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Magnetohydrodynamic flows: Boussinesq conjecture.

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Title: Magnetohydrodynamic flows: Boussinesq conjecture.
Authors: Labovsky, Alexander1 aelabovs@mtu.edu, Layton, William2 wjl@math.pitt.edu
Source: Journal of Mathematical Analysis & Applications. Feb2016, Vol. 434 Issue 2, p1665-1675. 11p.
Subjects: Magnetohydrodynamics, Boussinesq equations, Mathematical models of turbulence, Eddy viscosity, Navier-Stokes equations
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. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Mathematical Analysis & Applications is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Magnetohydrodynamic flows: Boussinesq conjecture.
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  Data: <searchLink fieldCode="AR" term="%22Labovsky%2C+Alexander%22">Labovsky, Alexander</searchLink><relatesTo>1</relatesTo><i> aelabovs@mtu.edu</i><br /><searchLink fieldCode="AR" term="%22Layton%2C+William%22">Layton, William</searchLink><relatesTo>2</relatesTo><i> wjl@math.pitt.edu</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Mathematical+Analysis+%26+Applications%22">Journal of Mathematical Analysis & Applications</searchLink>. Feb2016, Vol. 434 Issue 2, p1665-1675. 11p.
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  Data: <searchLink fieldCode="DE" term="%22Magnetohydrodynamics%22">Magnetohydrodynamics</searchLink><br /><searchLink fieldCode="DE" term="%22Boussinesq+equations%22">Boussinesq equations</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+models+of+turbulence%22">Mathematical models of turbulence</searchLink><br /><searchLink fieldCode="DE" term="%22Eddy+viscosity%22">Eddy viscosity</searchLink><br /><searchLink fieldCode="DE" term="%22Navier-Stokes+equations%22">Navier-Stokes equations</searchLink>
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  Data: 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. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Journal of Mathematical Analysis & Applications is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1016/j.jmaa.2015.09.045
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      – Code: eng
        Text: English
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        PageCount: 11
        StartPage: 1665
    Subjects:
      – SubjectFull: Magnetohydrodynamics
        Type: general
      – SubjectFull: Boussinesq equations
        Type: general
      – SubjectFull: Mathematical models of turbulence
        Type: general
      – SubjectFull: Eddy viscosity
        Type: general
      – SubjectFull: Navier-Stokes equations
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      – TitleFull: Magnetohydrodynamic flows: Boussinesq conjecture.
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              Text: Feb2016
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