2006/06/30 by Jasmine S. Linshiz, Edriss S. Titi · 2 citations
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Classical mechanics #Compressibility #Fluid Dynamics and Turbulent Flows #K-epsilon turbulence model #K-omega turbulence model #Magnetic field #Magnetohydrodynamic drive #Magnetohydrodynamic turbulence #Magnetohydrodynamics #Mathematical analysis #Mathematics #Mechanics #Navier-Stokes equation solutions #Navier–Stokes equations #Physics #Turbulence #Turbulence modeling #math.AP #msc:76D03 #msc:76F20 #msc:76F55 #msc:76F65 #msc:76W05
paper · pdf · doi:10.1063/1.2360145
published as J. Math. Phys. 48, 065504 (2007) (28 pages) · 26 pages, no figures, will appear in Journal of Math Physics; corrected typos, updated references
arxiv created 2006/12/01 · openalex publication_date 2007/06/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
In this paper we present an analytical study of a subgrid scale turbulence model of the three-dimensional magnetohydrodynamic (MHD) equations, inspired by the Navier-Stokes-α (also known as the viscous Camassa-Holm equations or the Lagrangian-averaged Navier-Stokes-α model). Specifically, we show the global well-posedness and regularity of solutions of a certain MHD-α model (which is a particular case of the Lagrangian averaged magnetohydrodynamic-α model without enhancing the viscosity for the magnetic field). We also introduce other subgrid scale turbulence models, inspired by the Leray-α and the modified Leray-α models of turbulence. Finally, we discuss the relation of the MHD-α model to the MHD equations by proving a convergence theorem, that is, as the length scale α tends to zero, a subsequence of solutions of the MHD-α equations converges to a certain solution (a Leray-Hopf solution) of the three-dimensional MHD equations.