Étude de la turbulence d’ondes élastiques et gravito-capillaires : de l’idéal théorique aux conditions réelles ?
PhD thesis under the supervision of:
Abstract
Weak turbulence theory (WTT) is a statistical theory applied to a large number of incoherent and dispersive waves. Based on the hypotheses of small non-linearity and infinite domain the theory predicts an energy cascade from the forcing scales to the dissipative scales. The confrontation of WTT to experiment for surface waves raises many inconsistencies. The strong hypotheses on which is developed the WWT may be the explanation of such disparity between experiment and theory. The aim of this Thesis is to investigate the impact of the invalidation of some of these conditions on the statistical properties of turbulence. Experiments of interfacial waves between two non-miscible fluids with different viscosities have been carried out to characterize the effect of the increase of viscous dissipation on the energy cascade. An experiment at the surface of water with an increasing confinement of the width of the vessel has been done in order to possibly observe a coexistence between discrete turbulence and classical turbulence. An experimental study of gravity-capillary waves with a decrease of dispersion led us to the observation of a transition to a solitonic regime. In order to verify whether such a transition can be observed in a different physical system, an experimental and numerical study were conducted on the waves in a prestressed elastic plate. In this medium, the effect of dispersion of bending waves is competing with the non-dispersive aspect of stretching waves. We also studied weakly and strongly non-linear regimes of purely stretching waves in a membrane.