An Open Boundary Condition for Numerical Coastal Circulation Models

Abstract

Open boundaries (OBs) are usually unavoidable in numerical coastal circulation simulations. At OBs, an appropriate open boundary condition (OBC) is required so that outgoing waves freely pass to the exterior without creating reflections back into the interior of the computational domain. In this paper, the authors derive, based on the shallow-water equations including bottom friction and neglecting Coriolis effect and by means of nonlinear characteristic analysis, an OBC formulation with two predictive parameters, phase speed c[subscript r], and decay time T[subscript f]. Simple idealized tests are performed to demonstrate the proposed OBC’s excellent skills in elimination of unwanted reflections at OBs when the motion is periodic, as assumed in its theoretical derivation. It turns out that the formulas for the two OBC parameters become independent of period in the limit of small friction and/or short period. This feature is used to derive an OBC applicable when information about the typical period of the motion to be simulated is unavailable. Simple, idealized tests of this period independent OBC demonstrate its ability to afford excellent results, even when the limitations inherent in its derivation are exceeded. Finally, the OBC is applied in more realistic simulations, including Coriolis effects of 2D tidal flows, and is shown to yield excellent results, especially for residual flows.