Large scale effects in turbulence

This manuscript describes how solutions of the Navier-Stokes equations behave in the large scales when forced in the small scales. It analyzes also the large scale behavior of magnetic fields solution of the kinetic induction equation when the velocity is in the small scales. The results were acquired with direct numeric simulation (DNS) using pseudo-spectral algorithms of the equations as well as their Floquet development. In the hydrodynamical case, the Floquet DNS were able to confirm the results of the AKA effect at low Reynolds number and extend them for Reynolds number of order one. The DNS were also used to study AKA-stable flows and identified a new instability that can be interpreted as a negative viscosity effect. In the magnetic case, the alpha effect is observe for a range of scale separation exceed know results by several orders of magnitude. It is also shown that the growth rate of the instability becomes independent of the scale separation once the magnetic field is destabilized in its small scales. The energy spectrum and the correlation time of absolute equilibrium solution of the truncated Euler equation are presented. A new regime where the correlation time is governed by helicity is exhibited. These results are also compared with those coming from large scale modes of solutions of the Navier-Stokes equation forced in the small scales. They show that the correlation time increases with the helicity of the flow.