Table 3: Some properties of the 2D simulations: number of grid points in radial ($N_{\rm r}$) and angular ( $N_{\theta }$) direction, radial ($\Delta r$ in 106 cm) and angular grid resolution ( $\Delta \theta $), characteristic length scale $l_{\rm c}$ of the flow (in 108 cm), characteristic rms velocity $v_{\rm c}$ of the flow (in $10^{6}\mbox{\ cm s${}^{-1}$ }$) averaged over the width of the convection zone R $\sim $ $l_{\rm c}$, Reynolds number $R_{\rm n}$ associated with the numerical viscosity of our code (Porter & Woodward 1994), damping timescale due to the numerical viscosity $t_{\rm n}$, typical convective turnover time $t_{\rm o} = 2~R/v_{\rm c}$, and maximum evolution time  $t_{\rm max}$ (in s), respectively.
Run Grid $\Delta r$ $\Delta \theta $ $l_{\rm c}$ $v_{\rm c}$ $R_{\rm n}$ $t_{\rm n}$ $t_{\rm o}$ $t_{\rm max}$
hefl.2d.1 180 $\times$ 90 5.55 $2\hbox{$^\circ$ }$ 4.7 1.29 1900 11 000 730 30 000
hefl.2d.2 270 $\times$ 180 3.70 $1\hbox{$^\circ$ }$ 4.7 1.79 8900 36 000 525 30 000
hefl.2d.3 360 $\times$ 240 2.77 $0.75\hbox{$^\circ$ }$ 4.7 1.84 21 000 83 000 510 30 000

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