This paper relates properties of the power spectrum of a passive scala
r convected by a chaotic fluid flow to the distribution of finite lime
Lyapunov exponents. The properties considered include tile early Lime
evolution of the power spectrum, the late time exponential decay of t
he scalar variance, and the wave number dependence or the power spectr
um in the presence of a source of scalar variance. Theoretical predict
ions are tested by comparing full numerical solutions of the relevant
partial differential equation to solutions of a model system which inc
ludes 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 ge
neral utility of the model equations for a broad range of problems inv
olving passive scalar convection. (C) 1996 American Institute of Physi
cs.