Hsia, Chun-Hsiung; Liu, Jian-Guo; Wang, Cheng Structural stability and bifurcation for 2-D incompressible flows with symmetry. (English) Zbl 1180.35410 Methods Appl. Anal. 15, No. 4, 495-512 (2008). Summary: 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. Cited in 2 Documents MSC: 35Q30 Navier-Stokes equations 35Q35 PDEs in connection with fluid mechanics 76D05 Navier-Stokes equations for incompressible viscous fluids 76M20 Finite difference methods applied to problems in fluid mechanics 76E20 Stability and instability of geophysical and astrophysical flows 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction Keywords:divergence-free velocity vector; structural stability and bifurcation; symmetric stability; saddle connection PDF BibTeX XML Cite \textit{C.-H. Hsia} et al., Methods Appl. Anal. 15, No. 4, 495--512 (2008; Zbl 1180.35410) Full Text: DOI Euclid OpenURL