  In this study we present a non-overlapping Schwarz waveform relaxation (SWR)
method applied to a one dimensional model problem representative of the
coupling between the ocean and the atmosphere. This problem includes nonlinear
interface conditions analogous to a quadratic friction law. We study the
convergence of the corresponding SWR at a semi-discrete level for a linear
friction and for a linearized quadratic friction at the interface. Using
numerical experiments we show that the convergence properties in the linearized
quadratic friction case are very close to the ones obtained with the full
nonlinear problem for the range of parameter values of interest. We investigate
the possibility to improve the convergence speed by adding a relaxation
parameter at the interface.
