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. 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.

Sensitivity of a Coarse‐Resolution Global Ocean Model to a Spatially Variable Neutral Diffusivity

“…In ACCESS‐OM2 the neutral diffusion operator is reduced to horizontal diffusion in the top surface layer (of thickness ∼2 m) and bottom topography grid cells (Ferrari et al., 2008; Treguier et al., 1997), meaning that the neutral diffusion parameterization can directly drive some dianeutral flux there, along with interactions with surface boundary layer turbulence and surface fluxes (de Lavergne et al., 2022). We also note that model implementations of rotated neutral diffusion are affected by various numerical discretization errors that can create spurious dianeutral fluxes that are nontrivial to quantify and are treated elsewhere (e.g., Beckers et al., 1998, 2000; Griffies et al., 1998; Groeskamp et al., 2019; Lemarié et al., 2012; Shao et al., 2020; Urakawa et al., 2020).…”

Coupled Aqua and Ridge Planets in the Community Earth System Model

“…To avoid the problems associated with layer thickness diffusion described by Holloway (1997), this scheme is implemented as an interface height diffusion. Following Solomon (1971) and Redi (1982), the second scheme represents the diffusive mixing of tracers along neutral surfaces, which is implemented using a finite-volume general-coordinate methodology (Shao et al, 2020). Again, a constant along-isopycnal tracer diffusivity of 2,000 m 2 s −1 is used.…”

Representing Eddy Diffusion in the Surface Boundary Layer of Ocean Models With General Vertical Coordinates

“…These experiments do not include dynamics and only neutral and horizontal diffusion are applied to the tracers (i.e., advection and vertical diffusion are turned off). The neutral diffusion algorithm is described in Shao et al (2020), and it is modified here to only act below z min ; neutral diffusion fluxes linearly increase from zero at z min to full strength at z max (see Section 2.2.3). Both, horizontal and neutral diffusion coefficients are set to 1,000 m 2 s −1 .…”

“…The neutral diffusion algorithm is described in Shao et al. (2020), and it is modified here to only act below z min ; neutral diffusion fluxes linearly increase from zero at z min to full strength at z max (see Section 2.2.3). Both, horizontal and neutral diffusion coefficients are set to 1,000 m 2 s −1 .…”

“…Furthermore, this tilt is determined dynamically, and it evolves in time. Although applying neutral diffusion in such models is also non-trivial, recently Shao et al (2020) have developed a neutral diffusion operator that is appropriate for this class of OGCMs. Therefore, only the horizontal diffusive part remains missing.…”