Abstract

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
Volume73
Issue number1-2
DOIs
StatePublished - May 15 1994

Fingerprint

Hamiltonians
Symmetry Breaking
Normal Form
Hydrodynamics
broken symmetry
hydrodynamics
Rotating Flow
rotating fluids
Rotating Fluid
Three-dimensional
Hamiltonian Structure
Streamlines
precession
fluid flow
Fluid Flow
Two Parameters
Flow of fluids
Vortex
Vortex flow
vortices

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistical and Nonlinear Physics

Cite this

Normal forms for three-dimensional parametric instabilities in ideal hydrodynamics. / Knobloch, Edgar; Mahalov, Alex; Marsden, Jerrold E.

In: Physica D: Nonlinear Phenomena, Vol. 73, No. 1-2, 15.05.1994, p. 49-81.

Research output: Contribution to journalArticle

@article{9bfe6fab10bb40d0bd38b16c1d822c50,
title = "Normal forms for three-dimensional parametric instabilities in ideal hydrodynamics",
abstract = "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.",
author = "Edgar Knobloch and Alex Mahalov and Marsden, {Jerrold E.}",
year = "1994",
month = "5",
day = "15",
doi = "10.1016/0167-2789(94)90225-9",
language = "English (US)",
volume = "73",
pages = "49--81",
journal = "Physica D: Nonlinear Phenomena",
issn = "0167-2789",
publisher = "Elsevier",
number = "1-2",

}

TY - JOUR

T1 - Normal forms for three-dimensional parametric instabilities in ideal hydrodynamics

AU - Knobloch, Edgar

AU - Mahalov, Alex

AU - Marsden, Jerrold E.

PY - 1994/5/15

Y1 - 1994/5/15

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0011581571&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0011581571&partnerID=8YFLogxK

U2 - 10.1016/0167-2789(94)90225-9

DO - 10.1016/0167-2789(94)90225-9

M3 - Article

AN - SCOPUS:0011581571

VL - 73

SP - 49

EP - 81

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 1-2

ER -