Dynamo Action with Wave Motion

It is shown that time dependent velocity fields in a fluid conductor can act as dynamos even when the same velocity fields frozen in at any particular time cannot. This effect is observed in propagating waves in which the time dependence is simply a steady drift of a fixed velocity pattern. The effect contributes to magnetic field generation in numerical models of planetary dynamos and relies on the property that eigenmodes of the induction equation are not all orthogonal to each other.

Figure 1

Growth rate $\mu$ of the eigenmode with the largest growth rate as a function of $v_d$ for $W=0.25$ and $\mathrm{Rm}=20$.

Figure 2

Left panel: The optimal value of the drift velocity $v_{d,\min }$ as a function of $W$. Right panel: The critical magnetic Reynolds number, ${\mathrm{Rm}}_{\min }$, when the drift velocity has its optimal value, divided by the critical magnetic Reynolds number of the same flow with zero drift velocity, ${\mathrm{Rm}}_0$, as a function of $W$.

Figure 3

Growth rate $p$, normalized by the free dipole decay rate, $|p_{\mathrm{dip}}|$, as a function of drift frequency ${\omega }_d$ for the velocity pattern taken from the benchmark dynamo.