Analysis of Schwarz waveform relaxation for the coupled Ekman boundary layer problem with continuously variable coefficients

In this paper, we present a global-in-time non-overlapping Schwarz method applied to the Ekman boundary layer problem. Such coupled problem is representative of large-scale atmospheric and oceanic flows in vicinity air-sea interface. waveform relaxation (SWR) algorithms provide attractive methods for ensuring “tight coupling” between ocean atmosphere. However, convergence study such context raises number challenges. Numerous studies have been carried out idealized settings, but underlying assumptions make these tractable may prohibit them be directly extended complexity climate models. We illustrate aspect on problem, which includes several essential features inherent modeling while being simple enough analytical results derived. investigate its well-posedness derive an appropriate SWR algorithm. Sufficient conditions different viscosity profiles are then established. Finally, relevance our theoretical analysis with numerical suggest ways improve computational cost coupling. Our emphasizes fact that properties can highly sensitive some model characteristics as geometry use continuously variable coefficients.