The interactions between atmosphere and ocean play a major role in many geo-physical phenomena, covering a wide range of temporal scales (e.g. diurnal cycle, tropical cyclones, global climate...). Therefore the numerical simulation of such phenomena require coupled atmospheric and oceanic models, which properly represent the behavior of the boundary layers encompassing the air-sea inter-face and their two-way interactions. We propose to couple such systems through a Schwarz iterative algorithm. In this talk we focus on a one dimension diffusion type coupling problem which can approach a simplified ocean-atmosphere coupling. The effects of turbulent boundary layers near interfaces are parameterized using a spatially variable viscosity coefficient. We will first study the impact of the Coriolis effect and the no-constant viscosity on chwarz algorithm convergence. Then we will explain what difficulty appears when we're approaching to realistic ocean-atmosphere coupling.