Lagrangian Chaos and the Effect of Drag on the Enstrophy Cascade in Two-Dimensional Turbulence

Abstract

We investigate the effect of drag force on the enstrophy cascade of two-dimensional Navier-Stokes turbulence. We find a power law decrease of the energy wave number $\left(k\right)$ spectrum that is faster than the classical (no-drag) prediction of $k^{-3\mathrm{}}$. It is shown that the enstrophy cascade with drag can be analyzed by making use of a previous theory for finite lifetime passive scalars advected by a Lagrangian chaotic fluid flow. Using this we relate the power law exponent of the energy wave number spectrum to the distribution of finite time Lyapunov exponents and the drag coefficient.