Numerical Mixing Suppresses Submesoscale Baroclinic Instabilities Over Sloping Bathymetry

Abstract

The impacts of spurious numerical salinity mixing $\left(M_{\mathrm{num}}\right)$ on the larger-scale flow and tracer fields are characterized using idealized simulations. The idealized model is motivated by realistic simulations of the Texas-Louisiana shelf and features oscillatory near-inertial wind forcing. $M_{\mathrm{num}}$ can exceed the physical mixing from the turbulence closure $\left(M_{\mathrm{phy}}\right)$ in frontal zones and within the mixed layer. This suggests that simulated mixing processes in frontal zones are driven largely by $M_{\mathrm{num}}$. Near-inertial alongshore wind stress amplitude is varied to identify a base case that maximizes the ratio of $M_{\mathrm{num}}$ to $M_{\mathrm{phy}}$ in simulations with no prescribed horizontal mixing. We then test the sensitivity of the base case with three tracer advection schemes (MPDATA, U3HC4, and HSIMT) and conduct ensemble runs with perturbed bathymetry. Instability growth is evaluated using the volume-integrated eddy kinetic energy $\left(EKE\right)$ and available potential energy $\left(APE\right)$. While all schemes have similar total mixing, the HSIMT simulations have over double the volume-integrated $M_{\mathrm{num}}$ and 20% less $M_{\mathrm{phy}}$ relative to other schemes, which suppresses the release of $APE$ and reduces the $EKE$ by roughly 25%. This results in reduced isohaline variability and steeper isopycnals, evidence that enhanced $M_{\mathrm{num}}$ suppresses instability growth. Differences in $EKE$ and $APE$ between the MPDATA and U3HC4 simulations are marginal. However, the U3HC4 simulations have 25% more $M_{\mathrm{num}}$. Experiments with variable horizontal viscosity and diffusivity coefficients show that small amounts of prescribed horizontal mixing improve the representation of the ocean state for all advection schemes by reducing the $M_{\mathrm{num}}$ and increasing the $EKE$.