New exact solutions of the Charney–Obukhov equation for the ocean are obtained in the form of a partial superposition of elementary solutions with different wave numbers. The boundary conditions for the ocean are satisfied due to the presence of a carrier zonal flow in the solution. The existing arbitrariness in the choice of wave numbers and other solution parameters makes it possible to simulate an arbitrary stream function profile at a fixed ocean depth on an interval of a fixed length using a Fourier series or in a circle of a fixed radius using a Fourier–Bessel series. An example of modeling a Gaussian stream function profile on the ocean surface in the presence of circular symmetry is considered.

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