Dresden 2014 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 37: Fluid Dynamics and Turbulence
DY 37.6: Talk
Thursday, April 3, 2014, 16:15–16:30, ZEU 146
Hierarchy of structure function relations for locally isotropic MHD turbulence — •Jan Friedrich1, Holger Homann2, Tobias Schäfer3, and Rainer Grauer1 — 1Theoretische Physik I, Ruhr-Universität, 44780 Bochum, Germany — 2Laboratoire J.-L. Lagrange, Universite de Nice-Sophia Antipolis, CNRS, France — 3Department of Mathematics, College of Staten Island, CUNY, USA
We investigate the structure of locally isotropic magneto-hydrodynamic (MHD) turbulence by means of exact equations for magnetic and velocity structure functions. To this end we make use of the calculus of isotropic tensors for MHD turbulence introduced by Chandrasekhar [1]. A hierarchy of structure function equations is obtained, beginning with the MHD analagon of Kolmogorov's four- fifths law of hydrodynamics. The influence of the mean-magnetic field is discussed within the context of the Iroshnikov-Kraichnan phenomenology [2], [3]. The next order equation relates the third- and fourth-order structure functions and is the first order which provides a direct dependence between the longitudinal and the transverse structure functions based on the dynamics. At this order, we have to deal for the first time with pressure contributions. The influence of the additional magnetic pressure is discussed in comparison to the hydrodynamic case and the obtained relations are checked by direct numerical simulations of three-dimensional MHD turbulence.
[1] S. Chandrasekhar, Proc. R. Soc. Lond. A, 204, 1079 (1951)
[2] P.S. Iroshnikov, Sov. Astron. 7, 566-71 (1964)
[3] R.H. Kraichnan, Phys. Fluids 8, 1385-7 (1965)