Spectral energy analysis of bulk three-dimensional active nematic turbulence

Abstract

We perform energy spectrum analysis of the active turbulence in a 3D bulk active nematic using continuum numerical modelling. Specifically, we calculate the spectra of the two main energy contributions – kinetic energy and nematic elastic energy – and combine this with the geometrical analysis of the nematic order and flow fields, based on direct defect tracking and calculation of autocorrelations. We show that the active nematic elastic energy is concentrated at scales corresponding to the effective defect-to-defect separation, scaling with activity as ∼ζ^0.5, whereas the kinetic energy is largest at somewhat larger scales of typically several 100 nematic correlation lengths. Nematic biaxiality is shown to have no role in active turbulence at most length scales, but can affect the nematic elastic energy by an order of magnitude at scales of the active defect core size. The effect of an external aligning field on the 3D active turbulence is explored, showing a transition from an effective active turbulent to an aligned regime. The work is aimed at providing a contribution towards understanding active turbulence in general three-dimensions, from the perspective of main energy-relevant mechanisms at different length scales of the system.