Diagnosing Kinetic Energy Scaling Using Lagrangian and Eulerian Metrics in Different Dynamical Regimes of the North Atlantic

Abstract

Understanding the multiscale dynamics of ocean surface turbulence requires diagnostics that reliably characterize variability at scales both larger and smaller than the Rossby radius of deformation. This study evaluates the consistency and interpretability of second‐order velocity structure functions derived from Eulerian and Lagrangian frameworks using high‐resolution simulations of the North Atlantic. Synthetic surface drifters were deployed following a Sierpiński Carpet fractal pattern to achieve efficient scale‐aware Lagrangian sampling across seven dynamically distinct subdomains, while Eulerian diagnostics were computed from representative subsets of grid‐point pairs. Kinetic energy spectra and structure functions were compared across spatial scales to assess the agreement with theoretical expectations. The relationship between spectral and structure‐function slopes exhibits clear scale dependence: correlation between the two diagnostics is higher at scales larger than the Rossby radius, reflecting coherent mesoscale dynamics, whereas at smaller scales the correspondence weakens, although Lagrangian structure functions remain slightly more consistent with theoretical scaling expectations. Spectral slopes are generally steeper than structure‐function slopes, while Lagrangian slopes exceed Eulerian ones within the structure‐function framework. These results demonstrate that, when properly sampled, Lagrangian structure functions provide a robust and scalable complement to Eulerian analyses for diagnosing surface turbulence. The combined diagnostics reveal distinct turbulence regimes, with Gulf Stream regions characterized by flatter, frontal‐dominated scaling and regions outside the jet exhibiting steeper, quasi‐geostrophic behavior. Their joint use improves the interpretation of scale‐dependent energy distributions and strengthens the methodological foundation for future observational and modeling studies of upper‐ocean dynamics.