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.

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

References in corpus (8)

• Observation of inertial energy cascade in interplanetary space plasma
• Nonhelical inverse transfer of a decaying turbulent magnetic field
• The Spectral Slope and Kolmogorov Constant of MHD turbulence
• Thermodynamic ground states of platinum metal nitrides
• Inverse cascade of non-helical magnetic turbulence in a relativistic fluid
• Energy transfer and dissipation in forced isotropic turbulence
• Spectral analysis of structure functions and their scaling exponents in forced isotropic turbulence
• Magnetic helicity and the evolution of decaying magnetohydrodynamic turbulence

Cited by in corpus (3)

• Enhanced Energy Transfer Rate in Solar Wind Turbulence Observed near the Sun from Parker Solar Probe
• Reynolds-number dependence of the dimensionless dissipation rate in homogeneous magnetohydrodynamic turbulence
• Smooth magnetogenesis