A simple, stable and accurate Dirichlet open boundary condition for ocean model downscaling

Dirichlet, or clamped, open boundary conditions are known for their reflective behaviour, and not normally recommended for use as open boundary conditions. However, when applied to 3D velocity fields using an implementation that leaves the elevation unconstrained, and linear terms in the momentum equations uninfluenced by the normal velocity boundary values, a robust and accurate scheme results. Here we present such a scheme and apply it within a 3D baroclinic regional coastal ocean model. The method is only applicable to situations where the boundary may be forced actively. Additionally, a local flux adjustment is required to prevent the total domain volume drifting over time. The local flux adjustment is non-steady, and allows local volume changes to occur in both time and space throughout the domain. The scheme is tested in an idealised domain and two realistic cases to demonstrate its functionality. Results show that there is no energy build-up within the domain or spurious boundary re-circulations, and volume is conserved.