Dynamo efficiency controlled by hydrodynamic bistability

Hydrodynamic and magnetic behaviors in a modified experimental setup of the von Kármán sodium flow—where one disk has been replaced by a propeller—are investigated. When the rotation frequencies of the disk and the propeller are different, we show that the fully turbulent hydrodynamic flow undergoes a global bifurcation between two configurations. The bistability of these flow configurations is associated with the dynamics of the central shear layer. The bistable flows are shown to have different dynamo efficiencies; thus for a given rotation rate of the soft-iron disk, two distinct magnetic behaviors are observed depending on the flow configuration. The hydrodynamic transition controls the magnetic field behavior, and bifurcations between high and low magnetic field branches are investigated.

Figure 1

Left: Experimental setup; arrows showing the rotation for positive $F_d$ and $F_p$. Right: $``s_1{t}_2\text{""}$ and $``s_1{t}_1\text{""}$ mean flows.

Figure 2

(a) Evolution of time-averaged torques as a function of $F_p$ for $F_d=13$ Hz. (b) Evolution of $\langle {\Gamma }_n\rangle$ as a function of $\Theta .$ (c) Evolution of $\langle v_{\theta }\rangle$ as a function of $F_p$. ($•$) $F_d=13$ Hz (colors stand for the amplitude of the magnetic field, see Fig. 3). ($\square$) Values at exact counter rotation $F_d=F_p$. ($◊$) Values for propeller rotation only ($F_d=0$).

Figure 3

(a) Amplitude of the magnetic field $B$ as a function of $\Theta$ for four values of $F_d$. Full symbols for H branch and open symbols for L branch. (b) Stationary points in the L and H branches at $\Theta =0.46$ (full lines) and points at $\Theta ={\Theta }_{\mathrm{LH}}$ (dashed line). See text for details.

Figure 4

Time series of (a) $E_{\mathrm{mag}}$ and zoom in logarithmic units (inset) and (b) ${\Gamma }_n$ at L-H transition ($F_d=14\mathrm{Hz},F_p=37$ Hz). Growing times $t_{\mathrm{s}}$ and $t_{\mathrm{l}}$ decrease from 0.41 s to 0.18 s and 0.05 s, and 1.4 s to 1 s and 0.4 s, respectively, when $F_d$ is increased from 13 to 15 Hz. (c) Phase-space $E_{\mathrm{mag}}^{*}\left({\Gamma }_n\right)$ at $\Theta ={\Theta }_{\mathrm{LH}}$. Signals averaged over 0.25 s.