On the Instabilities and Transitions of the Western Boundary Current (Communications in Computational Physics, 2019)
We study the stability and dynamic transitions of the western boundary currents in a rectangular closed basin. By reducing the infinite dynamical system to afinite dimensional one via center manifold reduction, we derive a non-dimensionaltransition number that determines the types of dynamical transition. We show bycareful 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 andstratification. The regions separating the continuous and catastrophic transitions aredelineated on the parameter plane.