A new integration of Munk's linear model of wind-driven ocean circulation

The integration of Munk's model of wind-driven ocean circulation depends critically on the additional conditions which are applied to the boundary of the fluid domain. On the other hand, the linear nature of this model implies the validity of the Sverdrup balance, with the consequent formation of the Sverdrup transport, in the eastern region of the oceanic basins. Thus, the circulation patterns must be consistent with the Sverdrup transport which, in turn, is quite independent of any additional condition. In the present paper, just this request of consistency is expressed in mathematical form, which leads, unlike all the existing models, to the derivation of two additional conditions, both being referred to the eastern wall of the reference basin and depending on the form of the forcing field. Thus, no additional condition is applied to the western boundary. Then, Munk's model is integrated in the presence of a class of wind-stress curls, which depend on a free parameter while, for conceptual simplicity, the eddy viscosity coefficient is taken constant. By suitably varying the parameter, we see how the forcing field determines the additional conditions and, hence, also the structure of the western boundary layer. Finally, the nonlinear stability, with respect to a suitably norm, of the so-obtained model solutions is proved.