2005/08/31 by J. Pietarila Graham, Jonathan Pietarila Graham, D. D. Holm +4 · 3 citations
Earth and Planetary Sciences · Engineering · Environmental Science · Physics and Astronomy · #Climate variability and models #Fluid Dynamics and Turbulent Flows #Meteorological Phenomena and Simulations #astro-ph #nlin.CD #physics.flu-dyn #physics.plasm-ph
paper · pdf · doi:10.1063/1.2194966
published as Phys.Fluids 18 (2006) 045106 · 34 pages, 7 figures author institution addresses added magnetic Prandtl number stated clearly
openalex publication_date 2006/04/01 · arxiv created 2006/04/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We present an extension of the Kármán-Howarth theorem to the Lagrangian averaged magnetohydrodynamic (LAMHD-α) 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 magnetohydrodynamic (MHD) turbulence, solving the MHD equations directly, and employing the LAMHD-α equations at 1∕2 and 1∕4 resolution. Linear scaling of the third-order structure function with length is observed. The LAMHD-α equations also capture the anomalous scaling of the longitudinal structure function exponents up to order 8.