Open AccessA General‐Coordinate, Nonlocal Neutral Diffusion Operator
Author(s) -
Shao Andrew E.,
Adcroft Alistair,
Hallberg Robert,
Griffies Stephen M.
Publication year - 2020
Publication title -
journal of advances in modeling earth systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.03
H-Index - 58
ISSN - 1942-2466
DOI - 10.1029/2019ms001992
Subject(s) - isopycnal , stencil , maxima and minima , discretization , advection , diffusion , diffusion equation , operator (biology) , grid , flux (metallurgy) , mathematical analysis , nonlinear system , physics , mathematics , geometry , geology , biochemistry , chemistry , economy , materials science , service (business) , repressor , climatology , quantum mechanics , gene , transcription factor , metallurgy , economics , thermodynamics
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.