Numerical study of 2d stratified turbulence forced by internal gravity waves
The oceanic motions are composed of eddies with a very large horizontal scale and 3D propagating internal gravity waves. Its kinetic energy spectra follow the well-known Garrett and Munk spectrum, which is usually interpreted as the signature of interacting internal gravity waves. Our main motivation is to reproduce the turbulence regime observed in nature by forcing waves.
Two-dimensional (2D) stratified flows on a vertical cross-section differ from its analogous three-dimensional flows in its lack of vertical vorticity, supporting only waves and shear modes. In this PhD work, we perform a numerical study of 2D stratified turbulence forced with internal gravity waves. We get rid of the shear modes, sustaining a system only with wave modes. Unlike precedent studies, the forcing is applied to a localized region of the spectral space, in which forced internal waves have a similar time scale. We force intermediate-scale waves to allow the dynamics to develop both upscale and downscale energy cascade.
We first present the different regimes of 2D stratified turbulence with a particular interest in the ocean-like regime, i.e. strong stratification and large Reynolds number. The dynamics of the energy cascade is analysed by means of the spectral energy budget.
Furthermore, we check if it is possible to obtain turbulence driven by weakly non linear ineracting waves by performing a spatio-temporal analysis. To conclude, we report results of numerical simulations forced either on the vorticity or on the eigenmode of the Navier-Stokes equations in order to study the degree of universality of 2D stratified turbulence with respect to the forcing.