  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
significant challenge. Computational efficiency, accuracy, and stability are
principal concerns. In this study, we focus on these issues. In particular,
implicit-explicit (IMEX) tight and loose coupling strategies are explored for
handling different time scales. For a simplified model for the air-sea
interaction problem, we consider coupled compressible 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.
We show both numerically and theoretically that our IMEX coupling methods are
mass conservative for a coupled compressible Navier-Stokes system with the
rigid-lid condition.
