Attribution of horizontal and vertical contributions to spurious mixing in an Arbitrary Lagrangian–Eulerian ocean model

Abstract

We examine the separate contributions to spurious mixing from horizontal and vertical processes in an ALE ocean model, MOM6, using reference potential energy (RPE). The RPE is a global diagnostic which changes only due to mixing between density classes. We extend this diagnostic to a sub-timestep timescale in order to individually separate contributions to spurious mixing through horizontal (tracer advection) and vertical (regridding/remapping) processes within the model. We both evaluate the overall spurious mixing in MOM6 against previously published output from other models (MOM5, MITGCM and MPAS-O), and investigate impacts on the components of spurious mixing in MOM6 across a suite of test cases: a lock exchange, internal wave propagation, and a baroclinically-unstable eddying channel. The split RPE diagnostic demonstrates that the spurious mixing in a lock exchange test case is dominated by horizontal tracer advection, due to the spatial variability in the velocity field. In contrast, the vertical component of spurious mixing dominates in an internal waves test case. MOM6 performs well in this test case owing to its quasi-Lagrangian implementation of ALE. Finally, the

The Atlantic Meridional Overturning Circulation in High‐Resolution Models

“…Processes known or suspected to be important for diapycnal mixing (e.g., internal wave/tide breaking) are not yet resolved in global models and are either dealt with using parameterizations or are not represented at all (e.g., De Lavergne et al, ; MacKinnon et al, ; Nikurashin & Ferrari, ). In addition to deficiencies in the representation of diapycnal mixing, models using depth ( z ) coordinates are subject to undesired numerical mixing of various degrees (e.g., Griffies, Boning, et al, ; Lee et al, 2002; Ilicak et al, ; Megann, 2018; Gibson et al, ) which again affects the ability of models to develop/maintain the correct water mass structure.…”

“…However, in isopycnal models the diapycnal mixing must be parameterized, and parameterizing subkilometer overflow plume dynamics or interaction with subgrid scale bathymetry remains a challenge (Treguier et al, ). Other approaches such as Z‐tilde and ALE (Arbitrary Lagrandian Eulerian) coordinates are designed to reduce spurious mixing in the presence of high‐frequency vertical isopycnal movements (e.g., linked to internal tides or inertial waves) and to improve the flow over sills (e.g., Petersen et al, 2015; Reckinger et al, 2015; Gibson et al, ).…”

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“…) yields errors from the truncation and unresolved scales, and from the different numerical schemes and vertical coordinates (for example, Gibson et al. ). For example, there have been recent developments in stabilizing the computational mode of the commonly used leapfrog time‐stepping scheme using the Robert–Asselin–Williams (RAW) filter (Williams, ; ; ).…”

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“…The use of an ALE vertical coordinate is a way to mitigate this issue. Despite the fact that Gibson et al (2017) suggest that the vertical component of spurious mixing dominates as horizontal resolution increases it should not overshadow that many components of dynamical cores can be a source of numerical mixing (e.g. horizontal advection, time-stepping, the stabilization of the mode-splitting procedure).…”