Emmanuel Lévêque's Website
RESEARCH ACTIVITIES


TURBULENCE IN FLUIDS
The word turbulence is employed to label many different physical phenomena, which exhibit the common characteristics of disorder and complexity. It is the ubiquitous presence of spontaneous (intrinsic) fluctuations, distributed over a wide range of length and time scales, that makes turbulence a worthwhile research topic. The very nature of the turbulent fluctuations is extremely peculiar. Turbulence has to do with non-linearity; there is no hint of the non-linear solutions in the linearized approximations, and strong departure from thermodynamic equilibrium.
Most natural and industrial flows are turbulent; turbulence lies at the core of so much of what we observe. Turbulence generally eclipses the laminar (steady and regular) behavior of the flow, and contributes to a largely enhanced energy dissipation, mixing, heat and mass transfer, etc. In astrophysics, interstellar turbulence is said to be one of the key ingredients of modern theories of star formation.

Modelling prospecting aims at elaborating numerically tractable mathematical models of turbulence.
  • An introduction to turbulence in fluids, and modelling aspects  
    in Stellar fluid dynamics and numerical simulations: from the sun to neutron stars (EDP sciences, 2006)
  • The physics of turbulence  
    in Structure Formation in Astrophysics (Cambridge University Press, 2009)
SELECTION OF CONTRIBUTIONS TO
THE STATISTICAL MECHANICS OF TURBULENCE:
It is devoted to the statistical description of turbulent motions, also called turbulent eddies. By analogy with a molecule, an eddy may be seen as a glob of fluid of a given size, or (spatial) scale, that has a certain structure and life history of its own. The turbulent activity of the bulk is the net result of the interactions between the eddies. It is characteristic of turbulence that these interactions are unpredictable in details; however, statistically distinct properties can be identified and profitably examined.
Scaling laws and intermittency:
  • Universal scaling laws in fully-developed turbulence 
    published in Physical Review Letters, 1994
  • Scaling laws for the turbulent mixing of a passive scalar in the wake of a cylinder 
    published in Physics of Fluids, 1999
  • Shear effects in nonhomogeneous turbulence 
    published in Physical Review Letters, 2000
  • Long time correlations in Lagrangian dynamics: A key to intermittency in turbulence 
    published in Physical Review Letters, 2002
  • Lagrangian velocity fluctuations in fully developed turbulence: Scaling, intermittency, and dynamics 
    published in Journal of Statistical Physics, 2003
  • Intermittency of velocity time increments in turbulence 
    published in Physical Review Letters, 2003
  • Experimental and numerical study of the Lagrangian dynamics of high Reynolds turbulence
    published in New Journal of Physics, 2004
  • On the rapid increase of intermittency in the near-dissipation range of fully developed turbulence 
    published in European Physical Journal B, 2005
  • Unified multifractal description of signed longitudinal velocity increments statistics in turbulence
    published in Physica D-nonlinear phenomena, 2006
  • Universal intermittent properties of particle trajectories in highly turbulent flows
    published in Physical Review Letters, 2009
  • A phenomenological theory of Eulerian and Lagrangian velocity fluctuations in turbulent flows
    published in CR Physique, 2012
Transport of material particles:
  • Acceleration statistics of finite-sized particles in turbulent flow: the role of Faxen forces
    published in Journal of Fluid Mechanics, 2009
  • Dynamics of inertial particles in a turbulent von-Karman flow
    published in Journal of Fluid Mechanics, 2011
  • Impact of trailing wake drag on the statistical properties and dynamics of finite-sized particle in turbulence
    published in PhysicaD, 2012
  • Multiple collisions in turbulent flows
    published in Physical Review E, 2013
Superfluid (or quantum) turbulence:

Helium-II at (finite) temperature below the transition T=2.17K can be described as the superposition of two interacting fluids. A normal fluid which has non-zero viscosity and an inviscid superfluid, in which vorticity is confined to quantized vortices. The large-scale dynamics of these two co-penetrating fluids obey respectively the Navier-Stokes and Euler equations (at low mach number) coupled together by a mutual friction force. This is the general framework of the so-called two-fluid model initiated by Landau and Tisza in 1941. Like in classical fluids, turbulent dynamics can be generated in superfluid helium II. This is refered to as superfluid turbulence in the literature. Since the pioneering experiments by Viven about half a century ago, quantum turbulence has been investigated mostly experimentally with the motivation to examine to what extent quantum turbulence resembles or differs from classical turbulence in ordinary fluids. Related theoretical and numerical works rely mainly on simplified one-way coupling (no back reaction) between the normal and the superfluid; wall boundary conditions are also often ignored. The studies have yielded significant progress, however, we are still a long way from a fulll understanding. In this regard, it is admitted that improved numerical simulations can be helpful.
  • Quantum turbulence at finite temperature: The two-fluids cascade
    published in EuroPhysics Letters, 2009
  • Mesoscale equipartition of kinetic energy in quantum turbulence
    published in EuroPhysics Letters, 2011
  • Energy cascade and the four-fifths law in superfluid turbulence
    published in EuroPhysics Letters, 2012
THE NUMERICAL MODELING OF TURBULENCE:
The prohibitive cost of direct numerical simulations (DNS) of turbulent engineering flows motivate the development of simplified models, requiring less computation, but still relevant (to some degree) for reproducing the large-scale dynamics. Under these circumstances, the modelling of turbulent flows near a solid boundary is of special interest. A boundary affects the kinetics of the flow through different mechanisms. The most prominent is that related to the mean shear, which is extreme at the boundary and responsible for the production of streamwise vortices and streaky structures, which eventually detach and sustain turbulence in the bulk. Thus, it is thought that understanding how the mean shear impacts on fluid motions is a key to improving the capabilities of numerical models.

  • A Shear-Improved Smagorinsky's model for wall-bounded flows
    published in Journal of Fluid Mechanics, 2007
  • Numerical studies towards practical large-eddy simulation
    published Journal of Thermal Science, 2007
It is desirable to account explicitly for the mean-flow gradients in the modeling of the subgrid-scale viscosity, also the canonical assumption of homogeneous and isotropic turbulence should be abandoned. This is particularly relevant for high-Reynolds flows, when the resolution is almost comparable to the large-scales of the flow. These features naturally call for a generic procedure to estimate numerically the mean flow and evaluate the subgrid-scale viscosity as the simulation progresses. Two distinc time-domain smoothing algorithms are proposed to estimate the mean flow, namely, an exponentially weighted moving average (exponential smoothing) and an adaptive low-pass Kalman filter. These algorithms highlight the longer-term evolution or cycles of the flow but erase short-term fluctuations. Indeed, it is our assumption that the mean flow (in the statistical sense) may be approximated to the low-frequency component of the velocity field, and that the turbulent part of the flow adds itself to this unsteady mean.
  • Smoothing algorithm for mean flow extraction in large-eddy simulations of complex turbulent flows
    published in Physics of Fluids, 2010
Vortex filaments in 3d Navier-Stokes turbulence
from Direct Numerical Simulation.
Three-dimensional trajectory of a fluid particle in homogeneous and isotropic turbulence reconstructed from acoustics signals.
N. Mordant, E. Lévêque, J.-F. Pinton, New Journal of Physics 6, 116 (2004)
Interestingly, numerical simulations of the two-fluids model at very low temperature give that the energy spectrum of a superfluid increases as k**2 at large wavenumbers.
Large-eddy simulation of the flow past a cylinder in the sub-critical turbulent regime at Re=47000
(SISM in the Turb'Flow solver).
Mean-flow extraction by exponential smoothing
(SISM in the Turb'Flow solver).
SISM in the Turb'Flow solver: Angular distributions of pressure coefficients (around the cylinder) compare very well with experimental data.
The frequency of the Kalman filter adapts itself to the fluctuations of the flow and suitably captures the turbulent vortex shedding (SISM in the Turb'Flow solver).