Symmetry breaking of decaying magnetohydrodynamic Taylor-Green flows and consequences for universality

Abstract

We investigate the evolution and stability of a decaying magnetohydrodynamic Taylor-Green flow, using pseudospectral simulations with resolutions up to 2048(3). The chosen flow has been shown to result in a steep total energy spectrum with power law behavior k(-2). We study the symmetry breaking of this flow by exciting perturbations of different amplitudes. It is shown that for any finite amplitude perturbation there is a high enough Reynolds number for which the perturbation will grow enough at the peak of dissipation rate resulting in a nonlinear feedback into the flow and subsequently break the Taylor-Green symmetries. In particular, we show that symmetry breaking at large scales occurs if the amplitude of the perturbation is σ(crit)∼Re(-1) and at small scales occurs if σ(crit)∼Re(-3/2). This symmetry breaking modifies the scaling laws of the energy spectra at the peak of dissipation rate away from the k(-2) scaling and towards the classical k(-5/3) and k(-3/2) power laws.