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

Hsia, Chun-Hsiung; Liu, Jian-Guo; Wang, Cheng

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.

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