k Spectrum of Finite Lifetime Passive Scalars in Lagrangian Chaotic Fluid Flows

The power law exponent for the wave number power spectrum of a passive scalar field in Lagrangian chaotic flows is found to differ from the classical value of −1 (Batchelor's law) when the passive particles have a finite lifetime for exponential decay. A theory based on the chaotic dynamics of the passive scalar is developed and compared to numerical simulation results.