日本地球惑星科学連合2019年大会

講演情報

[J] ポスター発表

セッション記号 M (領域外・複数領域) » M-IS ジョイント

[M-IS18] 地球流体力学:地球惑星現象への分野横断的アプローチ

2019年5月27日(月) 17:15 〜 18:30 ポスター会場 (幕張メッセ国際展示場 8ホール)

コンビーナ:伊賀 啓太(東京大学大気海洋研究所)、吉田 茂生(九州大学大学院理学研究院地球惑星科学部門)、柳澤 孝寿(海洋研究開発機構 地球深部ダイナミクス研究分野)、相木 秀則(名古屋大学)

[MIS18-P06] Two-dimensional or shallow water MHD waves on a rotating sphere with an imposed azimuthal magnetic field

*中島 涼輔1吉田 茂生2 (1.九州大学 大学院理学府 地球惑星科学専攻、2.九州大学 大学院理学研究院 地球惑星科学部門)

キーワード:MHD波動、MHD浅水波、トロイダル磁場、連続固有値、地球外核最上部安定成層

Magnetohydrodynamic (MHD) waves in a thin layer on a rotating sphere with an imposed toroidal magnetic field are investigated. The system is often considered as a model of the stably stratified outermost Earth's outer core or the tachocline of the Sun. The stratification of the outermost core is suggested on the basis of seismological evidence (e.g. Helffrich and Kaneshima, 2010; Kaneshima, 2018) and interpretations of the geomagnetic variations with MHD waves (e.g. Braginsky, 1993; Buffett, 2014; Chulliat et al., 2015). In order to provide constraints on the obscure stratified layer by comparing with wavy variations in the geomagnetic field, we studied the linear waves of the two-dimensional MHD and the MHD shallow water system over a rotating sphere.

We adopt an azimuthal equatorially antisymmetric field (BΦ(θ) = B0 sinθcosθ, where θ is colatitude, Φ is azimuth) as a background magnetic field. On the other hand, an equatorially symmetric field (BΦ(θ) = B0 sinθ) was assumed in Márquez-Artavia et al.(2017), whose results we replicated and reported in JpGU 2018.

Compared with previous results, the dispersion diagrams obtained with the toroidal equatorially antisymmetric field show that some fast magnetic Rossby branches remain, while slow magnetic Rossby waves disappear. Besides, a continuous spectrum is found in the range where an azimuthal phase velocity is coincident with a local Alfvén velocity divided by sinθ. Similar continuous spectra are also seen in various physical situations, including inviscid shear flow (e.g. Case, 1960; Balmforth and Morrison, 1995; Iga, 2013) and plasma oscillations (e.g. Van Kampen, 1955; Case, 1959; Barston, 1964; Sedláček, 1971). The continuous spectra are accompanied by a singular eigenfunction, which is physically meaningful only when they are integrated over the continuous spectra. Its integrated solutions generally decay with time, which is referred to as phase mixing. Unlike exponentially damped discrete modes, this decaying is proportional to negative powers of time.

In the case of the shallow water system with the antisymmetric field, discrete eigenvalues buried in the continuous spectrum is found, which include unstable modes. For the Earth-like parameters, polar trapped modes with decadal period and equatorial trapped Rossby waves with a few years period are found when the stratification is weak.