  We investigate chaos synchronization of small-scale motions in the
three-dimensional turbulent energy cascade, via pseudo-spectral simulations of
the incompressible Navier-Stokes equations. The modes of the turbulent velocity
field below about 20 Kolmogorov dissipation lengths are found to be slaved to
the chaotic dynamics of larger-scale modes. The dynamics of all
dissipation-range modes can be recovered to full numerical precision by solving
small-scale dynamical equations with the given large-scale solution as an
input, regardless of initial condition. The synchronization rate exponent
scales with the Kolmogorov dissipation time-scale, with possible weak
corrections due to intermittency. Our results suggest that all sub-Kolmogorov
length modes should be fully recoverable from numerical simulations with
standard, Kolmogorov-length grid resolutions.
