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Hopf bifurcation in quasi-geostrophic channel flow

Hopf bifurcation in quasi-geostrophic channel flow
Hopf bifurcation in quasi-geostrophic channel flow
In this article, we conduct a rigorous stability and bifurcation analysis for a highly idealized model of planetary-scale atmospheric and oceanic flows. The model is governed by the two-dimensional, quasi-geostrophic equation for the conservation of vorticity in an east-west oriented, periodic channel. The main result is the existence of Hopf bifurcation of the flow as the Reynolds number crosses a critical value.

The key idea in proving this result is translating the eigenvalue problem into a difference equation and treating the latter by continued-fraction methods. Numerical results are obtained by using a finite-difference scheme with high spatial resolution and these results agree closely with the theoretical predictions. The spatio-temporal structure of the limit cycle corresponds to a wave that propagates slowly westward and is symmetric about the midaxis of the channel. For plausible paramater values that correspond to midlatitude atmospheric flows, the period of this wave is 20-25 days.
0036-1399
343-368
Chen, Zhi-Min
e4f81e6e-5304-4fd6-afb2-350ec8d1e90f
Ghil, Michael
79f88375-ef09-4bfc-8ba6-32f146fed468
Simonnet, Eric
242d6b63-656d-4ab2-8b79-e6d680624898
Wang, Shouhong
14995334-3494-4476-a7b1-b23900b5c090
Chen, Zhi-Min
e4f81e6e-5304-4fd6-afb2-350ec8d1e90f
Ghil, Michael
79f88375-ef09-4bfc-8ba6-32f146fed468
Simonnet, Eric
242d6b63-656d-4ab2-8b79-e6d680624898
Wang, Shouhong
14995334-3494-4476-a7b1-b23900b5c090

Chen, Zhi-Min, Ghil, Michael, Simonnet, Eric and Wang, Shouhong (2003) Hopf bifurcation in quasi-geostrophic channel flow. SIAM Journal on Applied Mathematics, 64 (1), 343-368. (doi:10.1137/S0036139902406164).

Record type: Article

Abstract

In this article, we conduct a rigorous stability and bifurcation analysis for a highly idealized model of planetary-scale atmospheric and oceanic flows. The model is governed by the two-dimensional, quasi-geostrophic equation for the conservation of vorticity in an east-west oriented, periodic channel. The main result is the existence of Hopf bifurcation of the flow as the Reynolds number crosses a critical value.

The key idea in proving this result is translating the eigenvalue problem into a difference equation and treating the latter by continued-fraction methods. Numerical results are obtained by using a finite-difference scheme with high spatial resolution and these results agree closely with the theoretical predictions. The spatio-temporal structure of the limit cycle corresponds to a wave that propagates slowly westward and is symmetric about the midaxis of the channel. For plausible paramater values that correspond to midlatitude atmospheric flows, the period of this wave is 20-25 days.

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More information

Published date: October 2003
Organisations: Fluid Structure Interactions Group

Identifiers

Local EPrints ID: 345825
URI: https://eprints.soton.ac.uk/id/eprint/345825
ISSN: 0036-1399
PURE UUID: b7604192-4881-4f41-b9dc-02a245eaf03d

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Date deposited: 14 Dec 2012 16:19
Last modified: 18 Jul 2017 05:07

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