Aurore Naso

The interaction between a solid particle and a turbulent flow

The interaction between a fixed solid spherical particle and stationary turbulence with zero mean flow is investigated numerically. The object diameter, D, lies in the inertial range (D≈0.6L≈0.9λ≈8η, where L, λ and η, respectively, denote the integral scale, the Taylor microscale and the Kolmogorov length) and the particle Reynolds number is close to 20. It is found that the turbulence statistics at different distances from the solid/fluid interface are modified by the presence of the object in a region that extends more than 10 times further than the viscous layer. This estimate is confirmed by the analysis of the correlation between the force and torque on the particle and the force and torque on spherical surfaces surrounding the particle, although the torque decorrelates somewhat faster with increasing distance from the object surface. The angular slip velocity of the particle, a quantity of crucial importance for the modeling of the turbulent transport of large objects, is also characterized.

Statistical mechanics of Beltrami flows in axisymmetric geometry: Theory reexamined

A simplified thermodynamic approach of the incompressible axisymmetric Euler equations is considered based on the conservation of helicity, angular momentum, and microscopic energy. Statistical equilibrium states are obtained by maximizing the Boltzmann entropy under these sole constraints. We assume that these constraints are selected by the properties of forcing and dissipation. The fluctuations are found to be Gaussian, while the mean flow is in a Beltrami state. Furthermore, we show that the maximization of entropy at fixed helicity, angular momentum, and microscopic energy is equivalent to the minimization of macroscopic energy at fixed helicity and angular momentum. This provides a justification of this selective decay principle from statistical mechanics. These theoretical predictions are in good agreement with experiments of a von Kármán turbulent flow and provide a way to measure the temperature of turbulence and check fluctuation-dissipation relations. Relaxation equations are derived that could provide an effective description of the dynamics toward the Beltrami state and the progressive emergence of a Gaussian distribution. They can also provide a numerical algorithm to determine maximum entropy states or minimum energy states.

Dual non-Kolmogorov cascades in a von Kármán flow

The experimental spatial power spectrum of the velocity fluctuations in a von Karman flow is measured, in a wide range of Reynolds numbers, 102 105.

Introduction of longitudinal and transverse Lagrangian velocity increments in homogeneous and isotropic turbulence

Based on geometric considerations, longitudinal and transverse Lagrangian velocity increments are introduced as components along, and perpendicular to, the displacement of fluid particles during a time scale {\tau}. It is argued that these two increments probe preferentially the stretching and spinning of material fluid elements, respectively. This property is confirmed (in the limit of vanishing {\tau}) by examining the variances of these increments conditioned on the local topology of the flow. Interestingly, these longitudinal and transverse Lagrangian increments are found to share some qualitative features with their Eulerian counterparts. In particular, direct numerical simulations at turbulent Reynolds number up to 300 show that the distributions of the longitudinal increment are negatively skewed at all {\tau}, which is a signature of time irreversibility of turbulence in the Lagrangian framework. Transverse increments are found more intermittent than longitudinal increments, as quantified by the comparison of their respective flatnesses and scaling laws. Although different in nature, standard Lagrangian increments (projected on fixed axis) exhibit scaling properties that are very close to transverse Lagrangian increments.

Small-scale anisotropy induced by spectral forcing and by rotation in non-helical and helical turbulence

ABSTRACT We study the effect of large-scale spectral forcing on the scale-dependent anisotropy of the velocity field in direct numerical simulations of homogeneous turbulence. ABC-type forcing and helical or non-helical Euler-type forcing are considered. We propose a scale-dependent characterisation of anisotropy based on a modal decomposition of the two-point velocity tensor spectrum. This produces direction-dependent spectra of energy, helicity and polarisation. We examine the conditions that allow anisotropy to develop in the small scales due to forcing and we show that the theoretically expected isotropy is not exactly obtained, even in the smallest scales, for ABC and helical Euler forcings. When adding rotation, the anisotropy level in ABC-forced simulations is similar to that of lower Rossby number Euler-forced runs. Moreover, even at low rotation rate, the natural anisotropy induced by the Coriolis force is visible at all scales, and two distinct wavenumber ranges appear from our fine-grained characterisation, not separated by the Zeman scale but by a scale where rotation and dissipation are balanced.

Turbulence modification in the vicinity of a solid particle

The turbulent transport of material particles is a very general phenomenon, occuring in many natural (dust storms, pollutants in the atmosphere, plankton in the ocean, …) and industrial (fluidized beds, chemical reactors, …) systems. The dynamics of particles suspended in a turbulent flow depends on their size and on their mass density. Very small neutrally buoyant particles behave as passive tracers, co-moving with the fluid, whereas inertial and finite-size effects are expected to occur for larger objects which are buoyant or denser than the fluid. The dynamics of very small heavy particles has been studied by modeling the hydrodynamic forces acting on them as the sum of a (possibly corrected) Stokes drag, added mass, and other forces; in this way it has been possible to simulate the dynamics of millions of particles (see e.g. [1]).