This talk presents a B-spline based conforming finite-element method of the streamfunction formulation of the one-layer stationary quasi-geostrophic equations for the study of the large scale wind-driven ocean circulation. We develop the variational form of the method and establish its consistency. The method weakly enforces Dirichlet boundary conditions and stabilization is achieved via Nitsche's method. Numerical tests for the method of the stationary quasi-geostrophic equations and its standard simplications (i.e., the linear Stommel and Stommel-Munk models) are preformed. By benchmarking the numerical results against those in the published literature, we conclude that our finite-element discretization is accurate. Furthermore, we perform convergence studies for the finite-element discretization using cubic B-splines.