Dynamical phases in a model for active fluids

Active fluids such as dense bacterial and microtubule suspensions exhibit interesting dynamical phases, ranging from quasi-turbulence to well-ordered patterns. Motivated by recent attempts at modeling such flows, we study a class of equations which combine elements of pattern formation with an advective nonlinearity. Such a continuum description captures a rich variety of states such as polar phases, vortex lattices and turbulence. We explore its phase space, and investigate the stability as well as the transitions between the phases. In particular, we study the properties of a type of turbulent pattern formation leading to a quasi-stationary hexagonal vortex lattice after a long turbulent transient. Our results provide new insights into the dynamics of active fluids by combining tools from pattern formation and turbulence theory.