[MIS27-P04] Shallow water MHD waves trapped in the polar regions on a rotating sphere with an imposed azimuthal magnetic field
Keywords:MHD shallow water, toroidal magnetic field, polar trapped waves, slow magnetic Rossby waves, polar kink instability
Comprehensive searches for eigenmodes yield two polar trapped modes when the main magnetic field is weak (the Lehnert number α=VA/2ΩR2<0.5, where VA is the Alfvén wave velocity, Ω is the rotation rate and R is the sphere radius). One is the slow magnetic Rossby waves, which propagate eastward for zonal wave number m≧2 (Márquez-Artavia et al., 2017). As the Lamb's parameter ε=4Ω2R2/gh→0 (where g is the gravity acceleration and h is the equivalent depth), these branches asymptotically approach the eigenvalues of two-dimensional slow magnetic Rossby waves. Another is newly discovered westward polar trapped modes (Nakashima, Ph.D. thesis, 2020).
In the case when α>0.5 (the background field is strong), these novel westward modes merge with the westward-propagating fast magnetic Rossby waves. In addition, only when m=1, polar trapped unstable modes appear due to the interaction between these fast magnetic Rossby waves and westward-propagating slow magnetic Rossby waves. These growth modes are believed to be the polar kink (Tayler) instability (Márquez-Artavia et al., 2017).
In order to easily understand the propagation mechanisms and the force balances of polar trapped modes, we investigate a cylindrical model around a pole with an artificial boundary condition. This model provides the approximate dispersion relations and eigenfunctions of polar trapped modes, and indicates that stable polar trapped modes are governed by magnetostrophic balance and that the metric magnetic tension force causes the difference between the slow magnetic Rossby waves and the novel westward modes. For m=1 and α>0.5, the balance between Coriolis and Lorentz forces is disrupted and the part of magnetic tension with which Coriolis force can not compete induces kink instability.
[ Reference ]
 Gilman, P. A., Dikpati, M. (2002) Astrophys. J., 576, 1031. doi: 10.1086/341799
 Márquez-Artavia, X., Jones, C. A., Tobias, S. M. (2017) Geophys. Astrophys. Fluid Dyn., 111, 282. doi: 10.1080/03091929.2017.1301937
 Nakashima, R. (2020) Ph.D. thesis, Kyushu University. http://dyna.geo.kyushu-u.ac.jp/HomePage/nakashima/pdf/doctoral_thesis.pdf
 Heng, K., Workman, J. (2014) Astrophys. J. Sup., 213, 27. doi: 10.1088/0067-0049/213/2/27