Diapycnal Mixing and Tracer Dispersion in a Terrain-Following Coordinate Model

Diapycnal mixing, driven by small-scale turbulence, is crucial for the global ocean circulation, particularly for the upwelling of deep water masses. However, accurately representing diapycnal mixing in ocean models is challenging because numerical errors can introduce significant numerical mixing. In this study, we explore the diapycnal mixing in a high-resolution regional model of the North Atlantic subpolar gyre using the Coastal and Regional Ocean Community model (CROCO). CROCO uses terrain-following vertical coordinates that do not align with isopycnals. As such, tracer advection schemes produce spurious diapycnal mixing, which can nonetheless be reduced using rotated advection schemes. We focus on how different advection schemes and vertical resolutions affect numerical diapycnal mixing. Our approach includes online diagnostics of buoyancy fluxes and tracer release experiments to quantify the effective mixing, which combines parameterized and numerical diapycnal mixing. Our main results show that in flat-bottom regions, the effective diapycnal mixing is close to the parameterized mixing. However, in regions with steep topography, numerical mixing can locally significantly exceed parameterized mixing due to grid slope constraints imposed by the rotated mixing operator. While topography smoothing can mitigate this excessive mixing, it can also alter flow-topography interactions. In addition, while a higher vertical resolution reduces the numerical mixing induced by the vertical tracer advection, it can also increase numerical mixing in steep regions by introducing a stronger constraint on the grid slope. These results underscore that diapycnal mixing representation in a numerical model requires balancing high resolution and topographic smoothing with the control of numerical errors.