Open boundary conditions in stratified ocean models

In most applications of numerical ocean models, artificial boundaries are introduced to limit the domain. Along such a boundary we need to apply what is often referred to as an open boundary condition (OBC). In this paper a number of local methods used in barotropic ocean models are applied and discussed for the stratified case using a normal mode approach. The OBCs are the simple conditions: clamped, prescribed and zero gradient; the radiation conditions: Camerlengo–OʹBrien, Orlanski and a method of characteristics based on linear equations; and a sponge type condition: the flow relaxation scheme. The OBCs have been implemented in a 3-layer ocean model and examples of how the various OBCs perform for three simple flow situations are investigated. The cases are: internal wave radiation, a quasi-steady coastal jet and the response to a storm moving across a strait. It is found that the flow relaxation scheme and the method based on characteristics perform well for the test cases in general, although some of the simpler methods give better results in individual cases.