  We study the implications of translation invariance on the tangent dynamics
of extended dynamical systems, within a random matrix approximation. In a model
system, we show the existence of hydrodynamic modes in the slowly growing part
of the Lyapunov spectrum, which are analogous to the hydrodynamic modes
discovered numerically by [Dellago, Ch., Posch, H.A., Hoover, W.G., Phys. Rev.
E 53, 1485 (1996)]. The hydrodynamic Lyapunov vectors loose the typical random
structure and exhibit instead the structure of weakly perturbed coherent long
wavelength waves. We show further that the amplitude of the perturbations
vanishes in the thermodynamic limit, and that the associated Lyapunov exponents
are universal.
