Wave turbulence:
beyond weak turbulence
OPEN POSTDOCTORAL POSITIONS ON STRATIFIED 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 (inertiagravity 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. Is it (always) possible to observe weak turbulence in real systems ?

impact of finite size

possible instability of weak turbulence into a bath of localized structures

2. Beyond the KolmogorovZakharov spectrum ?

 anisotropic forcing

 investigation of the coupling between waves

 non stationary regimes

3. What if turbulence is not weak ?

 coherent structures ?

4. What about non dispersive waves ?

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

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

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

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

READ more on elastic plates
READ more on 1D wave FLUME
READ more on 2D GRAVITY WAVES
READ more on GRAVITYCAPILLARY WAVES
READ more on INTERNAL WAVES