Hamiltonian bifurcation theory for a rotating flow subject to elliptic straining field

Y. Fukumoto, Y. Mie

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

A weakly nonlinear stability theory is developed for a rotating flow confined in a cylinder of elliptic cross-section. The straining field associated with elliptic deformation of the cross-section breaks the SO(2)-symmetry of the basic flow and amplifies a pair of Kelvin waves whose azimuthal wavenumbers are separated by 2, being referred to as the Moore-Saffman-Tsai-Widnall (MSTW) instability. The Eulerian approach is unable to fully determine the mean flow induced by nonlinear interaction of the Kelvin waves. We establish a general framework for deriving the mean flow by a restriction to isovortical disturbances with use of the Lagrangian variables and put it on the ground of the generalized Lagrangian-mean theory. The resulting formula reveals enhancement of mass transport in regions dominated by the vorticity of the basic flow. With the mean flow at hand, we derive unambiguously the weakly nonlinear amplitude equations to third order for a nonstationary mode. By an appropriate normalization of the amplitude, the resulting equations are made Hamiltonian systems of four degrees of freedom, possibly with three first integrals identifiable as the wave energy and the mean flow.

Original languageEnglish
Article number014042
JournalPhysica Scripta
Volume88
Issue numberT155
DOIs
Publication statusPublished - Jul 1 2013

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Rotating Flow
Bifurcation Theory
Kelvin waves
Kelvin
Cross section
Amplitude Equations
Mass Transport
Nonlinear Interaction
Nonlinear Stability
Stability Theory
First Integral
Vorticity
cross sections
Hamiltonian Systems
Normalization
Nonlinear Equations
vorticity
Enhancement
Disturbance
Degree of freedom

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics
  • Mathematical Physics
  • Condensed Matter Physics

Cite this

Hamiltonian bifurcation theory for a rotating flow subject to elliptic straining field. / Fukumoto, Y.; Mie, Y.

In: Physica Scripta, Vol. 88, No. T155, 014042, 01.07.2013.

Research output: Contribution to journalArticle

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