A General-coordinate, nonlocal neutral diffusion operator




Shao, Andrew E.
Adcroft, Alistair
Hallberg, Robert
Griffies, Stephen M.

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The Journal of Advances in Modeling Earth Systems


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. Plain Language Summary One prominent effect of ocean turbulence is the mixing of quantities such as temperature, salinity, and other tracers carried by the seawater. For turbulence associated with geostrophic motions, this mixing occurs along neutral directions, which are directions where buoyancy does not change. In computer models that do not explicitly represent such geostrophic eddy motions, this type of turbulent mixing is parameterized by diffusion oriented along the neutral directions. A common means to represent neutral diffusion is via rotating the diffusion fluxes to align with neutral directions (which are typically not aligned with the model grid lines). Unfortunately, this rotation can result in spurious numerical artifacts such as the creation of new minimum or maximum values of tracer concentration (referred to as extrema). In this paper, we propose a new algorithm for calculating and applying neutral diffusion in sublayers of a numerical model. We show that this new method does not create extrema, and it provides a physically accurate representation of turbulent diffusive mixing along neutral directions.


We thank Sjoerd Groeskamp for discussions about their nonlocal observation-oriented approach in Groeskamp et al. (2019) and Bill Large for discussions on how to estimate the spurious diffusivity. We thank Brandon Reichl and Marshall Ward for providing feedback on an early draft of the manuscript. Lastly, we express our gratitude to George Nurser and two other anonymous reviewers for their constructive comments that greatly improved the manuscript. The statements, findings, conclusions, and recommendations are those of the authors and do not necessarily reflect the views of the National Oceanic and Atmospheric Administration, or the U.S. Department of Commerce.



Shao, A., Adcroft, A., Hallberg, R., & Griffies, S. M. (2020). A general‐coordinate, nonlocal neutral diffusion operator. Journal of Advances in Modeling Earth Systems, 12(12). https://doi.org/10.1029/2019ms001992