  Corrugation instabilities occurring for solutions of the Riemann problem in
relativistic hydrodynamics in which the fluid moves with a non-zero velocity
tangent to the initial discontinuity are studied numerically. We perform
simulations both for ultrarelativistic and perfect gas equations of state. We
focus on a set of problems with moderately relativistic velocities but
exhausting all possible wave patterns of solutions. Perturbations are applied
to the shape of the initial discontinuity. Instabilities that develop are only
restricted to a region around a contact discontinuity. Both shock and
rarefaction waves appear to be stable.
