Nonlinear Rossby-Alfvén Global Waves on the Surface of a Rotating Sphere
We consider two-dimensional nonlinear magnetohydrodynamic (MHD) waves of global scale for a thin magnetofluid layer on the surface of a rotating sphere. The fluid motions are assumed to be incompressible and the radial dimension is assumed to be in magnetohydrostatic balance. We are interested in a parameter regime in which horizontal spatial scales of wave motions, rotation rate of the background atmosphere, and the background zonal magnetic field strength are such that Rossby and Alfvén wave speeds are comparable. We obtain two kinds of finite-amplitude MHD waves propagating in the azimuthal directions relative to the uniformly rotating background atmosphere in the presence of a background zonal magnetic field and a steady differential zonal flow. These two kinds of nonlinear MHD waves are fundamentally due to the joint effects of uniform rotation of the background atmosphere and the background zonal magnetic field; the first is an inertial wave of the Rossby-Haurwitz type, modified by the presence of background zonal magnetic field, while the second is a magnetic Alfvén-like wave which is modified by the uniform rotation of background atmosphere. We discuss possible applications of these results in the context of geophysical and astrophysical systems.
KeywordsRossby Wave Alfven Wave Uniform Rotation Free Function Background Atmosphere
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