The role of chaotic orbits in the determination of power spectra passive scalars

This paper relates properties of the power spectrum of a passive scalar convected by a chaotic fluid flow to the distribution of finite lime Lyapunov exponents. The properties considered include the early Lime evolution of the power spectrum, the late time exponential decay of the scalar variance, and the wave number dependence or the power spectrum in the presence of a source of scalar variance. Theoretical predictions are tested by comparing full numerical solutions of the relevant partial differential equation to solutions of a model system which includes diffusion and involves integrations along the fluid orbits only. The model system is shown to give results in close agreement with the numerical solution of the full problem. This suggests the possible general utility of the model equations for a broad range of problems involving passive scalar convection. (C) 1996 American Institute of Physics.