Unidimensional surface wave turbulence, transition to a shock wave regime,
intermittency and Anderson localization

Speaker: Guillaume Ricard

Abstract: Wave turbulence is a phenomenon in which many weakly nonlinear waves
interact with each other. The theory of weak turbulence describes this phenomenon in
many domains in physics. It is however essential to know the experimental range of
validity of this theory which assumes many hypotheses. In this context, an experiment is
set up to evidence the existence of one-dimensional wave turbulence on the surface of a
fluid. This particular geometry has never been experimentally used in wave turbulence
before, and offers new opportunities thanks to its simplicity. As weak turbulence
assumes wave dispersivity, it is then significant to know whether nondispersive waves
can redistribute its energy across scales, or whether it focuses into coherent structures.
In the one-dimensional experiment, we have shown waves on the surface of a magnetic
liquid become nondispersive in presence of a magnetic field, leading to the emergence
of shock waves that drive the system dynamics. The intermittent nature of the
experimental shock wave regime is then evidenced, in agreement with a Burgers model
modified to take account of the finite steepness of the waves. Finally, the Anderson
localization of gravity waves is evidenced experimentally. This other phenomenon of
interaction between waves (interferences) is found to be in agreement with the linear
theory. The role of wave nonlinearity on the Anderson localization is also shown