Dynamo transition in a five-mode helical model

TL;DR

This paper presents an analytical five-mode helical dynamo model demonstrating dynamo transition via bifurcation, with critical magnetic Reynolds number behavior and complex dynamo states including chaos as forcing increases.

Contribution

It introduces a new five-mode helical dynamo model with analytical solutions, revealing bifurcation behavior and dynamo state transitions.

Findings

Critical magnetic Reynolds number asymptotes at low and high magnetic Prandtl numbers.

Dynamo transition occurs via supercritical pitchfork bifurcation.

Chaotic dynamo states emerge through quasi-periodic routes.

Abstract

We construct a five-mode helical dynamo model containing three velocity and two magnetic modes and solve it analytically. This model exhibits dynamo transition via supercritical pitchfork bifurcation. We show that the critical magnetic Reynolds number for dynamo transition ($\mathrm{Rm}_c$) asymptotes to constant values for very low and very high magnetic Prandtl numbers ($\mathrm{Pm}$). Beyond dynamo transition, secondary bifurcations lead to periodic, quasi-periodic, and chaotic dynamo states as the forcing amplitude is increased and chaos appears through a quasi-periodic route.