Dynamo action in the ABC flows using symmetries

DOI10.1080/03091929.2013.832762OpenAlexW2073583789WikidataQ114640233 ScholiaQ114640233MaRDI QIDQ5879302

Andrew D. Gilbert, S. E. Jones

Publication date: 28 February 2023

Published in: Geophysical & Astrophysical Fluid Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03091929.2013.832762

zbMATH Keywords

symmetriesArnoldi methodfast dynamokinematic dynamoABC flow

Mathematics Subject Classification ID

General and overarching topics; collections (00-XX)

Related Items (4)

Minimal \(D = 7\) supergravity and the supersymmetry of Arnold-Beltrami flux branes ⋮ Knots and links of invariant tori in Beltrami flows with cubic symmetry ⋮ Chaos from symmetry: Navier Stokes equations, Beltrami fields and the universal classifying crystallographic group ⋮ Analysis of stationary points and their bifurcations in the ABC-flow

Cites Work

• Unnamed Item
• On the nonlinear stability of the 1:1:1 ABC flow
• Spatially-periodic steady solutions to the three-dimensional Navier-Stokes equation with the \(ABC\)-force
• Rigorous bounds on the fast dynamo growth rate involving topological entropy
• Topological constraints associated with fast dynamo action
• Chaotic streamlines in the ABC flows
• Hydromagnetic screw dynamo
• Fast dynamo action in the Ponomarenko dynamo
• Dynamo action in simple convective flows
• Hopf bifurcation with cubic symmetry and instability of ABC flow
• Numerical simulations of kinematic dynamo action
• Revisiting the ABC flow dynamo
• ABC flows then and now
• Dissipative structures in a nonlinear dynamo

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