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
783-796
Chen, Zhi-Min
e4f81e6e-5304-4fd6-afb2-350ec8d1e90f
Price, W.G.
b7888f47-e3fc-46f4-9fb9-7839052ff17c
2005
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), .
(doi:10.1016/j.jmaa.2004.09.062).
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.
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Published date: 2005
Keywords:
hopf bifurcation, periodic solution, navier–stokes equation, bessel-potential space
Organisations:
Fluid Structure Interactions Group
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Local EPrints ID: 23648
URI: http://eprints.soton.ac.uk/id/eprint/23648
ISSN: 0022-247X
PURE UUID: d18e6893-6520-4e3b-8737-3fbfccdfb9ec
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Date deposited: 13 Mar 2006
Last modified: 15 Mar 2024 06:49
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Author:
Zhi-Min Chen
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