The statistical properties of turbulence in presence of smart small-scale forcing*

Fluid dynamics turbulence is characterized by intermittent fluctuations distributed over a wide range of space- and time-scales. In the limit of infinite Reynolds numbers, the number of dynamical degrees of freedom tends towards infinity. Are all these degrees of freedom equally relevant for the dynamics? By means of high-resolution and high-statistics numerical simulations, we compare the statistical properties of homogenous and isotropic turbulence to those of the Navier-Stokes equation where, thanks to a non-linear viscosity, small-scale vortex filaments are strongly depleted. This non-linear forcing can be seen as a small-scale forcing, selectively acting on high-vorticity regions. Our results indicate that the presence of this “smart” small-scale forcing can strongly reduce the intermittency. Additionally, by comparing our results with those  from an “a-posteriori” filtered analysis, we show that the influence of the small-scale forcing has an important influence on the dynamical evolution of turbulence. Our results pave the way towards a deeper understanding on the fundamental role of degrees of freedom in the dynamics of fluid dynamics turbulence as well as on the statistics vs. coherent structure duality.