title: Examination of the four-fifths law for longitudinal third-order moments in incompressible magnetohydrodynamic turbulence in a periodic box.
abstract: The four-fifths law for third-order longitudinal moments is examined, using direct numerical simulation (DNS) data on three-dimensional (3D) forced incompressible magnetohydrodynamic (MHD) turbulence without a uniformly imposed magnetic field in a periodic box. The magnetic Prandtl number is set to one, and the number of grid points is 512(3). A generalized Kármán-Howarth-Kolmogorov equation for second-order velocity moments in isotropic MHD turbulence is extended to anisotropic MHD turbulence by means of a spherical average over the direction of r. Here, r is a separation vector. The viscous, forcing, anisotropic and nonstationary terms in the generalized equation are quantified. It is found that the influence of the anisotropic terms on the four-fifths law is negligible at small scales, compared to that of the viscous term. However, the influence of the directional anisotropy, which is measured by the departure of the third-order moments in a particular direction of r from the spherically averaged ones, on the four-fifths law is suggested to be substantial, at least in the case studied here.
authors.affiliation: Department of Computational Science and Engineering, Nagoya University, Nagoya, 464-8603, Japan. yosimatu@fluid.cse.nagoya-u.ac.jp
authors.forename: Katsunori
authors.initials: K
authors.lastname: Yoshimatsu
mesh_terms: D019245:Compressive Strength; D003198:Computer Simulation; D057446:Hydrodynamics; D060526:Magnetic Fields; D008962:Models, Theoretical; D012212:Rheology / Q000379:methods*