Self-sustained patchy turbulence in shear-thinning active fluids

Bacterial suspensions and other active fluids can develop highly dynamical vortex states called mesoscale turbulence. Here, we reveal the pronounced effect of non-Newtonian rheology of the carrier fluid, concentrating on shear thinning. Remarkably, this leads to hysteretic emergence of the turbulent state as a function of activity. A self-sustained heterogeneous state of coexisting turbulent and quiescent areas is identified. We find the signature of a directed percolation transition. Our results are important, for instance, when addressing active objects in biological media.