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We perform energy spectrum analysis of the active turbulence in 3D bulkactive nematic using continuum numerical modelling. Specifically, we calculatethe spectra of two main energy contributions---kinetic energy and nematicelastic energy---and combine this with the geometrical analysis of the nematicorder and flow fields, based on direct defect tracking and calculation ofautocorrelations. We show that the active nematic elastic energy isconcentrated at scales corresponding to the effective defect-to-defectseparation, scaling with activity as $\sim\zeta^{0.5}$, whereas the kineticenergy is largest at somewhat larger scales of typically several 100 nematiccorrelation lengths. Nematic biaxiallity is shown to have no role in activeturbulence at most of length scales, but can affect the nematic elastic energyby an order of magnitude at scales of active defect core size. The effect of anexternal aligning field on the 3D active turbulence is explored, showing atransition from an effective active turbulent to an aligned regime. The work isaimed to provide a contribution towards understanding active turbulence ingeneral three-dimensions, from the perspective of main energy-relevantmechanisms at different length scales of the system.

Spectral energy analysis of bulk three-dimensional active nematic turbulence