Understanding processes associated with eddy-mean flow interactions helps our interpretation of ocean energetics, and guides the development of parameterizations. Here, we focus on the non-local nature of Kinetic Energy (KE) transfers between mean and turbulent reservoirs. Transfers are interpreted as non-local when the energy extracted from the mean flow does not locally sustain an growth of energy in the turbulent flow, or vice versa. The novelty of our approach is to use ensemble statistics to define the mean and the turbulent flow. Based on KE budget considerations, we first rationalize the eddy-mean separation in the ensemble framework, and discuss the interpretation of a mean flow driven by the prescribed (surface and boundary) forcing and a turbulent flow u′ driven by non-linear dynamics sensitive to initial conditions. We then analyze 120-day long, 20-member ensemble simulations of the Western Mediterranean basin run at resolution. Our main contribution is to recognize the prominent contribution of the cross energy term to explain non-local energy transfers, which provides a strong constraint on the horizontal organization of eddy-mean flow KE transfers since the cross energy term vanishes identically for perturbations orthogonal to the mean flow . We also highlight the prominent contribution of vertical turbulent fluxes for energy transfers within the surface mixed layer. Analyzing the scale dependence of non-local energy transfers supports the local approximation usually made in the development of meso-scale, energy-aware parameterizations for non-eddying models, but points out to the necessity of accounting for non-local dynamics in the meso-to-submeso scale range.

Key Points

Ensemble-based eddy-mean decomposition of kinetic energy budget supports the view of an ocean turbulence driven by internal dynamics

Turbulent fluxes of the cross energy term provide a potentially strong horizontal constraint on eddy-mean flow interactions

Non-localities are leading order at small scales and should be accounted for in submesoscale parameterizations

Plain Language Summary

The ocean constantly exchanges energy between its mean and its turbulent reservoirs. However, we are still lacking a clear understanding of eddy-mean flow interactions, which limits our ability to represent them in numerical ocean simulations that require turbulent closures. In particular, it has been recently shown that instabilities of midlatitude jets do not necessarly sustain the growth of turbulent eddies locally. Instead, the energy released by the jet can be transported over significant distances to either sustain turbulence or to reinforce the jet. Here, we analyze model outputs of submesoscale-permitting (horizontal resolution of 1-2 km) ensemble simulations of the Western Mediterranean basin with the view of better understanding this non-local dynamics. Starting from 20 initial conditions perturbed by small, independant perturbations, we analyse the development of the ensemble spread during 120-days long simulations exposed to identical forcing. We investigate the spatio-temporal structure of eddy-mean flow interactions through their kinetic energy expression. Our main contribution is to highlight trubulent fluxes of the cross energy term as a driving mechanism to explain non-local dynamics, a process that need to be accounted for in the development of submesoscale parametrizations.