Based on the nonlinear ocean vorticity equation derived by Constantin and Johnson (see [9]), this paper derives a vorticity equation incorporating variable eddy viscosity through the selection of appropriate parameters and suitable asymptotic approximations. The exact solution of the equatorial vorticity equation for the Pacific between \(160^{\circ }\) E and \(80^{\circ }\) W is provided, while a set of cubic functions is employed to describe the easterly jet stream above the thermocline \(z=-T\) in close proximity to the surface of the Equator, as well as the westerly strong jet stream near \(z=0\) . Moreover, we obtain the expression of the corresponding pressure field.
