Wave turbulence:

beyond weak turbulence


in experimental fluid mechanics (details here) and one in numerical fluid mechanics (details here)

My project WATU has been selected by the European Research Council in the Consolidator Grant Call 2014. It started in october 2015 and it was awarded about 2 M€. The goal of the project is to provide a strong advance in the experimental studies of wave turbulence. Indeed wave turbulence (as opposed to fluid turbulence) is characterized by many theoretical developments (in the wake of the Weak Turbulence Theory – WTT) but a relative lack of experimental data. The theory exists thanks to the possibility to observe weakly non linear waves and thus to perform an asymptotic development that leads to a statistical theory. The question is then whether such a weak turbulence can exist in real systems with finite size, finite wave amplitude and dissipation.


Wave turbulence can be observed in many dispersive wave systems such as solar winds (Alfven waves in the magnetized interstellar plasma), magnetized industrial plasmas (such as ITER), in non linear optics in fibers or non linear crystals, vibrated elastic plates or oceanic waves. For example, it plays a major role in the ocean dynamics. Indeed, the oceans are stratified in density due to variation in temperature and salinity. Thus they support the propagation of 3D internal waves supported by gravity. The rotation of the Earth plays also a role so that the waves dynamics is actually also influenced by the Coriolis force (inertia-gravity waves). These waves play a role in mixing of the density profile, in redistributing energy in the ocean (in terms of position but also of length scale) and also in dissipating the energy as an ultimate fate of the turbulent energy cascade. These feature have to be accurately parameterized in numerical simulations of long term ocean dynamics for weather forecast or climate predictions. This parameterization implies an accurate understanding of wave turbulence that is presently quite limited.

My project aims at answering open questions on weak turbulence in several physical systems but also to go beyond the weak turbulence hypothesis and investigate strong wave turbulence. More specifically, I will address the following questions:

  1. 1. Is it (always) possible to observe weak turbulence in real systems ?

  2. -impact of finite size

  3. -possible instability of weak turbulence into a bath of localized structures

  4. 2. Beyond the Kolmogorov-Zakharov spectrum ?

  5. - anisotropic forcing

  6. - investigation of the coupling between waves

  7. - non stationary regimes

  8. 3. What if turbulence is not weak ?

  9. - coherent structures ?

  10. 4. What about non dispersive waves ?

  11. 5. Inverse cascades ?

In order to provide answers to these many open questions, I will use a variety of physical systems in which to generate well-controlled wave turbulence. These experiments will be hosted in LEGI (Laboratoire des Ecoulements Géophysiques et Industriels / Laboratory of Geophysical and Industrial Flows) in Grenoble, France. The main technical goal is to develop space and time resolved measurements in all experiments so that to have access to the the full dynamics of the system. Indeed wave are characterized by the fact that they propagate. This propagation causes the dispersion relation in the linear case. In order to be able to differentiate waves from other structures, a space-time measurement is required. Such a measurement will generate huge amounts of data and the processing of such data is a main concern in this project. The physical systems that will be investigated experimentally in this project are:

  1. 1. flexion waves in a vibrated thin elastic plate (experiment and numerical simulations) (with Roumaissa HASSAINI, grad student)

  2. 2. surface gravity-capillary waves at the interface between two fluids (with Roumaissa Hassaini and Quentin Aubourg, grad students)

  3. 3. surface gravity waves either in 1D and 2D (with Quentin Aubourg, Ivan Redor, grad students, Antoine Campagne, post-doc, Samuel Viboud engineer, Eric Barthelemy, Hervé Michallet and Joel Sommeria)

  4. 4. inertia-gravity gravity waves in 3D (stratified and rotating turbulence) (with Antoine Campagne, post-doc, Samuel Viboud engineer, Pierre Augier and Joel Sommeria)

  5. READ more on elastic plates
    READ more on 1D wave FLUME