A zero-mode mechanism for spontaneous symmetry breaking in a turbulent von Kármán flow

We suggest that the dynamical spontaneous symmetry breaking reported in a turbulent swirling flow at Re = 40 000 by Cortet et al (2010 Phys. Rev. Lett. 105 214501) can be described through a continuous one parameter family transformation (amounting to a phase shift) of steady states. We investigate a possible mechanism of emergence of such spontaneous symmetry breaking in a toy model of out-of-equilibrium systems. We show that the stationary states are solutions of a linear differential equation. For a specific value of the Reynolds number, they are subject to a spontaneous symmetry breaking through a zero-mode mechanism. The associated susceptibility diverges at the transition, in a way similar to what is observed in the experimental turbulent flow. Overall, the susceptibility of the toy model reproduces the features of the experimental results, meaning that the zero-mode mechanism is a good candidate to explain the experimental symmetry breaking.