Magnetohydrodynamic Flows: Boussinesq Conjecture
Document Type
Article
Publication Date
2-15-2016
Department
Department of Mathematical Sciences
Abstract
The Boussinesq assumption that turbulent fluctuations have a dissipative effect on the mean flow is the basis for most turbulence models used in practical flow simulations. Data from computational tests and experiments has indicated that in 2d fluid flows an inverse energy cascade is expected. However, the Boussinesq assumption has recently been proven to hold in a time averaged sense for the Navier-Stokes equations. In Magnetohydrodynamic (MHD) flows, the dynamo effect suggests an inverse cascade of energy from small to large scales in both 2d and 3d, suggesting its re-evaluation for MHD flows. This article uses the MHD formulation in the Elsässer variables to show that the Boussinesq assumption also holds for MHD turbulence. A short discussion on the choice of eddy viscosity models is presented, as a consequence of the main result.
Publication Title
Journal of Mathematical Analysis and Applications
Recommended Citation
Labovsky, A.,
&
Layton, W.
(2016).
Magnetohydrodynamic Flows: Boussinesq Conjecture.
Journal of Mathematical Analysis and Applications,
434(2), 1665-1675.
http://doi.org/10.1016/j.jmaa.2015.09.045
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/6745
Publisher's Statement
© 2015 Elsevier Inc.