Open boundary conditions for nonlinear channel flow

Open boundary conditions are derived for the one-dimensional nonrotating two-layer shallow-water equations. The conditions are based on characteristics of the external and internal modes. It is possible to find exact nonlinear characteristic conditions for the external mode, as well as approximate nonlinear conditions for the internal mode. These conditions can also be linearised by Taylor expansion; the approximate linear conditions are similar to those used in several previous studies. Both of the nonlinear and linearised conditions perform well, indicating that either the nonlinear or linearised conditions may potentially be extended to the more general case of multi-layer flows.