Second-order velocity structure functions at submesoscales

Observations of ocean surface currents from the JPL Doppler Scatterometer (DopplerScatt) during the S-MODE campaignsreveal unexpectedly shallow second-order velocity structure function (SF) slopes at submesoscale separation scales (𝑟 < 10 km), deviatingfrom classical turbulence theory and prior modeling results. This discrepancy suggests missing physics in current submesoscale-resolvingnumerical ocean models or an incomplete interpretation of the DopplerScatt observations. To investigate this, we analyze high-resolutionRegional Ocean Modeling System (ROMS) simulations across a range of configurations that isolate the influence of model resolution,season, high-frequency forcings, and surface gravity wave effects on currents. We find that high-frequency motions associated withnear-inertial waves reduce the transverse SF amplitude, driving the ratio of longitudinal to transverse SFs close to unity at submesoscalesindependently of the season. Additionally, the inclusion of wave-current interactions, often omitted in standard submesoscale-resolvingmodels, can produce energetic small-scale motions, leading to broadband shallow structure function slopes. These results reveal a broadermechanism by which shallow structure function slopes can emerge: any process that injects kinetic energy at small scales over a narrowrange of wavenumbers will appear broadband in structure function space and produce shallow scalings. Wave effects are one such candidateand offer a plausible interpretation of the DopplerScatt observations under energetic wave conditions. However, under low wave conditions,other processes with similar spectral characteristics are required to account for the observed shallowness. Finally, the relatively largetransverse-to-longitudinal SF ratio in DopplerScatt may reflect its lateral averaging over part of an inertial period, a sampling strategy notreplicated in models and warranting further study.