  We study how fluctuations in fluid dynamic fields can be dissipated or
amplified within the characteristic spatio-temporal structure of a heavy ion
collision. The initial conditions for a fluid dynamic evolution of heavy ion
collisions may contain significant fluctuations in all fluid dynamical fields,
including the velocity field and its vorticity components. We formulate and
analyze the theory of local fluctuations around average fluid fields described
by Bjorken's model. For conditions of laminar flow, when a linearized treatment
of the dynamic evolution applies, we discuss explicitly how fluctuations of
large wave number get dissipated while modes of sufficiently long wave-length
pass almost unattenuated or can even be amplified. In the opposite case of
large Reynold's numbers (which is inverse to viscosity), we establish that
(after suitable coordinate transformations) the dynamics is governed by an
evolution equation of non-relativistic Navier-Stokes type that becomes
essentially two-dimensional at late times. One can then use the theory of
Kolmogorov and Kraichnan for an explicit characterization of turbulent
phenomena in terms of the wave-mode dependence of correlations of fluid dynamic
fields. We note in particular that fluid dynamic correlations introduce
characteristic power-law dependences in two-particle correlation functions.
