Turbulence at the Kolmogorov scale

If you stir strongly enough a viscous flow, it becomes turbulent and displays vortices and coherent structures of various sizes. The typical scale for energy dissipation is called the Kolmogorov scale $\eta$ and marks the transition between the power law behavior and a steep exponential decay in the wavenumber range. Therefore, scales smaller than $\eta$ contains a negligible fraction of the kinetic energy. Because of that, it is often thought that scales below $\eta$ are irrelevant and that nothing interesting is happening below $\eta$. For a long time, it was for example thought that a direct numerical simulation of a viscous fluid is well resolved if its minimal grid spacing is $\eta$. Recent theoretical and experimental progresses however suggest that many interesting phenomena do happen below $\eta$ and this may impact the validity of Navier-Stokes equations (NSE) as model for the dynamics of industrial, geophysical or astrophysical fluids. This talk discusses some of these phenomena using both numerical simulations and a dedicated large turbulent experiment.