Hydrodynamics of Dense Active Fluids: Turbulence-Like States and the Role of Advected Activity
Dense suspensions of self-propelled bacteria and related active fluids exhibit spontaneous flow generation, vortex formation, and spatiotemporally chaotic dynamics despite operating at vanishingly small Reynolds numbers. These phenomena, commonly referred to as active turbulence, display striking visual and statistical similarities to classical inertial turbulence while arising from fundamentally different nonequilibrium mechanisms. In this article, we present a combined review and theoretical study of hydrodynamic models for dense active fluids, with particular emphasis on bacterial suspensions described by the Toner--Tu--Swift--Hohenberg (TTSH) framework. We review key experimental and theoretical developments underlying the analogy between active and inertial turbulence, highlighting the emergence of multiple dynamical regimes and the conditions under which universal spectral and intermittent behavior arises in homogeneous systems. Moving beyond the conventional assumption of spatially uniform activity, we introduce a minimal model in which the activity field is heterogeneous and dynamically advected by the flow it generates. Thus treating activity as a spatiotemporally evolving field coupled to the TTSH dynamics, we investigate how advection and diffusion lead to sharp activity fronts, confinement of turbulent motion, and complex interfacial morphologies. Our numerical results demonstrate that spatial variations in activity can induce transient coexistence of distinct spectral regimes and that universality in active turbulence is inherently local and time-dependent in heterogeneous systems. These findings underscore the importance of treating activity as a dynamical field in its own right and provide a framework for studying active turbulence in more realistic, spatially structured biological and synthetic active matter systems.