Earth system models are composed of coupled components that separately model systems such as the global atmosphere, ocean, and land surface. While these components are well developed, coupling them in a single system can be a signiIcant challenge. Computational efficiency, accuracy, and stability are principal concerns. In this study we focus on these issues. In particular, implicit–explicit (IMEX) and Multirate coupling strategies are explored for handling different time scales. For a simplified model for the air–sea interaction problem, we consider coupled Navier–Stokes equations with an interface condition. Under the rigid-lid assumption, horizontal momentum and heat flux are exchanged through the interface. Several numerical experiments are presented to demonstrate the stability of the coupling schemes.