  We numerically study the dynamics of two-dimensional blue phases in active
chiral liquid crystals. We show that introducing contractile activity results
in stabilised blue phases, while small extensile activity generates ordered but
dynamic blue phases characterised by coherently moving half-skyrmions and
disclinations. Increasing extensile activity above a threshold leads to the
dissociation of the half-skyrmions and active turbulence. We further analyse
isolated active half-skyrmions in an isotropic background and compare the
activity-induced velocity fields in simulations to an analytical prediction of
the flow. Finally, we show that confining an active blue phase can give rise to
a system-wide circulation, in which half-skyrmions and disclinations rotate
together.
