Large-eddy simulation for decaying magnetohydrodynamic turbulence at low magnetic Reynolds number

Large-eddy simulations have been conducted to investigate the decay law of homogeneous turbulence influenced by a magnetic field within a cubic domain, employing periodic boundary conditions. The initial integral Reynolds number is approximately 1000, while the initial interaction number ranges from 0.1-100. The results reveal that the Joule cone angle, half of the Joule cone, decays as when. In the nonlinear stage, small-scale vortices gradually recover and restore three-dimensionality. Moreover, the corresponding critical state at small scales, marking the transition from quasi-two-dimensional structure to the onset of three-dimensionality, has been quantitatively defined. During the linear stage, based on the true magnetic damping number (, where, and denote the electrical conductivity, magnetic field and the angle between the wavevector and in Fourier space, respectively), Moffatt's decay law, manifests at distinct times and zones in the Fourier space, with signifying turbulent kinetic energy. In the nonlinear stage, for, a slope in the energy power spectrum is prominently observed over an extended period. The near-equivalence of the characteristic time scales of inertial and Lorentz forces in the inertial subrange suggests a quasiequilibrium state between energy transfer and Joule dissipation in Fourier space, thereby corroborating the hypothesis proposed by Alemany et al. 1979 Journal de Mecanique 18(2): 277-313. Additionally, it is observed that pressure mediates energy transfer from horizontal kinetic energy to vertical kinetic energy , accelerating the decay of. Notably, concurrent inverse and direct energy transfers emerge during the decay process. Our analysis reveals that the ratio of the maximum inverse to maximum direct energy flux correlates with the dimensionality of the turbulence, following the scaling law.