Searching for the fastest dynamo: Laminar ABC flows

TL;DR

This study investigates the dynamo instability growth rates in ABC flows through numerical simulations, revealing how different flow configurations become dynamo-active at various magnetic Reynolds numbers and identifying the fastest dynamo conditions.

Contribution

It provides a detailed analysis of the dynamo behavior in ABC flows at different scales and Rm values, highlighting the flow configurations that optimize dynamo growth rates.

Findings

2.5D flows are the first to result in dynamo at large scales.

The flow A=B=2C/5 becomes the fastest dynamo at high Rm.

Growth rates correlate with Lyapunov exponents and field line folding.

Abstract

The growth rate of the dynamo instability as a function of the magnetic Reynolds number Rm is investigated by means of numerical simulations for the family of the ABC flows and for 2 different forcing scales. For the ABC flows that are driven at the largest available length scale it is found that as the magnetic Reynolds number is increased: (a) The flow that results first in dynamo is the 2.5D flow for which A=B and C=0 (and all permutations). (b) The second type of flow that results in dynamo is the one for which A=B=2C/5 (and permutations). (c) The most symmetric flow A=B=C is the third type of flow that results in dynamo. (d) As Rm is increased, the A=B=C flow stops being a dynamo and transitions from a local maximum to a third-order saddle point. (e) At larger Rm the A=B=C flow re-establishes its self as a dynamo but remains a saddle point. (f) At the largest examined Rm the growth rate of the 2.5D flows starts to decrease, the A=B=C flow comes close to a local maximum again and the flow A=B=2C/5 (and permutations) results in the fastest dynamo with growth rate $\gamma~0.12$ at the largest examined Rm. For the ABC flows that are driven at the second largest available length scale it is found that (a) the 2.5D flows A=B, C=0 (and permutations) are again the first flows that result in dynamo with a decreased onset. (b) The most symmetric flow A=B=C is the second type of flow that results in dynamo. It is and remains a local maximum. (c) At larger Rm the flow A=B=2C/5 (and permutations) appears as the third type of flow that results in dynamo. As Rm is increased it becomes the flow with the largest growth rate. The growth rates appear to have some correlation with the Lyaponov exponents but constructive re-folding of the field lines appears equally important in determining the fasted dynamo flow.