Self-sustained patchy turbulence in shear-thinning active fluids

Bacterial suspensions and other active fluids are known to develop highly dynamical vortex states, denoted as active or mesoscale turbulence. We reveal the pronounced effect of non-Newtonian rheological conditions on these turbulent states, concentrating on shear thinning. A self-sustained heterogeneous state of coexisting turbulent and quiescent areas develops, which results in anomalous velocity statistics. The heterogeneous state emerges in a hysteretic transition when varying activity. We provide an extensive numerical analysis and observe features consistent with a directed percolation transition. Our results are important, for instance, when addressing active objects in biological media with complex rheological properties.