Boundary Layers in an Ocean Related System

The Primitive Equations of the ocean and the atmosphere are fundamental equations of geophysical fluid mechanics [10,15]. In the presence of viscosity, it has been shown—in various contexts—that these equations are well-posed (see e.g., [7,8], and the review article [14]). In the absence of viscosity, it is known that the PEs are not wellposed for any set of boundary conditions of local type. This difficulty is analyzed in [9] using a modal analysis in the vertical direction (see also [13]). To overcome this difficulty a modification of the PEs was proposed in [13], for which a set of local boundary conditions also given in [13] produces a decay of energy (in the absence of forcing), an important positive step in proving well-posedness. The modified PEs introduced in [13] contain an added friction term δw in the hydrostatic equation, so that the model is actually nonhydrostatic; we will call this system the δ-PEs equations.