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Abstract

We study the effects of inertia in dense suspensions of polar swimmers. The hydrodynamic velocity field and the polar order parameter field describe the dynamics of the suspension. We show that a dimensionless parameter R (ratio of the swimmer self-advection speed to the active stress invasion speed [Phys. Rev. X 11, 031063 (2021)]) controls the stability of an ordered swimmer suspension. For R smaller than a threshold R1, perturbations grow at a rate proportional to their wave number q. Beyond R1 we show that the growth rate is O(q2) until a second threshold R=R2 is reached. The suspension is stable for R>R2. We perform direct numerical simulations to characterize the steady-state properties and observe defect turbulence for R<R2. An investigation of the spatial organization of defects unravels a hidden transition: for small R≈0 defects are uniformly distributed and cluster as R→R1. Beyond R1, clustering saturates and defects are arranged in nearly stringlike structures.