ner_tags: O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O B-Model O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O B-Model O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O B-Model O B-Model O O O B-Model I-Model O O B-Model O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O B-Model I-Model O O O O O O O B-Model O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O B-Model O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O B-Model O B-Model O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
tokens: period (10,000–14,000 days in the MHD case), the large-scale magnetic field does not show any polarity reversal. We note that the polarity reversal is seen around 4500 and 8000 days. Figure 1. 3D volume rendering of the perturbation of the specific entropy multiplied by the background density for the (a) HD and (b) MHD cases are shown. A corresponding movie for panel (b) is available online. The animation continues for seven seconds covering 40 days of the global convection. The turbulent nature of the thermal convection is clearly seen in the animation. (An animation of this figure is available.) Figures 2 (a) and (c) show the streamline of the mass flux of the meridional flow for the HD and MHD cases, respectively, where includes the radial and latitudinal components of the velocity. The meridional flow in the HD case (Figure 2 (a)) shows a north-south aligned feature around the tangential cylinder. The overall flow pattern is counterclockwise (clockwise) in the northern (southern) hemisphere. In the MHD case (Figure 2 (c)), we see a clockwise (counterclockwise) meridional flow cell around the base of the convection zone in the northern (southern) hemisphere. Figures 2 (b) and (d) show the angular velocity for the HD and MHD cases, respectively. Because of the strong Lorentz force of the dynamo-generated magnetic field, the shear of the differential rotation, i.e., ΔΩ, decreased in the MHD case (see the difference in the color bar). In addition, the polar region is accelerated as well as the equator in the HD case. This feature is frequently seen in hydrodynamic calculations (Miesch et al. 2000 ; Gastine et al. 2012 ). The most important difference between the HD and MHD case concerns the Taylor–Proudman balance. In the HD case, the contour lines of the angular velocity are almost parallel to the rotational axis (Figure 2 (b)). This indicates that the HD case is in the Taylor–Proudman state. In contrast, the angular velocity in the MHD case shows significant deviation from the Taylor–Proudman state. This indicates that some terms in Equation ( 1 ) are balanced with the Coriolis force term. Figure 2. Panels (a) and (c) show the streamline of the meridional flow for the HD and MHD cases, respectively. The solid and dashed lines show the clockwise and counterclockwise flows, respectively. The angular velocity, Ω/(2 π ), is shown for the HD and MHD cases in panels (b) and (d), respectively, where Ω = v φ / λ + Ω 0 . To investigate the force balance on the meridional plane, we transpose Equation ( 1 ) as where is ignored, because the calculation is already in a statistically steady state. Figure 3 shows the balance in the MHD case. Minor contributions from the advection term ADV and the Lorentz force MAG around the top boundary are seen in Figures 3 (b) and (d), but the Coriolis force (COR, Figure 3 (a)) is mainly balanced with the baroclinic term, i.e., the entropy gradient (BAR, Figure 3 (c)). Although the difference in the differential