Normal Forms for Three–dimensional Parametric Instabilities in Ideal Hydrodynamics
We derive and analyze several low dimensional Hamiltonian normal forms describing system symmetry breaking in ideal hydrodynamics. The equations depend on two parameters (^є, λ), where ^є 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.
© 1994 Published by Elsevier B.V. October, 1992. This version: December 20, 1993. Research partially supported by NSF Contract DMS 89-19074 and CTS 89-06343. Research partially supported by DOE Contract DE-FGO3-92ER25129. We thank Mary Silber and Vivien Kirk for helpful discussions on the Hamiltonian structure of normal forms.
Updated - KnMaMa1994.pdf