Summary

In this chapter we have analyzed the effects of linear friction on the enstrophy cascade in two-dimensional turbulence.

By means of theoretical arguments based on the Lagrangian description of fluid transport we have shown the analogy between the non-linear problem described by two-dimensional Navier-Stokes with friction and the linear one described by the advection-diffusion-reaction equation of a passive scalar with finite lifetime.

This analogy has allowed to obtain quantitative predictions for the steepening of the enstrophy spectrum and the intermittency of the small scale statistics, which have been tested by means of numerical simulations.

We have shown that intermittency arises from the competition between exponential separation of Lagrangian trajectories and exponential decay of fluctuations due to friction, and can be predicted in terms of exit-times statistics.

Table 2.1: Parameters of numerical simulations

$N$	$\nu$	$k_f$
512	$\nu =5 \cdot 10^{-5}$	2
1024	$\nu = 1.5 \cdot 10^{-5}$	8
2048	$\nu=5 \cdot 10^{-6}$	2