The effects of finite lifetime of passive scalars and vorticity on their power spectra

The power law exponent for the wavenumber power spectrum of a passive scalar field with finite lifetime in Lagrangian chaotic flows and the enstrophy spectrum of two-dimensional Navier–Stokes turbulence with drag are investigated. The power law exponents are related to the distribution of finite-time Lyapunov exponents and the finite lifetime (or the drag coefficient).