Séminaire

The local mixing produced by turbulence in the ocean interior plays a crucial role in its global energy budget. This mixing partially drives large scale dynamics, as evidence in the meridional overturning circulation (MOC). The circulation is produced thanks to the downward transport of energy from the surface to the deep bottom of the ocean, possible thanks to vertical mixing. Many processes produce mixing in the ocean, mostly forced by interior tides and winds. In addition, fine measurements of the density in the ocean show that the stratification can vary quite abruptly at small scales. Nevertheless, the proportion of energy transferred from turbulent structures to effective mixing is very difficult to measure in the ocean, and the details of the distribution of the injected energy is yet not fully understood.  In order to answer these questions, a set of 3D Direct Numerical Simulations (DNS) of a turbulent stratified flow are performed by solving the Navier-Stokes equations under Boussinesq approximation. A classical Fourier pseudo-spectral method is used with 1024^3 grid points. A porous penalization region is introduced to take into account non-flux conditions at the bottom and at the top of the box. A turbulent velocity field is introduced at t=0 and perturbs the initially linear buoyancy profile which is then free to evolve in time.
The instantaneous irreversible mixing is compute by comparing the potential energy and the background potential energy of the system. The mixing efficiency, which is a form to measure how the injected energy is partitioned between available potential energy and kinetic energy, is computed for a broad range of degrees of stratification (characterized by the non-dimensional Richardson number, Ri). Our results indicate that the mixing efficiency presents a non trivial, yet simple, dependency with respect to the Richardson number. In addition, these results are captured by a statistical model developed by Venaille 2016. These results allow to improve notoriously the historical approach to model the mixing efficiency in oceanic conditions, which is often taken to be constant.

bruno.deremble@ens.fr