Spatially-periodic steady solutions to the three-dimensional Navier-Stokes equation with the \(ABC\)-force

DOI10.1016/S0167-2789(98)00292-9zbMath0943.76019MaRDI QIDQ1808286

Olga M. Podvigina

Publication date: 6 December 1999

Published in: Physica D (Search for Journal in Brave)

zbMATH Keywords

three-dimensional Navier-Stokes equationsbifurcationgroup of symmetriesABC-flowrotation group of cubesteady space-periodic solution

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Navier-Stokes equations (35Q30) Bifurcations in context of PDEs (35B32) Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics (76M60)

Related Items (7)

An extension of Prandtl–Batchelor theory and consequences for chaotic advection ⋮ Generation of a magnetic field by convective flows in a rotating horizontal layer ⋮ Modelling instability \(ABC\) flow using a mode interaction between steady and Hopf bifurcations with rotational symmetries of the cube ⋮ A staggered space-time discontinuous Galerkin method for the three-dimensional incompressible Navier-Stokes equations on unstructured tetrahedral meshes ⋮ Investigation of the ABC flow instability with application of centre manifold reduction ⋮ Revisiting the ABC flow dynamo ⋮ Dynamo action in the ABC flows using symmetries

Cites Work

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• Rigorous bounds on the fast dynamo growth rate involving topological entropy
• Chaotic streamlines in the ABC flows
• Instability criteria for the flow of an inviscid incompressible fluid
• Magnetic field generation by the motion of a highly conducting fluid
• Stretch, Twist, Fold: The Fast Dynamo
• Elements of applied bifurcation theory

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