Figure 1

Time-periodic boundary-driving azimuthal velocity $v_{\varphi }$ from Eq. (5) with oscillation amplitude $a=2$ as a function of polar angle $\theta$ at several moments over a period $T=2\pi /\omega$.Reuse & Permissions

Figure 2

Structure of (a) equilibrium velocity $\mathbf{v}$ and (b) fastest dynamo eigenmode $\mathbf{B}$ (with azimuthal number $m=1$) at four consecutive moments over a period $T=2\pi /\omega$. The flow parameters are $a=2$, $\omega =0.6$, $\mathrm{Re}=300$, $\mathrm{Rm}=30000$, the respective dynamo eigenvalue is $\gamma =0.059627+0.200510i$. Exponential growth and rotation associated with $\gamma$ are removed from the images of $\mathbf{B}$ by a suitable normalization (the resulting $\mathbf{B}$ is periodic with period $T$). The left half of each figure shows the modulus of the poloidal (lying in meridional plane) component, the right half shows a level plot of the azimuthal component. In velocity figures, contours with arrows are stream lines of poloidal velocity $v_{\mathrm{pol}}$, dashed curves denote levels of $v_{\varphi }<0$. In dynamo figures, lighting is used to emphasize the small-scale structure of the dynamo field. The listed parameters correspond to the MPDX fully ionized hydrogen plasma with the density $n_0\approx 2\times {10}^{12}{\mathrm{cm}}^{-3}$, the ion temperature $T_i\approx 1\mathrm{eV}$, the electron temperature $T_e\approx 100\mathrm{eV}$, the typical driving velocity $V_0\approx 12.5\mathrm{km}/\mathrm{s}$, the driving frequency $\omega /2\pi \approx 0.8\mathrm{kHz}$, and the dynamo growth rate ${\gamma }_r\approx 500{\mathrm{s}}^{-1}$ (see Ref. 24 for details).Reuse & Permissions

Figure 3

Poincaré plots for the equilibrium flow $\mathbf{v}$ for $\mathrm{Re}=300$, $\omega =0.6$, and three amplitudes $a$. Points are the footprints of trajectories of six fluid parcels shown in different colors at one meridional plane. Each trajectory is followed for $1000T$.Reuse & Permissions

Figure 4

Hydrodynamic stability boundaries of the equilibrium flow $\mathbf{v}$ on the plane of driving parameters ($\omega$, $a$) for different fluid Reynolds numbers Re. For every Re, curves are composed of several azimuthal modes $m$ (typically, $m=1–4$). The shown region of parameters is stable for $\mathrm{Re}<120$.Reuse & Permissions

Figure 5

Dynamo growth rate ${\gamma }_r$ of the fastest mode as a function of Rm for different values of (a) fluid Reynolds number Re, (b) oscillation amplitude $a$, (c) driving frequency $\omega$. Note that in (a) and (b) the fastest azimuthal modes are always $m=1$, while in (c) they vary with $\omega$.Reuse & Permissions

Figure 6

Square of the effective wave number in a dynamo eigenmode $k_{\mathrm{eff}}^2$ normalized by Rm and corresponding dynamo eigenvalue $\gamma ={\gamma }_r+i{\gamma }_i$ as functions of Rm. Flow parameters are $\mathrm{Re}=300$, $a=2$, $\omega =0.6$.Reuse & Permissions