Laboratory Experiments on Wave Turbulence

This review paper is devoted to a presentation of recent progress in wave turbulence. I first present the context and state of the art of this field of research both experimentally and theoretically. I then focus on the case of wave turbulence on the surface of a fluid, and I discuss the main results obtained by our group: caracterization of the gravity and capillary wave turbulence regimes, the first observation of intermittency in wave turbulence, the occurrence of strong fluctuations of injected power in the fluid, the observation of a pure capillary wave turbulence in low gravity environment and the observation of magnetic wave turbulence on the surface of a ferrofluid. Finally, open questions in wave turbulence are discussed. 1. Context and state of the art. When strong enough surface waves propagate in a medium, their interactions can generate waves of different wavelengths. This energy transfer through the different spatial scales can occur on a wide range of wavelengths. This stationary out-of-equilibrium state is called the wave turbulence: the energy of the system cascades through the scales from a scale where energy is injected up to a small scale where energy is dissipated. Wave turbulence thus concerns the study of dynamical and statistical properties of an ensemble of interacting nonlinear waves. The archetype of wave turbulence is the study of the random state of ocean surface waves generated by wind or current. But this is a very common phenomenon that is present in various situations: surface waves on the sea [28, 42, 50, 90], internal waves in the ocean [64], Alfvén waves in solar winds [82], radar waves in ionosphere, spin waves in solids, Rossby waves in geophysics, ion waves [66] and Langmuir waves [49, 96] in plasmas, waves in nonlinear optics [59], quantum waves in Bose condensates [9, 24, 30, 80] ... Wave turbulence is thus an interdisciplinary subject that involves different community: astrophysics, geophysics, mathematics, fluid mechanics and different fields of physics. Since the early developments of theoretical tools by applied mathematicians and physicists, the first ones to be interested on wave turbulence were oceanographers and meteorologists. Their motivations are numerous such as to develop climatic models, predict the sea state with more precision, or extract some energy from ocean waves as a source of alternative energy... At a more fundamental level, the goal is to understand the energy transfers between nonlinear interacting 2000 Mathematics Subject Classification. Primary: 7605, 76B15; Secondary: 76F99, 76D33.