Non Linear Physics Group - Eric Falcon

3D HYDRODYNAMIC TURBULENCE   (papers by our group)

Three-dimensional (3D) hydrodynamic turbulence is usually studied experimentally in closed containers where energy is injected at a large scale from a container boundary (e.g. via rotating blades or oscillating grids). We here introduce an original experimental technique where the fluid is forced in volume, randomly in space and time, using small immersed magnetic stirrers remotely driven [1,2].

Such a forcing, closer to those of direct numerical simulations, generate an excellent stationary, homogeneous and isotropic turbulence with almost no mean flow, as characterized by local and spatiotemporal fluid velocity measurements [4]. We also estimate the energy dissipation rate consistently in five different ways, a situation difficult to obtain experimentally otherwise [3]. Moreover, we confirm experimentally the prediction of Tennekes for 3D turbulence without mean flow, and we resolve the disagreement between previously suggested values of the Tennekes’ constant [4].

This new technique is useful to understand the properties of large scales in 3D turbulence (i.e., scales larger than the forcing scale - see below). It could be also implemented in geophysical- or astrophysical-like turbulent flows (rotating, stratified or multiphase flows), and could provide a technological breakthrough in turbulent mixing.

3D turbulence driven homogenously by magnetic particle (see article)

Fluid tracer trajectories within the PIV laser sheet over consecutive images (see article)

Are large scales in 3D turbulence in equilibrium?

The statistical equilibrium regime of large scales in 3D turbulence, predicted 70 years ago, has just been reported experimentally for the first time in 2022 [5].

The dynamics of turbulent flows at scales larger than the forcing scale is a topic that has been partially overlooked for years. Yet, large scales control many properties of industrial, geophysical or astrophysical 3D turbulent flows. Most of previous experiments and simulations on 3D turbulence had injected energy at a scale comparable to the size of the reservoir in order to study the turbulent cascade towards small scales.

We have managed to perform a scale separation between the forcing scale and the container size [5]. We inject energy into the fluid using centimeter-scale magnetic stirrers immersed in a large fluid reservoir put into the gap of a nearly one-ton electromagnet. By measuring the statistics of the fluid velocity field, we experimentally evidence that the large-scale modes of 3D turbulence possess the same energy [5]. This equipartition regime, or so-called statistical equilibrium regime, was predicted since 1952, but had not been observed experimentally so far. The large-scale dynamics can then be described with an effective temperature [5]. However, this large-scale dynamic is not isolated from the usual turbulent cascade, called Kolmogorov cascade, which develops towards small scales. This system is thus a remarkable example in which interactions occur between the degrees of freedom at equilibrium (large scales) with out-of-equilibrium structures (small scales) characteristic of turbulence.

These findings pave the way to use classical concepts (i.e., equilibrium statistical mechanics) to describe the large scales of 3D turbulence, with possible applications to climate modeling and large-scale dispersion of pollutants by turbulence.

Freely decaying 3D turbulence

Due to the inevitable mean flow in open systems as wind tunnels, current theoretical models of freely decaying 3D turbulence, such as Saffman’s model and Batchelor’s model, are difficult to test experimentally. We use a novel forcing technique, based on the erratic motions of magnetic stirrers immersed in a closed container, to produce homogeneous decaying turbulence, overcoming the previous limitations. Our experimental observations robustly support the Saffman’s model, while the large-scale turbulent energy spectrum conserves a self-similar scaling during the decay [7]. The connection between the Saffman invariant for freely decaying turbulent flows, and the large-scale behavior of their energy spectrum is also experimentally evidenced, for the first time [7].

New technique of forcing a fluid in volume, randomly in space and time: Movies (with air)    or     Movie (within water)

PUBLICATIONS on 3D HYDRODYNAMIC TURBULENCE

In water:

7. J.-B. Gorce and E. Falcon 2024
     Physical Review Letters 132, 264001 (2024) 
     Freely Decaying Saffman Turbulence Experimentally Generated by Magnetic Stirrers

6. J.-B. Gorce and E. Falcon, 2023
    Physical Review E 107, 034903 (2023)
    Statistics of a two-dimensional immersed granular gas magnetically forced in volume

5. J.-B. Gorce and E. Falcon, 2022 
      Physical Review Letters 129, 054501 (2022)
      Statistical Equilibrium of Large Scales in Three-Dimensional Hydrodynamic Turbulence

4. A. Cazaubiel, J.-B. Gorce, J.-C. Bacri, M. Berhanu, C. Laroche, and E. Falcon, 2021 
      Physical Review Fluids 6, L112601 (2021)
      Three-dimensional turbulence generated homogeneously by magnetic particles

3. E. Falcon, J.-C. Bacri & C. Laroche, 2017

      Physical Review Fluids 2, 102601(R) (2017) - Rapid Communication

      Dissipated power within a turbulent flow forced homogeneously by magnetic particles


In air (granular gas):

2. E. Falcon, J.-C. Bacri, and C. Laroche 2013
      AIP Conf. Proc. 1542, pp. 815-818 (2013)
      Experimental study of a granular gas homogeneously driven by particle rotations

1. E. Falcon, J.-C. Bacri, and C. Laroche 2013
      EPL (Europhysics Letters) 103, 64004 (2013)
      Equation of state of a granular gas homogeneously driven by particle rotations
   

In water (forcing by jets):

8. T. Jamin, M. Berhanu, and E. Falcon 2024
     submitted to Physical Review Fluids (2024) 
     Experimental study of three-dimensional turbulence under a free surface

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