Numerical simulation of flows with locally characteristic boundaries

Numerical modeling of oceanic circulation on synoptic scales leads to interesting boundary value problems. Data sets with sufficient spatial resolution to be useful for model initialization are usually restricted to limited areas. Consequently, open boundary models are required, but they do not appear to yield well-posed problems, and it is not clear how the schemes currently in use in ocean forecasting experiments perform under such circumstances. The difficulties which occur due to incompatibilities in the specification of boundary conditions may arise in cases in which the open region isembedded in a larger domain in which the flow is very smooth. These effectsare thus distinct from the development of discontinuities which form as a result of advection of nonuniform fields, i.e., kinematic frontogenesis. Thepractical effect of the results presented here is to emphasize the need forregular reinitialization of the forecast fields through some data assimilation process.

The difficulties with the boundary value problem are illustrated here through simple analytical examples, and through nonlinear numerical experiments using finite difference and finite element methods. The utility of numerical filters is examined. A review of relevant theoretical investigations is also presented.