling (DVFS) techniques, assisted by the power and energy monitoring capabilities of modern processors in order to tune applications for energy efficiency. We run selected kernels and a full HPC application on two high-end processors widely used in the HPC context, namely an NVIDIA K80 GPU and an Intel Haswell CPU. We evaluate the available trade-offs between energy-to-solution and time-to-solution, attempting a function-by-function frequency tuning. We finally estimate the benefits obtainable running the full code on a HPC multi-GPU node, with respect to default clock frequency governors. We instrument our code to accurately monitor power consumption and execution time without the need of any additional hardware, and we enable it to change CPUs and GPUs clock frequencies while running. We analyze our results on the different architectures using a simple energy-performance model, and derive a number of energy saving strategies which can be easily adopted on recent high-end HPC systems for generic applications

On the Global Regularity of a Helical-decimated Version of the 3D Navier-Stokes Equations

We study the global regularity, for all time and all initial data in $H^{1/2}$, of a recently introduced decimated version of the incompressible 3D Navier-Stokes (dNS) equations. The model is based on a projection of the dynamical evolution of Navier-Stokes (NS) equations into the subspace where helicity (the $L^2-$scalar product of velocity and vorticity) is sign-definite. The presence of a second (beside energy) sign-definite inviscid conserved quadratic quantity, which is equivalent to the $H^{1/2}-$Sobolev norm, allows us to demonstrate global existence and uniqueness, of space-periodic solutions, together with continuity with respect to the initial conditions, for this decimated 3D model. This is achieved thanks to the establishment of two new estimates, for this 3D model, which show that the $H^{1/2}$ and the time average of the square of the $H^{3/2}$ norms of the velocity field remain finite. Such two additional bounds are known, in the spirit of the work of H. Fujita and T. Kato \cite{kato1,kato2}, to be sufficient for showing well-posedness for the 3D NS equations. Furthermore, they are directly linked to the helicity evolution for the dNS model, and therefore with a clear physical meaning and consequences

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

Role of helicity for large- and small-scale turbulent fluctuations

The effect of the helicity on the dynamics of the turbulent flows is investigated. The aim is to disentangle the role of helicity in fixing the direction, the intensity and the fluctuations of the energy transfer across the inertial range of scales. We introduce an external parameter, $\alpha$, that controls the mismatch between the number of positive and negative helically polarized Fourier modes. We present the first set of direct numerical simulations of Navier-Stokes equations from the fully symmetrical case, $\alpha=0$, to the fully asymmetrical case, $\alpha=1$, when only helical modes of one sign survive. We found a singular dependency of the direction of the energy cascade on $\alpha$, measuring a positive forward flux as soon as only a few modes with different helical polarities are present. On the other hand, small-scales fluctuations are sensitive only to the degree of mode-reduction, leading to a vanishing intermittency already for values of $\alpha \sim 0.1$ and independently of the degree of mirror symmetry-breaking. Our findings suggest that intermittency is the result of a global mode-coupling in Fourier space.Comment: 4 Fig

Helicity Transfer in Turbulent Models

Helicity transfer in a shell model of turbulence is investigated. We show that a Reynolds-independent helicity flux is present in the model when the large scale forcing breaks inversion symmetry. The equivalent in Shell Models of the ``2/15 law'', obtained from helicity conservation in Navier-Stokes eqs., is derived and tested. The odd part of helicity flux statistic is found to be dominated by a few very intense events. In a particular model, we calculate analytically leading and sub-leading contribution to the scaling of triple velocity correlation.Comment: 4 pages, LaTex, 2 figure