Energy cascade and the four-fifths law in superfluid turbulence

The 4/5-law of turbulence, which characterizes the energy cascade from large to small-sized eddies at high Reynolds numbers in classical fluids, is verified experimentally in a superfluid 4He wind tunnel, operated down to 1.56 K and up to R_lambda ~ 1640. The result is corroborated by high-resolution simulations of Landau-Tisza's two-fluid model down to 1.15 K, corresponding to a residual normal fluid concentration below 3 % but with a lower Reynolds number of order R_lambda ~ 100. Although the K\'arm\'an-Howarth equation (including a viscous term) is not valid \emph{a priori} in a superfluid, it is found that it provides an empirical description of the deviation from the ideal 4/5-law at small scales and allows us to identify an effective viscosity for the superfluid, whose value matches the kinematic viscosity of the normal fluid regardless of its concentration.Comment: 6 pages, 7 figure

Kolmogorov cascade and equipartition of kinetic energy in numerical simulation of Superfluid turbulence

International audienceThe turbulence of a superfluid is investigated by direct numerical simulations at finite temperature and high Reynolds numbers using the continuous model. The superfluid component is described by the Euler equation while the normal fluid component is described by the Navier-Stokes equation, both being coupled by mutual friction. In the high temperature limit, the Kolmogorov cascade is recovered, as expected from previous numerical and experimental studies. As the temperature decreases, the Kolmogorov cascade remains present at large scales while, at small scales, the system evolves towards a statistical equipartition of kinetic energy among spectral modes

Investigation of intermittency in superfluid turbulence

International audienceThis paper reports new experimental and simulation velocity data for superfluid steady turbulence above 1 K. We present values for the scaling exponent of the absolute value of velocity-increment structure functions. In both experiments and simulations, they evidence that intermittency occurs in superfluid flows in a quite comparable way to classical turbulence. In particular, the deviation from Kolmogorov 1941 keeps the same strength as we cross the superfluid transition. To the best of our knowledge, this is the first confirmation of the superfluid 4He experimental results from Maurer et al. EPL 1998 and the first numerical evidence of intermittency in superfluid turbulence

Direct and Large-Eddy Simulation of Turbulent Flows on Composite Multi-Resolution Grids by the Lattice Boltzmann Method

In order to properly address the simulation of complex (weakly compressible) turbulent flows, the lattice Boltzmann method, originally designed for uniform structured grids, needs to be extended to composite multi-domain grids displaying various levels of spatial resolution. Therefore, physical conditions must be specified to determine the mapping of statistical information (about the populations of moving particles) at the interface between two domains of different resolutions. It is here argued that these conditions can express quite simply in terms of the probability distributions of the underlying discrete-velocity Boltzmann equation. Namely, the continuity of the mass density and fluid momentum is fulfilled by imposing the continuity of the equilibrium part of these distributions, whereas the discontinuity of the rate-of-strain tensor is ensured by applying a ''spatial transformation'' to the collision term of the discrete-velocity Boltzmann equation. This latter condition allows us to explicitly account for the subgrid-scale modeling in the treatment of resolution changes. Test computations of a turbulent plane-channel flow have been considered. The lattice Boltzmann scheme relies on the standard D3Q19 lattice in a cell-vertex representation, and uses the BGK approximation for the collision term. A shear-improved Smagorinsky viscosity is used for the subgrid-scale modeling. In a quasi-Direct Numerical Simulation at $\mathrm{Re}_\tau=180$ (with two levels of resolution) the results are found in excellent agreement with reference data obtained by a high-resolution pseudo-spectral simulation. In a Large-Eddy Simulation at $\mathrm{Re}_\tau=395$ (with three levels of resolution) the results compare very well with high-resolution reference data. The accuracy is improved in comparison with a large-eddy simulation based on finite-volume discretization with the same subgrid-scale viscosity model and comparable grid resolution. This study demonstrates the good capabilities of the lattice Boltzmann method to handle both Direct and Large-Eddy Simulations of turbulent flows with grid resolutions comparable to those commonly used in simulations based on standard discretization methods, \emph{e.g.} pseudo-spectral or finite-volume methods

Rare-event sampling applied to the simulation of extreme mechanical eorts exerted by a turbulent ow on a blu body

This study evaluates the relevance of rare-event sampling techniques to accelerate the simulation of extreme mechanical eorts exerted by a turbulent ow impinging onto a blu body. The main idea is to replace a long simulation by a set of much shorter ones, running in parallel, with dynamics that are replicated or pruned in order to sample large-amplitude events more frequently. Such techniques have been shown to be ecient for a wide range of problems in statistical physics, computer science, biochemistry, enabling the simulation of rare events otherwise out of reach by direct sampling. This work is the rst application to uid-structure interaction problems. The drag experienced by a squared obstacle placed in a turbulent ow (in two dimensions) is taken as a representative case study to investigate the performance of two major rare-event sampling algorithms, namely the Adaptive Multilevel Splitting (AMS) and the Giardina-Kurchan-Tailleur-Lecomte (GKTL) algorithms. Practical evidence is given that the fast sweeping-time of uid structures past the obstacle has a drastic inuence on the eciency of these two algorithms. While it is shown that the AMS algorithm does not yield signicant run-time savings, the GKTL algorithm appears to be ecient to sample extreme uctuations of the time-averaged drag and estimate related statistics such as return times. Beyond the study of applicability of rare-event sampling techniques to a uid-mechanical problem, this work also includes a detailed phenomenological description of extreme-drag events of a turbulent ow on a blu body

Advanced lattice Boltzmann scheme for high-Reynolds-number magneto-hydrodynamic flows

International audienceIs the lattice Boltzmann method suitable to investigate numerically high-Reynolds-number magneto-hydrodynamic (MHD) ows? It is shown that a standard approach based on the Bhatnagar-Gross-Krook (BGK) collision operator rapidly yields unstable simulations as the Reynolds number increases. In order to circumvent this limitation, it is here suggested to address the collision procedure in the space of central moments for the uid dynamics. Therefore, an hybrid LB scheme is introduced, which couples a central-moment scheme for the velocity with a BGK scheme for the space-and-time evolution of the magnetic field. This method outperforms the standard approach in terms of stability, allowing us to simulate high-Reynolds-number MHD ows with non-unitary Prandtl number while maintaining accuracy and physical consistency

Local and nonlocal pressure Hessian effects in real and synthetic fluid turbulence

The Lagrangian dynamics of the velocity gradient tensor A in isotropic and homogeneous turbulence depend on the joint action of the self-streching term and the pressure Hessian. Existing closures for pressure effects in terms of A are unable to reproduce one important statistical role played by the anisotropic part of the pressure Hessian, namely the redistribution of the probabilities towards enstrophy production dominated regions. As a step towards elucidating the required properties of closures, we study several synthetic velocity fields and how well they reproduce anisotropic pressure effects. It is found that synthetic (i) Gaussian, (ii) Multifractal and (iii) Minimal Turnover Lagrangian Map (MTLM) incompressible velocity fields reproduce many features of real pressure fields that are obtained from numerical simulations of the Navier Stokes equations, including the redistribution towards enstrophy-production regions. The synthetic fields include both spatially local, and nonlocal, anisotropic pressure effects. However, we show that the local effects appear to be the most important ones: by assuming that the pressure Hessian is local in space, an expression in terms of the Hessian of the second invariant Q of the velocity gradient tensor can be obtained. This term is found to be well correlated with the true pressure Hessian both in terms of eigenvalue magnitudes and eigenvector alignments.Comment: 10 pages, 4 figures, minor changes, final version, published in Phys. Fluid

Towards practical large-eddy simulations of complex turbulent flows

International audienceA Shear-Improved Smagorinsky model (SISM) allowing to address non-homogeneous and unsteady flow configurations in a physically-sound manner, without adding significant complication and computation compared to the standard Smagorinsky model, is studied and implemented. Interestingly, the SISM does not call for any adjustable parameter nor ad-hoc damping function. It makes use here of an exponential smoothing algorithm to estimate the ensemble-average of the strain from the temporal evolution of the flow. Application on a flow past a circular cylinder is used as a test of the method