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The main objectives of this paper are to adapt an efficient and accurate spectralprojection method for a wind-driven, double-gyre, mid-latitude, quasi-geostrophic ocean model, and to study the double-gyre phenomenon from numerical and structural analysis points of view. A number of numerical simulations are carried out and their structural stability and structural transition/bifurcation are investigated using a new dynamical systems theory of two-dimensional incompressible flows.