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

Abstract

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. 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. We use two methods to estimate numerical mixing offline based on the residuals of the salinity squared s² and volume-mean salinity variance budgets. The budget overestimates the time-averaged online numerical mixing by 60% at hourly output. The s² budget compares poorly due to large truncation errors associated with the tendency and advection terms. The residual of the s² budget starts to converge to the budget as output frequency increases to 10 min—an unrealistic frequency for long-term coastal ocean simulations—but neither method unconditionally converges to the online method and therefore cannot be recommended for generic analysis of numerical mixing. We also investigate the effects of horizontal resolution on numerical mixing using a two-way nested grid with the online method. 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 numerical mixing is reduced by 35% on average in the nested model, likely due to new dynamical processes that emerge in the nested simulation.