Internal wave turbulence in a stratified fluid with and without eigenmodes of the experimental domain

Abstract: We present laboratory experiments on turbulence in a linearly stratified fluid driven by an ensemble of internal gravity waves which approaches statistical homogeneity and axi-symmetry. In a way similar to several recent experimental works, non-linearities develop through the establishment of a set of internal wave modes at discrete frequencies, when the forcing amplitude is increased. We show that the most energetic of these modes are resonant eigenmodes of the fluid domain. The discretization of the energy in frequency and wavenumber associated to the emergence of these modes prevents the flow from approaching a regime described by the Weak/Wave Turbulence Theory, in which a forward cascade carried by a statistical ensemble of weakly non-linear waves in an infinite domain forms an energy continuum in the frequency and wavenumber spaces. We then show that the introduction of slightly tilted panels at the top and at the bottom of the fluid domain allows to inhibit the emergence of the discrete wave modes. In this new configuration, the non-linear regime results in a continuum of energy over one decade of frequencies which is mainly carried by internal gravity waves verifying the dispersion relation. We therefore achieved a turbulent flow approaching a three-dimensional internal wave turbulence regime with no discretization of the energy in the frequency and wavenumber domains. These results constitute a significant step forward in the search of the laboratory observation of a fully-developed weakly-non-linear internal-gravity-wave turbulence.