  We derive the evolution equation of the average uncertainty energy for
periodic/homogeneous incompressible Navier-Stokes turbulence and show that
uncertainty is increased by strain rate compression and decreased by strain
rate stretching. We use three different direct numerical simulations (DNS) of
non-decaying periodic turbulence and identify a similarity regime where (a) the
production and dissipation rates of uncertainty grow together in time, (b) the
parts of the uncertainty production rate accountable to average strain rate
properties on the one hand and fluctuating strain rate properties on the other
also grow together in time, (c) the average uncertainty energies along the
three different strain rate principal axes remain constant as a ratio of the
total average uncertainty energy, (d) the uncertainty energy spectrum's
evolution is self-similar if normalised by the uncertainty's average
uncertainty energy and characteristic length and (e) the uncertainty production
rate is extremely intermittent and skewed towards extreme compression events
even though the most likely uncertainty production rate is zero. Properties
(a), (b) and (c) imply that the average uncertainty energy grows exponentially
in this similarity time range. The Lyapunov exponent depends on both the
Kolmogorov time scale and the smallest Eulerian time scale, indicating a
dependence on random large-scale sweeping of dissipative eddies. In the two DNS
cases of statistically stationary turbulence, this exponential growth is
followed by an exponential of exponential growth, which is in turn followed by
a linear growth in the one DNS case where the Navier-Stokes forcing also
produces uncertainty.
