Structure Function Statistics to Detect Submesoscale Cascades

Lagrangian trajectories coupled with pairwise velocity and tracer statistics are an important piece in unraveling the complexities of mesoscale, submesoscale and boundary layer turbulence. Typical characterizations of turbulence are often theoretically attainable under certain simplified assumptions and conditions, but they are often hard to apply with current methods because of gaps or irregularities in observations. Many observational platforms provide measurements at separated, random locations within a turbulent flow. This presentation analyzes the structure function statistics obtained from these measurements toward identifying classes of turbulence.In varying submesoscale models where forward and inverse kinetic and potential energy cascades, vigorous internal gravity waves, fronts, filaments, and mixed layer eddies are directly diagnosed, we simulate drifter observations of velocity and tracers. Through this analysis, optimization of array size, sampling, and uncertainty can be made rigorous. Different classes of turbulence (3d, 2d, quasigeostrophic, wave, and Langmuir) can be distinguished using these techniques with sufficient numbers of pairs at varying scales. General scaling laws, such as the Richardson scaling, tend to arise under certain types of averaging for many distinct classes of turbulence. Future work will refine the use of higher order structure functions and turbulence characterizations in anisotropic and heterogeneous settings.