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 deri...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.展开更多
基金supported by a seed fund of the Material Research Center at Missouri University of Science and TechnologyMarco Hernandez was supported in part by the National Science Foundation(NSF)grant DMS-1515024,and by the Office of Naval Research(ONR)grant N00014-15-1-2662Quan Wang was supported by the NSFC(No.11771306).
文摘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.
