Formation of the f-plane quasi-geostrophic three-dimensional ocean circulation under wind-driven and the application of mass conservation

In this paper, we divide the idealized South China Sea basin into Ekman layer, inertial layer and friction layer in the vertical. Motion in the Ekman layer is driven by wind stress, and the perturbation pressure on the bottom will be the upper boundary condition of the inertial layer. Motion in the inertial layer is controlled by potential vorticity conservation derived from the f-plane three-dimensional nonlinear equation under quasi-geostrophic approximation, and then we can get the elliptic equation of the inertial layer. Considering that the horizontal-scale is small below the inertial layer, we introduce linear control equation with bottom friction. The upper boundary condition of the equation is that the perturbation pressure on the interface of the inertial layer and the friction layer is equal. Supposing that the sea water has no heat exchange with the wall, the temperature along the basin wall can be set to zero. From the aboving, we calculated every level' s perturbation pressure and quasi-geostrophic flow by using the ellipse equations in the inertial and friction layer. The results indicate that circulation in each level is cyclonic dominatingly, the velocity decreases with depth, however, there is anticyclonic circulation in summer. It's according with the observation in some degree.