  Using a multi-scaled, chaotic flow known as the KS model of turbulence, we
investigate the dependence of Lyapunov exponents on various characteristics of
the flow. We show that the KS model yields a power law relation between the
Reynolds number and the maximum Lyapunov exponent, which is similar to that for
a turbulent flow with the same energy spectrum. Our results show that the
Lyapunov exponents are sensitive to the advection of small eddies by large
eddies, which can be explained by considering the Lagrangian correlation time
of the smallest scales. We also relate the number of stagnation points within a
flow to the maximum Lyapunov exponent, and suggest a linear dependence between
the two characteristics.
