The University of Southampton
University of Southampton Institutional Repository

Steady-state bifurcation analysis of a fully nonlinear quasi-geostrophic vorticity equation

Steady-state bifurcation analysis of a fully nonlinear quasi-geostrophic vorticity equation
Steady-state bifurcation analysis of a fully nonlinear quasi-geostrophic vorticity equation
The quasi-geostrophic vorticity equation studied in the present paper is a simplified form of the atmospheric circulation model introduced by Charney and DeVore [J. Atmos. Sci. 36(1979), 1205–1216] on the existence of multiple steady states to the understanding of the persistence of atmospheric blocking. The fluid motion defined by the equation is driven by a zonal thermal forcing and an Ekman friction forcing measured by ?. It is proved that the steady-state solution is globally unique for large ? values while multiple steady-state solutions branch off the basic steady-state solution for ?<?crit where the critical value ?crit is less than one. Without involvement of viscosity, the equation has fully non-linear property as its non-linear part contains the highest order derivative term. Steady-state bifurcation analysis is essentially based on the compactness, which can be simply obtained for semilinear equations such as the Navier–Stokes equations but is not available for the fully nonlinear quasi-geostrophic vorticity equation in the Euler formulation. Therefore the Lagrangian formulation of the equation is employed to gain the required compactness.
quasi-geostrophic vorticity equation, steady-state bifurcation, lagrange formulation, fully non-linear equation
0022-247X
1-24
Chen, Zhi-Min
e4f81e6e-5304-4fd6-afb2-350ec8d1e90f
Chen, Zhi-Min
e4f81e6e-5304-4fd6-afb2-350ec8d1e90f

Chen, Zhi-Min (2015) Steady-state bifurcation analysis of a fully nonlinear quasi-geostrophic vorticity equation. Journal of Mathematical Analysis and Applications, 1-24. (doi:10.1016/j.jmaa.2015.05.035).

Record type: Article

Abstract

The quasi-geostrophic vorticity equation studied in the present paper is a simplified form of the atmospheric circulation model introduced by Charney and DeVore [J. Atmos. Sci. 36(1979), 1205–1216] on the existence of multiple steady states to the understanding of the persistence of atmospheric blocking. The fluid motion defined by the equation is driven by a zonal thermal forcing and an Ekman friction forcing measured by ?. It is proved that the steady-state solution is globally unique for large ? values while multiple steady-state solutions branch off the basic steady-state solution for ?<?crit where the critical value ?crit is less than one. Without involvement of viscosity, the equation has fully non-linear property as its non-linear part contains the highest order derivative term. Steady-state bifurcation analysis is essentially based on the compactness, which can be simply obtained for semilinear equations such as the Navier–Stokes equations but is not available for the fully nonlinear quasi-geostrophic vorticity equation in the Euler formulation. Therefore the Lagrangian formulation of the equation is employed to gain the required compactness.

Text
Chen_Steady-State.pdf - Accepted Manuscript
Download (342kB)

More information

e-pub ahead of print date: 21 May 2015
Keywords: quasi-geostrophic vorticity equation, steady-state bifurcation, lagrange formulation, fully non-linear equation
Organisations: Faculty of Engineering and the Environment

Identifiers

Local EPrints ID: 377448
URI: http://eprints.soton.ac.uk/id/eprint/377448
ISSN: 0022-247X
PURE UUID: ffc01e81-c9c2-4c83-b2e9-4f7894f483e9

Catalogue record

Date deposited: 27 May 2015 11:47
Last modified: 17 Dec 2019 06:56

Export record

Altmetrics

Contributors

Author: Zhi-Min Chen

University divisions

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 http://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.

×