Figure 1

Schematic illustration of the geodynamo problem. Three factors, electrically conducting fluids, convection, and rotation, are necessary for the MHD geodynamo. We focus on the effect of rotational speed change.Reuse & Permissions

Figure 2

(a),(b) Time variation of physical values in no LOD variation case. The horizontal axis shows time. The vertical axis shows (a) magnetic energy (red) and convection kinetic energy (blue) in the core. (b) The dipole moment coefficient $a_1^0$ (red) and other higher modes $a_2^0\sim a_{10}^0$ in the expansion of the magnetic field at CMB ($r=r_o$), $B_r(r_o)=\sum _{l\ge 1}\sum _{m=-l}^l{a}_l^m{Y}_l^m$, where $B_r$ is the radial component of the magnetic field and $Y_l^m$ is a spherical harmonic. (c),(d),(e) Time variation in physical values with LOD variation. The horizontal axis shows time. The vertical axis shows (c) magnetic energy (red) and convection kinetic energy (blue) integrated in the core. (d) Magnetic dipole moment coefficient $a_1^0$. (e) Total heat flux at CMB. In (c),(d),(e), clear periodic variations are observed, which are not seen at all in the case without LOD variation. For scaling of values, the unit of energy is ${\rho }_0{v}_0^2{l}_0^3\approx 8.7\times {10}^{18}\mathrm{J}$ and the unit of time is $l_0/v_0\approx 1.1\times {10}^9\mathrm{s}$. The unit of magnetic field intensity is $\sqrt{{\rho }_0{v}_0^2{\mu }_0}\approx 5\times {10}^{-4}\mathrm{T}$, where ${\mu }_0$ is the magnetic permeability. The unit of heat flux is given by the unit of energy and time.Reuse & Permissions

Figure 3

Time variation in the zonal flow. (a) A part of Fig. 2c. Only magnetic energy is shown. (b) The change of $\Omega$ in the same time span. From (c) to (g), the time variation of zonal flow $\overline{v_{\varphi }}$ on a meridional plane is shown. (c) At time $t=7760$; (d) $t=7900$; (e) $t=8020$; (f) $t=8160$; (g) $t=8300$. Not only the magnitude of the $\overline{v_{\varphi }}$, but also the direction of the $\overline{v_{\varphi }}$ changes as the LOD changes.Reuse & Permissions

Figure 4

Phase relation among magnetic energy, dynamo action, Joule heating, and heat flux variation. (a) The same as Fig. 3a, for comparison of the phase relation with panels (b) and (c). (b) Time (horizontal axis) versus the $-\mathbf{v}·\mathbf{J}\times \mathbf{B}$ integrated in the core. (c) Time (horizontal axis) versus the Joule heating $\eta J^2$ integrated in the core. (d) The same as (a), for comparison of phase relation with panels (e) and (f). Magnetic energy increasing phase (between green dotted lines) and decreasing phase (blue dotted lines) are indicated. (e) The time (horizontal axis) versus the heat flux at the CMB (blue) and ICB (orange). (f) The time derivative of the magnetic energy, which also corresponds to $-\mathbf{v}·\mathbf{J}\times \mathbf{B}-\eta J^2$ integrated in the core.Reuse & Permissions