Evaluating Turbulence Parameterizations at Gray Zone Resolutions for the Ocean Surface Boundary Layer

Turbulent mixing in ocean boundary layers is often fully parameterized as a subgrid-scale process in realistic ocean simulations. However, recent submesoscale modeling studies have advanced to a horizontal grid spacing of $O$(10 m) that is comparable to, or even smaller than, the typical depth of the turbulent surface boundary layer. Meanwhile, efforts toward realistic large-eddy simulations (LES) nested within regional models require subdomains with similar grid spacings, where turbulent eddies are partially resolved in the mixed layer. The range of intermediate grid spacings, often known as the “gray zone,” presents challenges for model configuration and analysis, including uncertainties regarding the behavior of common turbulence closures outside of their ideal use cases. In this study, we evaluate three common configurations for subgrid turbulence—$k$-$ϵ$, Smagorinsky, and an implicit no-closure method—in the gray zone resolutions for the ocean surface mixed layer. Results indicate that, in the gray zone with partially resolved boundary layer turbulence, $k$-$ϵ$ can produce accurate mixed layer profiles with little sensitivity to grid spacing. However, it overly damps turbulent motions, significantly reducing small-scale variability that could otherwise be captured. The Smagorinsky closure and the implicit method, in contrast, exhibit higher sensitivity to grid spacing, initially performing poorly but converging toward baseline solutions at finer grids. Our findings provide guidance for submesoscale and turbulent-scale modeling, recommending Smagorinsky or implicit methods for nested domains which prioritize resolved turbulence, such as LES. The $k$-$ϵ$ closure is suitable for simulations that aim to achieve accurate mean-state representations rather than explicitly resolving detailed three-dimensional turbulence.