Direct numerical simulation of axisymmetric turbulence

International audienceThe dynamics of decaying strictly axisymmetric, incompressible turbulence is investigated using direct numerical simulations. It is found that the angular momentum is a robust invariant of the system. It is further shown that long-lived coherent structures are generated by the flow, associated with stationary solutions of the Euler equations. The structures obey relations in agreement with predictions from selective decay principles, compatible with the decay laws of the system. Two different types of decay scenarios are highlighted. The first case results in a quasi-two-dimensional flow with a dynamical behaviour in the poloidal plane similar to freely decaying two-dimensional turbulence. In a second regime, the long-time dynamics is dominated by a single three-dimensional mode

Large-scale bottleneck effect in two-dimensional turbulence

The bottleneck phenomenon in three-dimensional turbulence is generally associated with the dissipation range of the energy spectrum. In the present work, it is shown by using a two-point closure theory, that in two-dimensional turbulence it is possible to observe a bottleneck at the large scales, due to the effect of friction on the inverse energy cascade. This large-scale bottleneck is directly related to the process of energy condensation, the pile-up of energy at wavenumbers corresponding to the domain size. The link between the use of friction and the creation of space-filling structures is discussed and it is concluded that the careless use of hypofriction might reduce the inertial range of the energy spectrum

On the Structure and Dynamics of Sheared and Rotating Turbulence: Anisotropy Properties and Geometrical Scale-Dependent Statistics

This study is based on a series of nine direct numerical simulations of homogeneous turbulence, in which the rotation ratio f/S of Coriolis parameter to shear rate is varied. The presence of rotation stabilizes the flow, except for a narrow range of rotation ratios 0\u3cf/

Three-dimensional turbulence without vortex stretching

International audienceWe consider three-dimensional turbulence from which vortex stretching is removed. The resulting system conserves enstrophy, but does not conserve kinetic energy. Using spectral closure, it is shown that enstrophy is transferred to small scales by a direct cascade. The inviscid truncated system tends to an equipartition of enstrophy over wave vectors. No inverse cascade is observed once the scales larger than the forcing scale are in equipartition

Grid turbulence near the grid

In grid turbulence, not so far behind the grid, an average flow can be observed with a close to sinusoidal velocity profile, corresponding to the wakes behind the grid bars. The kinetic energy of this mean flow decays rapidly and a close to isotropic flow is observed further downstream. We show how these wakes behind the grid-bars influence the downstream turbulence. In particular, we investigate the decay rate of kinetic energy, the behavior of the normalized dissipation rate, and the sensitivity of the flow on initial conditions. We show that the initial value of the ratio of the lengthscale of the turbulence to the mesh-size determines the precise decay of the mean-flow and the generation of the turbulent kinetic energy. We further show how a simple turbulence model can estimate the degree of non-equilibrium of a flow

On the anisotropy of the turbulent passive scalar in the presence of a mean scalar gradient

International audienceWe investigate the origin of the scalar gradient skewness in isotropic turbulence on which a mean scalar gradient is imposed. The problem of the advection of an anisotropic scalar field is reformulated in terms of the advection of an isotropic vector field. For this field triadic closure equations are derived. It is shown how the scaling of the scalar gradient skewness depends on the choice of the timescale used for the Lagrangian decorrelation of the vector field. The persistent anisotropy in the small scales for the third-order statistics is shown to be perfectly compatible with Corrsin-Obukhov scaling for second-order quantities, since second- and third-order scalar quantities are governed by a different triad correlation timescale. Whereas the inertial range dynamics of second-order scalar quantities are governed by the Lagrangian velocity correlation time, the third-order quantities remain correlated over a time related to the large-scale dynamics of the scalar field. It is argued that this time is determined by the average time it takes for a fluid particle to travel between ramp-cliff scalar structures

Production and dissipation of kinetic energy in grid turbulence

International audienceIn grid turbulence, not so far behind the grid, an average flow can be observed with a close to sinusoidal velocity profile, corresponding to the wakes behind the grid bars. The kinetic energy of this mean flow decays rapidly and a close to isotropic flow is observed further downstream. We show how these wakes behind the grid bars influence the downstream turbulence. In particular, we investigate the decay rate of kinetic energy, the behavior of the normalized dissipation rate, and the sensitivity of the flow on initial conditions. We show that the initial value of the ratio of the length scale of the turbulence to the mesh-size determines the precise decay of the mean-flow and the generation of the turbulent kinetic energy. We further show how a simple turbulence model can estimate the degree of nonequilibrium and inhomogeneity of grid turbulence and how this model can be extended to take into account disequilibrium observed in direct numerical simulations of decaying isotropic turbulence

The temperature spectrum generated by frictional heating in isotropic turbulence

International audienceIn every turbulent flow with non-zero viscosity, heat is generated by viscous friction. This heat is then mixed by the velocity field. We consider how heat fluctuations generated this way are injected and distributed over length scales in isotropic turbulence. A triadic closure is derived and numerically integrated. It is shown how the heat fluctuation spectrum depends on the Reynolds and Prandtl numbers

Passive scalar mixing in turbulent flow

The mixing of a passive scalar in turbulent flow is studied. First, Direct Numerical Simulation (DNS), Large Eddy Simulation (LES) and dimensional arguments are used to investigate the scalar flux spectrum in isotropic turbulence with a mean scalar gradient. A scaling law allowing for inertial range slopes varying from -5/3 to -7/3 is derived. The LES results support a K^{-2} expression. Subsequently, using a two-point closure (EDQNM), we show that at very high Reynolds numbers, the scalar flux spectrum in the inertial range behaves as predicted by the classical dimensional analysis of Lumley (1967) and scales as K^{-7/3}. At Reynolds numbers corresponding to laboratory experiments the closure leads to a spectrum closer to K^{-2}. It is shown that the K^{-2} scaling in the LES is induced by large scale forcing. The closure is then applied to homogeneous shear flow and the spectra of cross-stream and streamwise scalar fluxes are investigated. The streamwise scalar flux spectrum is found to scale as K^{-23/9}. This result is in agreement with experiments but disagrees with classical dimensional analysis. Eventually, we show that the link between particle dispersion and scalar mixing allows to formulate a Markovian two-point closure for the velocity and scalar that does not involve any model constant.Le mélange d'un scalaire passif par un écoulement turbulent est étudié. D'abord, la simulation numérique directe (DNS), la simulation des grandes échelles (LES) et des arguments dimensionnels sont employés pour étudier le spectre du flux de scalaire dans une turbulence isotrope avec un gradient moyen uniforme de scalaire. Une loi d'échelle est dérivée. Cette loi conduit à des pentes du spectre variant entre -5/3 et -7/3 en zone inertielle. De premiers résultats de LES plaident en faveur d'un comportement en K^-2. Ensuite, en utilisant une fermeture en deux points (EDQNM), nous montrons qu'aux nombres de Reynolds très élevés, le spectre de flux de scalaire dans la zone intertielle se comporte en K^-7/3. Ce résultat est en accord avec l'analyse dimensionnelle classique de Lumley (1967). Aux nombres de Reynolds correspondant aux expériences de laboratoire, la fermeture conduit à des spectres plus près de K^-2. Nous montrons ensuite que le comportement en K^-2 trouvé en LES est induit par le forçage à grande échelle. La fermeture est alors appliquée au cas des écoulements homogènes cisaillés et les spectres du flux de scalaire longitudinal et transverse sont étudiés. Le spectre du flux longitudinal est trouvé proportionnelle à K^-23/9. Ce résultat est en accord avec l'expérience mais est en désaccord avec l'analyse dimensionnelle classique. Finalement, nous montrons que le lien entre la dispersion de particules et le mélange d'un scalaire permet de formuler une fermeture en deux points et un temps qui ne nécessite l'introduction d'aucune constante dans le modèle

The influence of walls on Lagrangian statistics in two-dimensional turbulence

International audienceThe influence of solid walls on the Lagrangian statistics of statistically stationary two-dimensional turbulence is investigated by comparing the flow in a circular wall-bounded and in an unbounded periodic domain. A Fourier pseudo-spectral method is used, which is combined in the wall bounded case with a volume penalization technique to impose no-slip conditions. A particular emphasis is put on the acceleration of fluid particles. It is investigated to what extent the impact of the boundaries influences the shape of the probability density functions of Lagrangian velocity increments. It is shown that the influence of walls is not confined to a small near-wall region but alters the statistics in the entire flow domain. This can be explained by the vorticity generation in the turbulent boundary layer which destabilizes and leads to the formation of vortices that subsequently detach and travel into the bulk flow. The enstrophy level is thus increased with respect to the one in the unbounded periodic domain