Third-order WENO transport scheme for simulating the baroclinic eddying ocean on an unstructured grid

摘要

Despite the recent success achieved by the unstructured-grid SCHISM (Semi-implicit Cross-scale Hydroscience Integrated System Model) in multi-resolution studies, its skill in simulating the baroclinic eddying ocean needs to be further improved. In particular, the classical 2nd-order transport schemes for estuaries and coastal zones are too dissipative to resolve the baroclinic dynamics associated with strong boundary currents, such as meso-scale meanders and eddies. To close this gap, this paper presents a newly designed 3rd-order finite volume transport scheme, based on the Weighted Essentially Non-Oscillatory (WENO) formalism. This new scheme strikes a delicate balance among accuracy, efficiency, and monotonicity for the transport in the eddying regime. Idealized numerical benchmark experiments demonstrate that the WENO scheme is very effective in limiting numerical diffusion. The scheme is then applied in a realistic simulation of the Gulf Stream and the surrounding circulation, further confirming its capability of resolving baroclinic meso-scale eddies and meanders. This new high-order transport scheme is therefore ideal for extending the ability of SCHISM to study cross-scale baroclinic applications that range from the river dynamics to the eddying ocean processes.