Large-scale quasi-geostrophic magnetohydrodynamics

Journal Article · Mon Dec 01 04:00:00 EST 2014 · Astrophysical Journal

DOI:https://doi.org/10.1088/0004-637X/796/2/143· OSTI ID:22370126

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.

• OSTI ID: 22370126
• Journal Information: Astrophysical Journal, Journal Name: Astrophysical Journal Journal Issue: 2 Vol. 796; ISSN ASJOAB; ISSN 0004-637X
• Country of Publication: United States
• Language: English

Related Subjects

79 ASTRONOMY AND ASTROPHYSICS
APPROXIMATIONS
ATMOSPHERES
EQUATIONS
MAGNETIC FIELDS
MAGNETOHYDRODYNAMICS
PLANETS
ROTATION
SPECTRA
STARS
TURBULENCE
WATER