This paper consider a class of perturbed mechanism for the western boundary undercurrents in the Pacific.The model of generalized governing equations is studied.Using the perturbation method,it constructs the asymptotic solution of the model.And the accuracy of asymptotic solution is proved by the theory of differential inequalities.Thus the uniformly valid asymptotic expansions of the solution are obtained. This paper consider a class of perturbed mechanism for the western boundary undercurrents in the Pacific. The model of generalized governing equations is studied. Using the perturbation method, it constructs the asymptotic solution of the model. And the accuracy of asymptotic solution is proved by the theory of differential inequalities. thus well-being asymptotic expansions of the solution are obtained.