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 Cϵ=Cϵ,∞+C/R-+O(1/R-(2)), where R- is a generalized Reynolds number. The constant Cϵ,∞ 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 Cϵ,∞ 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.
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