Spatio-temporal characterization of Capillary Wave Turbulence

Wave Turbulence concerns the study of the statistical properties of a set of numerous non-linear interacting waves. The archetype of this phenomenon are waves on the surface of a fluid [1]. We report a space-time characterization of Capillary Wave Turbulence, produced in the laboratory at the air-water interface. The three-dimensional shape of the free interface is measured as a function of time, by using an optical method, the ``Diffusing Light Photography'' [2], associated with a fast camera. Linear and non-linear dispersion relations are extracted by the computation of the spatio-temporal power spectrum of wave amplitude. When Wave Turbulence regime is reached, we observe power-law spectra both in time and in space, whose exponents are in agreement with the theoretical predictions of Wave Turbulence theory~[3].\\[4pt] [1] A. C. Newell and B. Rumpf, Annu. Rev. Fluid Mech. 43, 59 (2011) [2] W. B. Wright, R. Budakian and S. J. Putterman, Phys. Rev. Lett. 76, 4528 (1996)\\[0pt] [3] V. Zakharov, V. L'vov and G. Falkovich (1992) ``Kolmogorov spectra of turbulence'' Springer-Verlag