  Motion of an ultra-relativistic perfect fluid in space-time with the Kasner
metrics is investigated by the Hamiltonian method. It is found that in the
limit of small times a tendency takes place to formation of strong
inhomogeneities in matter distribution. In the case of slow flows the effect of
non-stationary anisotropy on dynamics of sound waves and behaviour of frozen-in
vortices is considered. It is shown that hydrodynamics of slow vortices on the
static homogeneous background is equivalent to the usual Eulerian
incompressible hydrodynamics, but in the presence of an external non-stationary
strain velocity field.
