  Chaotic flow is studied in a series of numerical magnetohydrodynamical
simulations that use the shearing box formalism. This mimics important features
of local accretion disk dynamics. The magnetorotational instability gives rise
to flow turbulence, and quantitative chaos parameters, such as the largest
Lyapunov exponent, can be measured. Linear growth rates appear in these
exponents even when the flow is fully turbulent. The extreme sensitivity to
initial conditions associated with chaotic flows has practical implications,
the most important of which is that hundreds of orbital times are needed to
extract a meaningful average for the stress. If the evolution time in a disk is
less than this, the classical $\alpha$ formalism will break down.
