Methods and Applications of Analysis

Volume 15 (2008)

Number 4

Structural Stability and Bifurcation for 2-D Incompressible Flows with Symmetry

Pages: 495 – 512

DOI: http://dx.doi.org/10.4310/MAA.2008.v15.n4.a6

Authors

Chun-Hsiung Hsia

Jian-Guo Liu

Cheng Wang

Abstract

This article studies the structure and its evolution of incompressible flows with the anti-symmetry using a combination of rigorous analysis and numerical simulations, with an application to an example of oceanic flow. In particular, necessary and sufficient conditions for 2D divergence-free vector fields with anti-symmetry are obtained, and a detailed numerical simulation for a simplified model of Marsigli oceanic flow is provided to explore and verify the structure and its transitions of the flow. It is expected that the study will lead to useful insights to the understanding of the flow dynamics from both the mathematical and physical points of view.

Keywords

Divergence-free velocity vector; structural stability and bifurcation; symmetric stability; saddle connection

2010 Mathematics Subject Classification

35Q30, 35Q35, 65M06, 76D05

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