Generation of bursting magnetic fields by nonperiodic torsional flows

A mechanism for the cyclic generation of bursts of magnetic fields by nonlinear torsional flows of complex time dependence but very simple spatial structure is described. These flows were obtained numerically as axisymmetric solutions of convection in internally heated rotating fluid spheres in the Boussinesq approximation. They behave as repeated transients, which start with nearly periodic oscillations of the velocity field of slowly increasing amplitude. This regime is followed by a chaotic fast increase and a final decrease of the amplitude of, at least, one order of magnitude. The magnetic field decays due to the magnetic diffusion during the regular oscillations, but it grows in the form of bursts during the intervals of irregular time dependence of the velocity. The magnetic field is strongly localized in spirals, with spatial- and temporal-dependent intensity.

Figure 1

Radial component of the velocity at a point of the sphere (oscillatory curve, black online) and norm of the potentials of the magnetic field (curve with the fast growth at $t=0.810$, blue online) showing the timescale of the temporally chaotic motion. The parameters are $\mathrm{Ek}={10}^{-4},\mathrm{Pr}={10}^{-3},\mathrm{Ra}={10}^4$, and ${\mathrm{Pr}}_{\mathrm{m}}=75$.

Figure 2

Potentials of the velocity field [(a), (b)] at $t=1.071$ during the regular oscillations and [(c), (d)] at $t=1.2836$ during the irregular motion. The parameters are $\mathrm{Ek}={10}^{-4},\mathrm{Pr}={10}^{-3},\mathrm{Ra}={10}^4$, and ${\mathrm{Pr}}_{\mathrm{m}}=62$. The times indicated correspond to Fig. 3.

Figure 3

(a–d) Time evolution of the $l_2$ norm of the potentials of the magnetic field for ${\mathrm{Pr}}_{\mathrm{m}}=150,75,62,50$ in logarithmic scale. In (a) it is shown also the time evolution of $v_r(r_o/3,\pi /6,\phi )$ (right axis). The other parameters are $\mathrm{Ek}={10}^{-4},\mathrm{Pr}={10}^{-3},\text{and}\mathrm{Ra}={10}^4.$

Figure 4

(a–f) Details of Fig. 3. Panels (a), (c), and (f) are plotted in linear scale.

Figure 5

Time sequences for the resolutions $N_r\times L=60\times 60$ (middle curve at $t=1.1$, magenta online), $100\times 50$ (lower curve at $t=1.1$, black online), and $150\times 80$ (upper curve at $t=1.1$, blue online) for $\mathrm{Ek}={10}^{-4},\mathrm{Pr}={10}^{-3},\mathrm{Ra}={10}^4$, and ${\mathrm{Pr}}_{\mathrm{m}}=75$.

Figure 6

Contour plots of $B_{\phi }$ on a spherical surface taken at $r>0.9$ in (a), (d), (m), and (p), and at $r=0.02$ in (g) and (f). Equatorial sections in the second column, and meridional planes in the third, indicated by dashed lines. In (a)–(c) $t=1.4746$, (d)-(f) $t=1.6741$, (g)–(i) $t=1.6873$, (j)–(l) $t=1.6947$, (m)–(o) $t=1.7925$, and (p)–(r) 1.8697. The arrows are the projections of $\mathit{B}$ on each section. The parameters are $\mathrm{Ek}={10}^{-4},\mathrm{Pr}={10}^{-3},\mathrm{Ra}={10}^4$, and ${\mathrm{Pr}}_{\mathrm{m}}=62$.

Figure 7

Time evolution of the $l_2$ norm of the potentials of the magnetic field for ${\mathrm{Pr}}_{\mathrm{m}}=27$. The other parameters are $\mathrm{Ek}={10}^{-3},\mathrm{Pr}=0.01$, and $\mathrm{Ra}=21250.$ The horizontal line (blue online) is the exponential fit of the solution.