Lagrangian chaos and the effect of drag on the enstrophy cascade in two-dimensional turbulence

We investigate the effect of drag force on the enstrophy cascade of two-dim ensional Navier-Stokes turbulence. We find a power law decrease of the ener gy wave number (k) spectrum that is faster than the classical (no-drag) pre diction of k(-3). It is shown that the enstrophy cascade with drag can he a nalyzed by making use of a previous theory for finite lifetime passive scal ars advected by a Lagrangian chaotic fluid flow. Using this we relate the p ower law exponent of the energy wave number spectrum to the distribution of finite time Lyapunov exponents and the drag coefficient.