kSpectrum of Passive Scalars in Lagrangian Chaotic Fluid Flows

An eikonal-type description for the evolution of $k$ spectra of passive scalars convected in a Lagrangian chaotic fluid flow is shown to accurately reproduce results from orders of magnitude more time consuming computations based on the full passive scalar partial differential equation. Furthermore, the validity of the reduced description, combined with concepts from chaotic dynamics, allows new theoretical results on passive scalar $k$ spectra to be obtained. Illustrative applications are presented to long-time passive scalar decay, and to Batchelor's law $k$ spectrum and its diffusive cutoff.