For a closed basin, the lateral boundary conditions are quite straightforward. The conditions of zero mass, momentum, heat, salt and turbulence fluxes must be satisfied at a solid lateral boundary. However, at open boundaries, the influence of the region exterior to the model domain must be specified in one form or another. Open lateral boundary conditions are therefore the hardest to prescribe, since the external conditions are usually unknown. If sufficient observational data exist at the open boundary or conditions there are known from another model containing the exterior region, it would not be a problem to prescribe the lateral boundary conditions. But these conditions are seldom satisfied and various approximations, some more close to reality than others, need to be made. In general, the model results are usually only as good as the prescribed lateral boundary conditions and sufficient care must be exercised to assure that the prescription leads to meaningful results.
Nevertheless, it is possible to lay down some general rules. As far as scalars , S, and l are concerned, whether there is inflow or outflow determines the form of the lateral boundary conditions. When there is inflow, and S need to be prescribed, while for outflow, and S need to be advected out:
where n denotes the coordinate normal to the lateral boundary. As far as and l are concerned, it is fairly accurate to ignore any advection at the lateral boundaries.
Prescription of mass and momentum conditions at an open boundary is more difficult, since this is really a function of the interaction with the exterior domain, which is a priori unknown when modeling a limited region. Nevertheless, inflow and outflow must be specified somehow as a function of time. The most important requirement is to satisfy the mass balance. Thus open boundary conditions must be specified such that there is no net mass increase over a specified period of time. For tidal (or barotropic) calculations, the free surface elevation may be prescribed on the boundary. Often a Sommerfeld radiation condition of the form
is used, where is any quantity such as , , ... and c is the phase speed of a disturbance approaching the boundary from the interior of the domain. Equation (66) is designed to not bottle up transient disturbances generated inside. However its application is often not unambiguous, especially since the phase speed of the disturbance is not known a priori and also it is difficult to decide which disturbances should be propagated out. One strategy to alleviate the former is to compute the phase speed in the interior immediately adjacent to the open boundary from the interior solutions and use it in equation (66). This is the so-called Orlonski approach . Its application requires considerable care since it can lead to very noisy values for c, which in turn can affect the interior solutions .
It is important to remember that conditions such as equation (66) are no substitutes for knowing how the exterior region is effecting the open lateral boundary conditions.