A General-Coordinate, Nonlocal Neutral Diffusion Operator

Abstract

We present a neutral diffusion operator appropriate for an ocean model making use of general vertical coordinates. The diffusion scheme uses polynomial reconstructions in the vertical, along with a horizontally local but vertically nonlocal stencil for estimates of tracer fluxes. These fluxes are calculated on a vertical grid that is the superset of model columns in a neutral density space. Using flux-limiters, the algorithm dissipates tracer extrema locally, and no new extrema are created. A demonstration using a linear equation of state in an idealized configuration shows that the algorithm is perfectly neutral. When using the nonlinear TEOS-10 equation of state with a constant reference pressure, the algorithm compares nearly exactly to a case discretized onto isopycnal surfaces and using along-layer diffusion. The algorithm's cost is comparable to that of tracer advection and can be readily implemented into ocean general circulation models.