Inertial-subrange structures of isotropic incompressible magnetohydrodynamic turbulence in the Lagrangian renormalized approximation

Abstract

The structures of isotropic incompressible magnetohydrodynamic (MHD) turbulence in the inertial subrange are studied within the Lagrangian renormalized approximation (LRA). It is confirmed that LRA derives the total energy spectrum which is consistent with the Iroshnikov-Kraichnan (IK) spectrum. The residual energy spectrum in LRA is found to obey k−2 scaling law, where k is the wave number. Given are the quantitative estimates of (i) the dimensionless constants in the total and residual energy spectra, (ii) contribution of triad interactions to the energy flux, and (iii) the eddy viscosity and the eddy magnetic diffusivity. A direct numerical simulation (DNS) of a forced quasi-isotropic incompressible MHD turbulence is performed to find that the obtained total energy spectrum is in good agreement with the one derived within LRA both in its scaling exponent and in the dimensionless constant. The residual energy spectrum obtained in the DNS agrees with that derived in LRA with respect to the scaling exponent and the sign of the dimensionless constant, which is negative, although the magnitude of the dimensionless constant is about four times larger.