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Title: Large-scale quasi-geostrophic magnetohydrodynamics

Abstract

We consider the ideal magnetohydrodynamics (MHD) of a shallow fluid layer on a rapidly rotating planet or star. The presence of a background toroidal magnetic field is assumed, and the 'shallow water' beta-plane approximation is used. We derive a single equation for the slow large length scale dynamics. The range of validity of this equation fits the MHD of the lighter fluid at the top of Earth's outer core. The form of this equation is similar to the quasi-geostrophic (Q-G) equation (for usual ocean or atmosphere), but the parameters are essentially different. Our equation also implies the inverse cascade; but contrary to the usual Q-G situation, the energy cascades to smaller length scales, while the enstrophy cascades to the larger scales. We find the Kolmogorov-type spectrum for the inverse cascade. The spectrum indicates the energy accumulation in larger scales. In addition to the energy and enstrophy, the obtained equation possesses an extra (adiabatic-type) invariant. Its presence implies energy accumulation in the 30° sector around zonal direction. With some special energy input, the extra invariant can lead to the accumulation of energy in zonal magnetic field; this happens if the input of the extra invariant is small, while the energy inputmore » is considerable.« less

Authors:
 [1]
  1. Department of Mathematics, University of Utah, Salt Lake City, UT 84112 (United States)
Publication Date:
OSTI Identifier:
22370126
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal; Journal Volume: 796; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; APPROXIMATIONS; ATMOSPHERES; EQUATIONS; MAGNETIC FIELDS; MAGNETOHYDRODYNAMICS; PLANETS; ROTATION; SPECTRA; STARS; TURBULENCE; WATER

Citation Formats

Balk, Alexander M., E-mail: balk@math.utah.edu. Large-scale quasi-geostrophic magnetohydrodynamics. United States: N. p., 2014. Web. doi:10.1088/0004-637X/796/2/143.
Balk, Alexander M., E-mail: balk@math.utah.edu. Large-scale quasi-geostrophic magnetohydrodynamics. United States. doi:10.1088/0004-637X/796/2/143.
Balk, Alexander M., E-mail: balk@math.utah.edu. 2014. "Large-scale quasi-geostrophic magnetohydrodynamics". United States. doi:10.1088/0004-637X/796/2/143.
@article{osti_22370126,
title = {Large-scale quasi-geostrophic magnetohydrodynamics},
author = {Balk, Alexander M., E-mail: balk@math.utah.edu},
abstractNote = {We consider the ideal magnetohydrodynamics (MHD) of a shallow fluid layer on a rapidly rotating planet or star. The presence of a background toroidal magnetic field is assumed, and the 'shallow water' beta-plane approximation is used. We derive a single equation for the slow large length scale dynamics. The range of validity of this equation fits the MHD of the lighter fluid at the top of Earth's outer core. The form of this equation is similar to the quasi-geostrophic (Q-G) equation (for usual ocean or atmosphere), but the parameters are essentially different. Our equation also implies the inverse cascade; but contrary to the usual Q-G situation, the energy cascades to smaller length scales, while the enstrophy cascades to the larger scales. We find the Kolmogorov-type spectrum for the inverse cascade. The spectrum indicates the energy accumulation in larger scales. In addition to the energy and enstrophy, the obtained equation possesses an extra (adiabatic-type) invariant. Its presence implies energy accumulation in the 30° sector around zonal direction. With some special energy input, the extra invariant can lead to the accumulation of energy in zonal magnetic field; this happens if the input of the extra invariant is small, while the energy input is considerable.},
doi = {10.1088/0004-637X/796/2/143},
journal = {Astrophysical Journal},
number = 2,
volume = 796,
place = {United States},
year = 2014,
month =
}
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