Sheared Stratified Turbulence and Mixing Across Geophysical Regimes: a DNS Database and Dimensional Framework

In the ocean and atmosphere, density-stratified turbulence and mixing span an extreme hierarchy of scales, from large energy-containing motions to fine dissipative structures far below the resolution of current Earth system models. Despite their central role in the climate system, such multi-scale dynamics are difficult to observe and fully sample in the field, and existing numerical simulations have only sparsely explored the parameter regimes of direct relevance to geophysical flows. Here we present the largest three-dimensional direct numerical simulations (DNS) to date of statistically stationary, shear-driven, stably stratified turbulence, and openly share the datasets alongside interactive download and visualization tools. These simulations, with resolutions of up to four trillion grid points, span a wide range of buoyancy Reynolds numbers and Prandtl numbers directly relevant to natural flows, exhibit energetic balances consistent with field and laboratory studies, and fully resolve velocity and buoyancy fields across more than four orders of magnitude in length. Flow visualizations reveal strong scale separation, self-organization, anisotropy, intermittency, and localized regions of intense dissipation and mixing that bear on the interpretation of field observations and the development of model parameterizations. We introduce a practical dimensional framework that uses measured or model-resolved stratification and dissipation, together with fluid properties, to identify compatible simulations and recover unresolved turbulent length scales and fluctuation amplitudes across oceanic and atmospheric regimes.