Stability Analysis of Coupled Advection-Diffusion Models with Bulk Interface Condition

Numerical stability is of critical importance in general circulation models because it affects the design of algorithms, time to solution, and computational costs associated with the simulations, which are very expensive in practice. In this paper we extend the stability analysis for ocean-atmosphere coupling proposed in [Zhang et al., J. Sci. Comput. 84, 44(2020)] to a more realistic model that includes horizontal advection. We analyze various time-stepping strategies. We find that advection has a stabilizing effect in scenarios common to climate models when bulk interface condition and explicit flux coupling are used. We also show that our method can be used to study the stability impact of advection for other interface conditions such as Dirichlet–Neumann conditions.