Dynamic Transitions and Bifurcations for a Class of Axisymmetric Geophysical Fluid Flow

Abstract

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.

Department(s)

Mathematics and Statistics

Research Center/Lab(s)

Center for High Performance Computing Research

Comments

National Science Foundation, Grant DMS-1515024

Keywords and Phrases

Axially symmetric problems; Baroclinic flows; Dynamic transitions; Quasi-geostrophic models; Topographic effects

International Standard Serial Number (ISSN)

1536-0040

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2021 Society for Industrial and Applied Mathematics (SIAM), All rights reserved.

Publication Date

01 Jan 2021

Link to Full Text

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