  Motivated by the existence of unstable modes of compact stars that eventually
grow large, we study the bulk viscosity of dense matter, taking into account
non-linear effects arising in the large amplitude regime, where the deviation
mu_Delta of the chemical potentials from chemical equilibrium fulfills mu_Delta
> T. We find that this supra-thermal bulk viscosity can provide a potential
mechanism for saturating unstable modes in compact stars since the viscosity is
strongly enhanced. Our study confirms previous results on strange quark matter
and shows that the suprathermal enhancement is even stronger in the case of
hadronic matter. We also comment on the competition of different weak channels
and the presence of suprathermal effects in various color superconducting
phases of dense quark matter.
