Generation of magnetic fields by large-scale vortices in rotating convection

We propose a self-consistent dynamo mechanism for the generation of large-scale magnetic fields in natural objects. Recent computational studies have described the formation of large-scale vortices in rotating turbulent convection. Here we demonstrate that for magnetic Reynolds numbers below the threshold for small-scale dynamo action, such turbulent flows can sustain large-scale magnetic fields, i.e., fields with a significant component on the scale of the system.

Figure 1

Parameter values in $(\text{Ek},\widetilde{\text{Ra}})$ parameter space for previous studies of convective planar dynamos. For compressible convection: Käpylä et al. [10] $(\square )$ and Favier and Bushby [11] $(◯)$. For Boussinesq convection: Stellmach and Hansen [1] $\left(▵\right)$, Cattaneo and Hughes [8] $(▽)$, and Tilgner [7] $(\times )$. Gray (open) symbols indicate dynamos producing large-scale (small-scale) magnetic fields for $\text{Pm}=O\left(1\right)$. The crosses and the dashed line indicate the transition between the two types of dynamos identified in Tilgner [7]. The red region represents where LSVs occur in nonmagnetic convection for aspect ratio $\lambda =1$ and $\text{Pr}=1$ [15]; the plus symbol is the case studied here.

Figure 2

Horizontal cross sections of $B_x$ at $z=0.25$ for (a) $\text{Pm}=0.2$ and (b) $\text{Pm}=2.5$.

Figure 3

Kinetic $\left(E_u\right)$ and magnetic $\left(E_b\right)$ energies as a function of $\text{Pm}$. The dots indicate the mean values, and the black vertical lines the range of variation of the energies in the saturated phase. The red vertical bars show the mean kinetic energy in the LSV [i.e., the energy corresponding to the horizontal wave number $(k_x,k_y)=(1,1)$], and the blue bars the energy in the remainder of the flow.

Figure 4

Horizontal cross sections of the axial vorticity at $z=0.25$ for (a) $\text{Pm}=0$, (b) $\text{Pm}=2.5$, and (c) $\text{Pm}=0.2$ at $t_{max}$ and (d) $t_{min}$. The color scale is bounded by $\pm 0.8$ in all the cases.

Figure 5

Horizontal power spectra of (a) the velocity $\left(e_u\right)$ and (b) the magnetic field $\left(e_b\right)$. In (b), the squares and crosses represent the horizontal and vertical components of the magnetic field, respectively, for $\text{Pm}=0.2$ at $t=t_{max}$ (red symbols) and $\text{Pm}=2.5$ (black).

Figure 6

Time series of the kinetic $(E_u$, solid black line) and magnetic $(E_b$, gray) energies for $\text{Pm}=0.2$. The vertical dashed (dotted) line indicates the time $t=t_{\text{max}}$ $\left(t=t_{\text{min}}\right)$.