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Structural stability and bifurcation for 2-D incompressible flows with symmetry. (English) Zbl 1180.35410

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.

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
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