Diagnosing the Fluxes and Distributions of Mesoscale Energy, Enstrophy and Other Variances using Structure Functions

Turbulent flows are characterized by the transport (or ‘cascade’) of properties, such as enstrophy and kinetic energy, between scales. Turbulence in the ocean thus provides a critical mechanism for getting energy and enstrophy from the length-scales of their injection to the scales of their removal (e.g. from baroclinic instabilities or wind stress to viscous dissipation or form drag). These cascade rates are often difficult to diagnose due to limited data, or due to the anisotropy, heterogeneity, and non-stationarity of ocean flows. This work will assess the potential of structure functions, which depend on spatial autocorrelations and are amenable to sparse data, as a tool for diagnosing the cascade rates of the ocean mesoscale using output from a hierarchy of numerical models. New structure function theories are developed to extend their utility to anisotropic flows. In addition to diagnosing cascade rates, we shall also investigate whether additional structure functions can quantify the scale-distribution of variances in mesoscale dynamics, providing a real-space alternative to power spectra.