  We consider a rotating neutron star with the presence of hyperons in its
core, using an equation of state in an effective chiral model within the
relativistic mean field approximation. We calculate the hyperonic bulk
viscosity coefficient due to nonleptonic weak interactions. By estimating the
damping timescales of the dissipative processes, we investigate its role in the
suppression of gravitationally driven instabilities in the $r$-mode. We observe
that $r$-mode instability remains very much significant for hyperon core
temperature of around $10^8 $K, resulting in a comparatively larger instability
window. We find that such instability can reduce the angular velocity of the
rapidly rotating star considerably upto $\sim0.04 \Omega_K$, with $\Omega_K$ as
the Keplerian angular velocity.
