Statistical characterization of oceanic flows has been a long standing issue; such information is invaluable for formulating hypotheses and testing them. Another motivation stems from the fact that it allows us to understand the energy pathways within the ocean, which is highly turbulent. Here, we apply the wavelet approach to wavenumber spectral analysis, which has recently been proved to be beneficial in quantifying its spatially heterogeneous and anisotropic nature. We utilize an eddy-rich ensemble simulation of the North Atlantic and examine the spectral transfers of eddy kinetic energy (EKE) and effect of potential energy, here defined via dynamic enthalpy, on the EKE spectral budget. We find that vertical advection of EKE modulates the up- and down-scale direction and strength of EKE spectral flux throughout the North Atlantic domain. The vertical eddy buoyancy flux tends to be small below the mixed layer, suggesting that the flow is largely adiabatic. In maintaining this adiabatic nature, the eddy advection of dynamic enthalpy and practical salinity tend to partially compensate for the eddy advection of potential temperature, a phenomenon similar to the thermodynamic spice variable.

The ‘eddying’ ocean, recognized for several decades, has been the focus of much observational and theoretical research. We here describe a generalization for the analysis of eddy energy, based on the use of ensembles, that addresses two key related issues: the definition of an ‘eddy’ and the general computation of energy spectra. An ensemble identifies eddies as the unpredictable component of the flow, and permits the scale decomposition of their energy in inhomogeneous and non-stationary settings. We present two distinct, but equally valid, spectral estimates: one is similar to classical Fourier spectra, the other reminiscent of classical EOF analysis. Both satisfy Parseval’s equality and thus can be interpreted as length-scale dependent energy decompositions. The issue of ‘tapering’ or ‘windowing’ of the data, used in traditional approaches, is also discussed. We apply the analyses to a mesoscale ‘resolving’ (1/12$^\circ$) ensemble of the separated North Atlantic Gulf Stream. Our results reveal highly anisotropic spectra in the Gulf Stream and zones of both agreement and disagreement with theoretically expected spectral shapes. In general, we find spectral slopes that fall off faster than the steepest slope expected from quasi-geostrophic theory.