I shall present in this talk a joint work with T. Ma on structure analysis of 2D incompressible flows and its applications to ocean dynamics. The main motivation is to understand the topological and geometrical structure of the Lagrange dynamics of two-dimensional incompressible fluid flows. On the theoretical side, I shall address 1). the global structural classification of divergence-free vector fields, 2). structural and block stability of divergence-free vector fields, 3) structural bifurcation of the solutions of the 2D Navier-Stokes equations. Then I shall apply the dynamical systems theory to the structure analysis of a wind-driven, double gyre, quasi-geostrophic ocean model, and the relavant numerical simulation is also given.

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