This talk will consider, for a greatly simplified version of the dynamic core of coupled ocean-atmosphere climate models, two issues that arise in its approximate solution. The first issue is how to couple across the ocean-atmosphere interface ocean codes and atmosphere codes. The ocean and atmosphere have greatly different time and space scales. The complexity of the numerous parameterizations of physical processes has led the individual models to be described as having -Y“brittle bone syndrome” (J. Boyd in SIAM News). With these factors in mind, we consider partitioned time stepping methods in which the coupled problem can be solved by solving alternately the uncoupled sub problems and passing fluxes across the interface. We gave a new method of doing this that is unconditionally stable and allows different time steps in the atmosphere and ocean. The second issue is concerned with turbulence. In 1960 (already) J. Smagorinsky noted that a fundamental question is “How does the fluid velocity produced from a numerical simulation on a fixed grid communicate with molecular viscosity?” Many ways have been tried to do this. The second part of the talk will present a fairly new approach based on filter based stabilization for evolution equations. The approach of “evolve then filter” is very attractive for complex simulations as it is modular (can be added to, e.g., a black box atmosphere code as an independent module) , systematic and parallel. The work described in this talk is joint with Monika Neda (UNLV), Vince Ervin (Clemson Univ.) and Jeff Connors (U Pittsburgh).