Cascade or not cascade? Energy transfer and elastic effects in active nematics

Abstract: We numerically study the multi-scale properties of a 2d active gel to address the energy transfer mechanism. We find that activity is able to excite long-ranged distortions of the nematic pattern giving rise to spontaneous laminar flows and to a chaotic regime by further increasing the rate of active energy injection. By means of a scale-to-scale spectral analysis we find that the gel is basically driven by the local balancing between active injection and viscous dissipation, without any signal of non-linear hydrodynamical transfer and turbulent cascades. Furthermore, elasticity may qualitatively play an important role by transferring energy from small to larger scales through nemato-hydrodynamic interactions.