Volume 26, Issue 1
On the Instabilities and Transitions of the Western Boundary Current

Daozhi Han, Marco Salvalaglio & Quan Wang

Commun. Comput. Phys., 26 (2019), pp. 35-56.

Published online: 2019-02

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  • Abstract

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.

  • Keywords

Western boundary current, dynamic transition, instability, Hopf bifurcation, spectral method.

  • AMS Subject Headings

37D45, 35Q99, 34C23, 76U05, 76D03

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-26-35, author = {}, title = {On the Instabilities and Transitions of the Western Boundary Current}, journal = {Communications in Computational Physics}, year = {2019}, volume = {26}, number = {1}, pages = {35--56}, abstract = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0066}, url = {http://global-sci.org/intro/article_detail/cicp/13025.html} }
TY - JOUR T1 - On the Instabilities and Transitions of the Western Boundary Current JO - Communications in Computational Physics VL - 1 SP - 35 EP - 56 PY - 2019 DA - 2019/02 SN - 26 DO - http://dor.org/10.4208/cicp.OA-2018-0066 UR - https://global-sci.org/intro/article_detail/cicp/13025.html KW - Western boundary current, dynamic transition, instability, Hopf bifurcation, spectral method. AB -

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.

Daozhi Han, Marco Salvalaglio & Quan Wang. (2019). On the Instabilities and Transitions of the Western Boundary Current. Communications in Computational Physics. 26 (1). 35-56. doi:10.4208/cicp.OA-2018-0066
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