Normal forms for three-dimensional parametric instabilities in ideal hydrodynamics

Edgar Knobloch, Alex Mahalov, Jerrold E. Marsden

Research output: Contribution to journalArticlepeer-review

34 Scopus citations


We derive and analyze several low dimensional Hamiltonian normal forms describing system symmetry breaking in ideal hydrodynamics. The equations depend on two parameters (ε{lunate}, λ), where ε{lunate} is the strength of a system symmetry breaking perturbation and λ is a detuning parameter. In many cases the resulting equations are completely integrable and have an interesting Hamiltonian structure. Our work is motivated by three-dimensional instabilities of rotating columnar fluid flows with circular streamlines (such as the Burger vortex) subjected to precession, elliptical distortion or off-center displacement.

Original languageEnglish (US)
Pages (from-to)49-81
Number of pages33
JournalPhysica D: Nonlinear Phenomena
Issue number1-2
StatePublished - May 15 1994

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


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