We study the stability and dynamic transitions of the western boundary currents in a rectangular closed basin. By reducing the infinite dynamical system to a finite dimensional one via center manifold reduction, we derive a non-dimensional transition number that determines the types of dynamical transition. We show by careful numerical evaluation of the transition number that both continuous transitions (supercritical Hopf bifurcation) and catastrophic transitions (subcritical Hopf bifurcation) can happen at the critical Reynolds number, depending on the aspect ratio and stratification. The regions separating the continuous and catastrophic transitions are delineated on the parameter plane.
D. Han et al., "On the Instabilities and Transitions of the Western Boundary Current," Communications in Computational Physics, vol. 26, no. 1, pp. 35-56, Global-Science Press, Jul 2019.
The definitive version is available at https://doi.org/10.4208/cicp.OA-2018-0066
Mathematics and Statistics
Keywords and Phrases
Dynamic Transition; Hopf Bifurcation; Instability; Spectral Method; Western Boundary Current
International Standard Serial Number (ISSN)
Article - Journal
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01 Jul 2019