NASA Logo

NTRS

NTRS - NASA Technical Reports Server

Back to Results
An explicit example of Hopf bifurcation in fluid mechanicsIt is observed that a complete and explicit example of Hopf bifurcation appears not to be known in fluid mechanics. Such an example is presented for the rotating Benard problem with free boundary conditions on the upper and lower faces, and horizontally periodic solutions. Normal modes are found for the linearization, and the Veronis computation of the wave numbers is modified to take into account the imposed horizontal periodicity. An invariant subspace of the phase space is found in which the hypotheses of the Joseph-Sattinger theorem are verified, thus demonstrating the Hopf bifurcation. The criticality calculations are carried through to demonstrate rigorously, that the bifurcation is subcritical for certain cases, and to demonstrate numerically that it is subcritical for all the cases in the paper.
Document ID
19840036987
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
Authors
Kloeden, P.
(Murdoch University Murdoch; Western Australia, University, Nedlands, Australia)
Wells, R.
(Pennsylvania State University University Park, PA, United States)
Date Acquired
August 12, 2013
Publication Date
December 8, 1983
Publication Information
Publication: Proceedings, Series A - Mathematical and Physical Sciences
Volume: 390
Issue: 1799
ISSN: 0080-4630
Subject Category
Fluid Mechanics And Heat Transfer
Accession Number
84A19774
Funding Number(s)
CONTRACT_GRANT: NAS8-33794
CONTRACT_GRANT: NSF ATM-79-08354
Distribution Limits
Public
Copyright
Other

Available Downloads

There are no available downloads for this record.
No Preview Available