Dynamic Transitions and Bifurcations for a Class of Axisymmetric Geophysical Fluid Flow
In this article, we aim to classify the dynamic transitions and bifurcations for a family of axisymmetric geophysical fluid problems of a generic fourth-second order structure. A transition theorem is established by reducing the governing partial differential equations to a complex-valued ordinary differential equation, derived by employing approximate invariant manifolds. We develop an algorithm for the numerical determination of the transition/bifurcation types. Finally we apply the transition theorem and algorithm to examine the baroclinic instability in a two-layer quasi-geostrophic system in an annular channel and with different bathymetry profiles. Our numerical results show that with concave bathymetry the transition (bifurcation) is always continuous (supercritical Hopf bifurcation), whereas for convex bathymetry a jump transition (subcritical Hopf bifurcation) may occur in the basic azimuthal currents that rotate in the same direction.
D. Han et al., "Dynamic Transitions and Bifurcations for a Class of Axisymmetric Geophysical Fluid Flow," SIAM Journal on Applied Dynamical Systems, vol. 20, no. 1, pp. 38 - 64, Society for Industrial and Applied Mathematics (SIAM), Jan 2021.
The definitive version is available at https://doi.org/10.1137/20M1321139
Mathematics and Statistics
Center for High Performance Computing Research
Keywords and Phrases
Axially symmetric problems; Baroclinic flows; Dynamic transitions; Quasi-geostrophic models; Topographic effects
International Standard Serial Number (ISSN)
Article - Journal
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01 Jan 2021