Abstract
Abstract The paper considers a dynamo generated by a shallow fluid layer in a celestial body (planet or star). This dynamo is based on the extra invariant for interacting magnetic Rossby waves.
Highlights
Magnetic field of a celestial body often crucially depends on the shallow fluid layer
In the case of Earth, researchers often assume the existence of stably stratified layer at the top of the liquid iron outer core, the stratified ocean of the core in terminology of [3]
We consider magnetohydrodynamics (MHD) of such layer locally in the plane 3D layer tangent to the planet or star. We linearize this dynamics on the background of strong toroidal magnetic field B0 and note the possibility to separate variables for an arbitrary stratification
Summary
Magnetic field of a celestial body often crucially depends on the shallow fluid layer. We consider magnetohydrodynamics (MHD) of such layer locally in the plane 3D layer tangent to the planet or star We linearize this dynamics on the background of strong toroidal magnetic field B0 and note the possibility to separate variables for an arbitrary stratification. We use the adiabatic invariant [4, 5] to show that the energy mainly accumulates in zonal magnetic field, and so, the background field B0 is maintained This extra invariant was found for the usual hydrodynamic Rossby waves and plasma drift waves. Since the dispersion law (1.2b) differs from the well known Rossby dispersion law only by a Doppler shift, the extra invariant holds for the magnetic Rossby waves as well We consider the build-up of magnetic field in the process resembling sunspot activity
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