Dynamics and stability of 1D patterns in active polar fluids

Abstract

Turbulence in active fluids has been proposed as a new universality class of turbulence. However, the mechanisms governing these flows are poorly understood. In this work, we study numerically the formation of uni-dimensional patterns in a minimal model for an active polar nematic fluid, for arbitrary values of the ow alignment coeffcient v. In addition, we determine analytically the linear stability of the asymptotic states, as a function v. We describe the complete bifurcation diagram for uniform states in 1D and show the existence of transversal (2D) instabilities, in particular in the so-called flow alignment regime jvj > 1. This result shows that the secondary instabilities leading to turbulence are not specifc of the case v = 0, thus reinforcing the conclusion that active flows constitute a new universality class of turbulence.