Nonuniversality and finite dissipation in decaying magnetohydrodynamic turbulence

Abstract

A model equation for the Reynolds number dependence of the dimensionless dissipation rate in freely decaying homogeneous magnetohydrodynamic turbulence in the absence of a mean magnetic field is derived from the real-space energy balance equation, leading to $C_{\varepsilon}=C_{\varepsilon, \infty}+C/R_- +O(1/R_-^2))$, where $R_-$ is a generalized Reynolds number. The constant $C_{\varepsilon, \infty}$ describes the total energy transfer flux. This flux depends on magnetic and cross helicities, because these affect the nonlinear transfer of energy, suggesting that the value of $C_{\varepsilon,\infty}$ is not universal. Direct numerical simulations were conducted on up to $2048^3$ grid points, showing good agreement between data and the model. The model suggests that the magnitude of cosmological-scale magnetic fields is controlled by the values of the vector field correlations. The ideas introduced here can be used to derive similar model equations for other turbulent systems.