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 $C_{\epsilon }=C_{\epsilon ,\infty }+C/R_{-}+O(1/R_{-}^2))$, where $R_{-}$ is a generalized Reynolds number. The constant $C_{\epsilon ,\infty }$ 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 $C_{\epsilon ,\infty }$ 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.

arXiv comment5 pages, 1 figure, plus 4 pages and 4 figures of Supplemental Material. Accepted for publication in Physical Review Letters

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Cited by in corpus (16)

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• Bounded solutions of ideal MHD with compact support in space-time
• Proof of Taylor's conjecture on magnetic helicity conservation
• Reynolds Number and Intermittency in the Expanding Solar Wind: Predictions Based on Voyager Observations
• A local approach to the study of energy transfers in incompressible magnetohydrodynamic turbulence
• Reynolds-number dependence of the dimensionless dissipation rate in homogeneous magnetohydrodynamic turbulence
• Onset criteria for freely decaying isotropic turbulence
• Evolution of similarity lengths in anisotropic magnetohydrodynamic turbulence
• Superhorizon magnetic fields
• Comparison of forcing functions in magnetohydrodynamic turbulence
• The dimensionless dissipation rate and the Kolmogorov (1941) hypothesis of local stationarity in freely decaying isotropic turbulence
• Smooth magnetogenesis
• On the scaling and anisotropy of two subranges in the inertial range of solar wind turbulence
• Finite Dissipation in Anisotropic Magnetohydrodynamic Turbulence
• Does intermittency affect the inertial transfer rate in stationary isotropic turbulence?