## Normal forms for threedimensional parametric instabilities (1994)

Venue: | Physica D |

Citations: | 9 - 8 self |

### BibTeX

@INPROCEEDINGS{Knobloch94normalforms,

author = {Edgar Knobloch and Alex Mahalov and Jerrold E. Marsden},

title = {Normal forms for threedimensional parametric instabilities},

booktitle = {Physica D},

year = {1994},

pages = {49--81}

}

### Years of Citing Articles

### OpenURL

### Abstract

We derive and analyze several low dimensional Hamiltonian normal forms describing system symmetry breaking in ideal hydrodynamics. The equations depend on two parameters (ɛ, λ), where ɛ 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. 1