Dynamo Enhancement and Mode Selection Triggered by High Magnetic Permeability

We present results from consistent dynamo simulations, where the electrically conducting and incompressible flow inside a cylinder vessel is forced by moving impellers numerically implemented by a penalization method. The numerical scheme models jumps of magnetic permeability for the solid impellers, resembling various configurations tested experimentally in the von Kármán sodium experiment. The most striking experimental observations are reproduced in our set of simulations. In particular, we report on the existence of a time-averaged axisymmetric dynamo mode, self-consistently generated when the magnetic permeability of the impellers exceeds a threshold. We describe a possible scenario involving both the turbulent flow in the vicinity of the impellers and the high magnetic permeability of the impellers.

Figure 1

(Re, Rm) parameter space showing nondynamo (blue empty circle) and dynamo runs (red square) and the dynamo onset (black dotted line) for ${\mu }_r=1$. Below the dynamo onset at ${\mu }_r=1$, dynamos were observed for ${\mu }_r>8$ (green diamonds). Right: Isocontours of the time-averaged dynamo magnetic energy field in the growing phase for $\mathrm{Re}=333$ and $\mathrm{Re}=1500$ ($Pm=1$).

Figure 2

(a) Time evolution of magnetic energy $E_b$, (b) dynamo growth rates, (c) dynamo energy ratio in modes $m=0$ and $m=1$, and (d) normalized lifetime of the magnetic field line winding number in the vicinity of the impellers and as a function of ${\mu }_r$. See the text for details.

Figure 3

(a) Azimuthal mode decomposition of magnetic energy, (b) azimuthally averaged $H_{\varphi }$, and (c) $H_z$ components normalized to the maximum value in the linear regime for $\mathrm{Re}=1500$, $\text{Rm}=500$, and ${\mu }_r=14$. (b) Vectors show the poloidal dynamo field.

Figure 4

(a) $H_z$, (b) $H_r$, (c) $H_{\varphi }$ isoamplitude contours (red, positive value; blue, opposite negative value), and (d) magnetic streamlines colored by the $H_{\varphi }$ value. $\mathrm{Re}=1500$, $\text{Rm}=500$, and ${\mu }_r=14$.