Although the two-way nesting is the most usual coupling method in the ocean community, it does not address the correct problem but an approximation, and does not ensure enough regularity through the interface between the two models1. The correct approach consisting in a full coupling is more difficult and expensive than the two-way nesting, since it requires to find and implement an algorithm ensuring that the solutions in each domain satisfy the regularity conditions through the interface. The global-in-time non-overlapping Schwarz algorithm is particularly well suited for such a coupling, and can lead to improved physical results. Our work thus aims at improving the ocean coupling by determining efficient interface conditions for the usual ocean equations (the so-called 3-D primitive equations). These ones are composed of advection-diffusion equations for tracers such as temperature and salinity, and dynamics equations, which can be approximated in the 2-D case by the shallow-water equations.