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Y. Chen, F. K. Lamb, D. Markovic (U. Illinois)
Rezzolla, Lamb, & Shapiro (2000) showed that magnetic fields can affect the structure and stability of r (Rossby) waves in rotating magnetic stars. Magnetic fields generally also introduce new, hybrid waves, which we call Alfvén-Rossby waves. We study the evolution of these hybrid waves in a thin, uniformly rotating spherical shell of magnetized fluid. We derive the governing equations and compute for the first time the mode functions and frequencies of purely Alfvénic and Alfvén-Rossby waves in a variety of background magnetic fields. The Alfvén-Rossby dispersion relation has two branches, one corresponding to magnetically-modified Rossby waves and the other to rotationally-modified Alfvén waves. We show that certain Alfvén-Rossby waves are exact solutions of the fully nonlinear MHD equations. These solutions can be expressed in closed analytical form.
We also study weakly nonlinear interactions between the Alfvén-Rossby waves using a spherical harmonic representation of the waves. In this representation, the interaction between modes is described by the coupling coefficients between different spherical harmonics, which can be computed analytically. Using these coefficients, we recast the relevant system of nonlinear partial differential equations into a system of coupled, first-order ordinary differential equations. Solving this system numerically offers advantages in speed, accuracy, and stability compared to previous methods. A typical disturbance excites a quasi-periodic oscillation with a period comparable to the time for an Alfvén wave to cross the system. The kinematic drift induced by the disturbance secularly distorts the magnetic field of the system. The resulting magnetic tension eventually reverses the original drift, creating a very-long-period oscillation. A simple model that includes a dozen or so of the lowest-order Alfvén-Rossby modes reproduces the velocity field and frequency of this oscillation.
This work was supported in part by NSF grant AST 0098399, NASA grant NAG5-12030, and funds of the Fortner Endowed Chair at Illinois.
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Bulletin of the American Astronomical Society, 37 #4
© 2005. The American Astronomical Soceity.