Submesoscale Eddy Vertical Correlations and Dynamical Constraints from High-Resolution Numerical Simulations

The Surface Water Ocean Topography (SWOT) satellite will observe surface elevation due to small-scale features on a global scale for the first time. The relationship between these small-scale surface expressions and their underlying depth structure remains poorly understood. We analyze yearlong, high-resolution (1 km) numerical simulations of the western Pacific, Gulf of Mexico, and Arabian Sea to quantify these dynamics. Large- and small-scale fields are separated using a spatial filter with length scale based on the regional Rossby radius of deformation. A mask based on the Okubo-Weiss parameter isolates submesoscale eddies. In each region, the number of submesoscale eddies is correlated with the depth of the area-averaged mixed layer. The cyclonic eddies consistently dominate the number of submesoscale eddies. Submesoscale eddy vertical correlations are concentrated within the mixed layer and have vertical scales that are smaller than the mesoscale. Submesoscale cyclonic (anticyclonic) eddies exhibit a classic eddy vertical depth structure, whereby temperature anomalies from the large-scale background are negative (positive) and adjust isopycnals upwards (downwards) implying an approximate geostrophic balance. A two-dimensional submesoscale dynamical constraint is proposed and tested. When using small-scale sea surface height (SSH), including velocity tendency and advection produces lower errors than the simple geostrophic assumption. In regions with strong tides and associated internal waves (western Pacific & Arabian Sea), using the mixed layer integrated small-scale steric height within the dynamical equations produces the lowest magnitude errors. In areas with weak tides (Gulf of Mexico), using small-scale SSH produces the lowest magnitude errors. Though the largest variability associated with submesoscale eddies is in the mixed layer, integration through much deeper layers is required to recover a submesoscale eddy with the correct magnitude and rotation.