Magnetohydrodynamic flows: Boussinesq conjecture

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• 作者：Alexander Labovsky^a ; ^{aelabovs@mtu.edu" class="auth_mail" title="E-mail the corresponding author} ; William Layton^b ; ¹ ; ^{wjl@math.pitt.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Boussinesq conjecture ; Eddy viscosity ; Magnetohydrodynamics ; Turbulence
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：15 February 2016
• 年：2016
• 卷：434
• 期：2
• 页码：1665-1675
• 全文大小：309 K

文摘

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.