The University of Southampton
University of Southampton Institutional Repository

Bifurcating periodic solutions of the wind-driven circulation equations

Bifurcating periodic solutions of the wind-driven circulation equations
Bifurcating periodic solutions of the wind-driven circulation equations
The existence of bifurcating periodic flows in a quasi-geostrophic mathematical model of wind-driven circulation is investigated. In the model, the Ekman number r and Reynolds number R control the stability of the motion of the fluid. Through rigorous analysis it is proved that when the basic steady-state solution is independent of the Ekman number, then a spectral simplicity condition is sufficient to ensure the existence of periodic solutions branching off the basic steady-state solution as the Ekman number varies across its critical value for constant Reynolds number. When the basic solution is a function of Ekman number, an additional condition is required to ensure periodic solutions.
hopf bifurcation, periodic solution, navier–stokes equation, bessel-potential space
0022-247X
783-796
Chen, Zhi-Min
e4f81e6e-5304-4fd6-afb2-350ec8d1e90f
Price, W.G.
b7888f47-e3fc-46f4-9fb9-7839052ff17c
Chen, Zhi-Min
e4f81e6e-5304-4fd6-afb2-350ec8d1e90f
Price, W.G.
b7888f47-e3fc-46f4-9fb9-7839052ff17c

Chen, Zhi-Min and Price, W.G. (2005) Bifurcating periodic solutions of the wind-driven circulation equations. Journal of Mathematical Analysis and Applications, 304 (2), 783-796. (doi:10.1016/j.jmaa.2004.09.062).

Record type: Article

Abstract

The existence of bifurcating periodic flows in a quasi-geostrophic mathematical model of wind-driven circulation is investigated. In the model, the Ekman number r and Reynolds number R control the stability of the motion of the fluid. Through rigorous analysis it is proved that when the basic steady-state solution is independent of the Ekman number, then a spectral simplicity condition is sufficient to ensure the existence of periodic solutions branching off the basic steady-state solution as the Ekman number varies across its critical value for constant Reynolds number. When the basic solution is a function of Ekman number, an additional condition is required to ensure periodic solutions.

Full text not available from this repository.

More information

Published date: 2005
Keywords: hopf bifurcation, periodic solution, navier–stokes equation, bessel-potential space
Organisations: Fluid Structure Interactions Group

Identifiers

Local EPrints ID: 23648
URI: https://eprints.soton.ac.uk/id/eprint/23648
ISSN: 0022-247X
PURE UUID: d18e6893-6520-4e3b-8737-3fbfccdfb9ec

Catalogue record

Date deposited: 13 Mar 2006
Last modified: 17 Jul 2017 16:16

Export record

Altmetrics

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of https://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×