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A note on multiple flow equilibria (1989)

Jacobs, S. J.

Springer

Pure and applied geophysics 130 (1989), S. 743-749

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ISSN: 1420-9136

Keywords: Dynamic systems ; multiple equilibrium ; stability

Source: Springer Online Journal Archives 1860-2000

Topics: Geosciences , Physics

Notes: Abstract A set of ordinary differential equations describing a mechanical system subject to forcing and dissipation is considered. A topological argument is employed to show that if all time-dependent solutions of the governing equations are bounded, the equations admitN steady solutions, whereN is a positive odd integer and where at least (N−1)/2 of the steady solutions are unstable. The results are discussed in the context of atmospheric flows, and it is shown that truncated forms of the quasigeostrophic equations of dynamic meteorology and of Budyko-Sellers climate models satisfy the hypotheses of the theorem.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF00881609

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