  In order to better understand deviations from equilibrium in turbulent flows,
it is meaningful to characterize the dynamics rather than the statistics of
turbulence. To this end, the Lyapunov theory provides a useful description of
turbulence through the study of the perturbation dynamics. In this work, the
Lyapunov spectrum of forced homogeneous isotropic turbulent flows is computed.
Using the Lyapunov exponents of a flow at different Reynolds numbers, the
scaling of the dimension of the chaotic attractor for a three-dimensional
homogeneous isotropic flow (HIT) is obtained for the first time through direct
computation. The obtained Gram-Schmidt vectors (GSV) are analyzed. For the
range of conditions studied, it was found that the chaotic response of the flow
coincides with regions of large velocity gradients at lower Reynolds numbers
and enstrophy at higher Reynolds numbers, but does not coincide with regions of
large kinetic energy. Further, the response of the flow to perturbations is
more and more localized as the Reynolds number increases. Finally, the energy
spectrum of the GSV is computed and is shown to be almost insensitive to the
Lyapunov index.
