Statistics of curvature in the submesoscale surface ocean

Leo Middleton , Andrey Y. Shcherbina , J. Thomas Farrar

Ocean submesoscale (1--10\,km) variability is hypothesised to contribute substantially to upper-ocean vertical exchange and heat fluxes, but the three-dimensional turbulent nature of the variability makes it difficult to interpret submesoscale variability dynamically. Statistics of velocity gradients are often analyzed to characterize the nature of submesoscale dynamics. Previous analyses show that intense convergence is concentrated in strain-dominated regions and have commonly associated these regions with fronts; however, straining can have many different forms, so strain dominance is not uniquely diagnostic of frontogenesis. Here, we introduce a flow-following (natural-coordinate) decomposition of the horizontal velocity gradients that separates vorticity and divergence into four components: shearing, curving, extension, and confluence/diffluence. We apply this decomposition to airborne Doppler scatterometer surface velocities, surface drifter trajectories, and a data-assimilating Navy Coastal Ocean Model simulation from the Submesoscale Ocean Dynamics Experiment (S-MODE). Across these datasets we find a pronounced cyclonic asymmetry not only in vorticity but also in its shearing and curving, implying that submesoscale strain asymmetry reflects both shear-dominant and curvature-dominant kinematics. Using idealised representations of surface quasi-geostrophic dynamics, Garrett--Munk internal waves, and wind-driven inertial oscillations, we show that these processes occupy distinct regions of the joint distributions, providing a conceptual dynamical basis for interpreting observed velocity-gradient statistics.