Quantification of Physical and Numerical Mixing in a Coastal Ocean Model Using Salinity Variance Budgets

Journal Article · 16 April 2023 · Journal of Advances in Modeling Earth Systems

DOI: https://doi.org/10.1029/2022ms003380 · OSTI ID:1983586

Schlichting, Dylan  ^[1]; Qu, Lixin  ^[2]; Kobashi, Daijiro  ^[1]; Hetland, Robert D.  ^[3]

---

1. Texas A&M University, College Station, TX (United States)
2. Shanghai Jiao Tong University (China)
3. Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)

Numerical mixing, the spurious mixing primarily generated by the discretization of advection, is often significant in estuarine and coastal models due to sharp, energetic fronts. In this study, we compare on- and offline estimates of numerical mixing in a submesoscale-resolving realistic simulation of the ocean state over the Texas-Louisiana continental shelf. While offline estimates of numerical mixing differ from online estimates, offline methods may be the only analysis available. This study offers insight into the differences between the on- and offline methods. We use two methods to estimate numerical mixing offline, based on salinity squared $s^2$ and volume-mean salinity variance $$s^{\prime^2}$$. Numerical mixing estimated from the $$s^{\prime^2}$$ budget is generally within 60\% of the magnitude for the online method but captures the temporal variability well. However, the $s^2$ budget compares poorly due to larger truncation errors associated with the tendency and advection terms, which can be reduced by increasing the model output frequency. We also investigate the effects of horizontal resolution on numerical mixing using a two-way nested grid. The volume-integrated numerical mixing constitutes 57\% of the bulk physical mixing -- the mixing prescribed by the turbulence closure scheme -- in the coarse model and may exceed the physical mixing by half an order of magnitude. We find that numerical mixing is reduced by 35\% on average in the nested model, less than expected based on scaling of the numerical mixing for an upwind advection scheme, likely due to new dynamical processes that emerge in the nested simulation.

• Research Organization: Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), Biological and Environmental Research (BER)
• Grant/Contract Number: AC05-76RL01830
• OSTI ID: 1983586
• Report Number(s): PNNL-SA-181725
• Journal Information: Journal of Advances in Modeling Earth Systems, Journal Name: Journal of Advances in Modeling Earth Systems Journal Issue: 4 Vol. 15; ISSN 1942-2466
• Publisher: American Geophysical Union (AGU)Copyright Statement
• Country of Publication: United States
• Language: English