Inertial Range Scaling, Karman-Howarth Theorem and Intermittency for Forced and Decaying Lagrangian Averaged MHD in 2D

Abstract

We present an extension of the Karman-Howarth theorem to the Lagrangian averaged magnetohydrodynamic (LAMHD-alpha) equations. The scaling laws resulting as a corollary of this theorem are studied in numerical simulations, as well as the scaling of the longitudinal structure function exponents indicative of intermittency. Numerical simulations for a magnetic Prandtl number equal to unity are presented both for freely decaying and for forced two dimensional MHD turbulence, solving directly the MHD equations, and employing the LAMHD-alpha equations at 1/2 and 1/4 resolution. Linear scaling of the third-order structure function with length is observed. The LAMHD-alpha equations also capture the anomalous scaling of the longitudinal structure function exponents up to order 8.

34 pages, 7 figures author institution addresses added magnetic Prandtl number stated clearly

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• Exact scaling laws for helical three-dimensional two-fluid turbulent plasmas
• The Lagrangian-averaged model for magnetohydrodynamics turbulence and the absence of bottleneck
• High Reynolds number magnetohydrodynamic turbulence using a Lagrangian model
• Lagrangian analysis of alignment dynamics for isentropic compressible magnetohydrodynamics
• The effect of subfilter-scale physics on regularization models
• Modeling of anisotropic turbulent flows with either magnetic fields or imposed rotation
• The role of field correlations on turbulent dissipation
• A Characteristic Mapping Method with Source Terms: Applications to Ideal Magnetohydrodynamics