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Abstract Statistical characterization of oceanic flows has been a long standing issue; such information is invaluable for formulating hypotheses and testing them. It also 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 the spatially heterogeneous and anisotropic nature of oceanic flows. Utilizing an eddy‐rich ensemble simulation of the North Atlantic, we are able to 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; this partial cancellation between temperature and salinity is similar to the thermodynamic spice variable. 

Abstract We examine the ocean energy cycle where the eddies are defined about the ensemble mean of a partially air–sea coupled, eddy-rich ensemble simulation of the North Atlantic. The decomposition about the ensemble mean leads to a parameter-free definition of eddies, which is interpreted as the expression of oceanic chaos. Using the ensemble framework, we define the reservoirs of mean and eddy kinetic energy (MKE and EKE, respectively) and mean total dynamic enthalpy (MTDE). We opt for the usage of dynamic enthalpy (DE) as a proxy for potential energy due to its dynamically consistent relation to hydrostatic pressure in Boussinesq fluids and nonreliance on any reference stratification. The curious result that emerges is that the potential energy reservoir cannot be decomposed into its mean and eddy components, and the eddy flux of DE can be absorbed into the EKE budget as pressure work. We find from the energy cycle that while baroclinic instability, associated with a positive vertical eddy buoyancy flux, tends to peak around February, EKE takes its maximum around September in the wind-driven gyre. Interestingly, the energy input from MKE to EKE, a process sometimes associated with barotropic processes, becomes larger than the vertical eddy buoyancy flux during the summer and autumn. Our results question the common notion that the inverse energy cascade of wintertime EKE energized by baroclinic instability within the mixed layer is solely responsible for the summer-to-autumn peak in EKE and suggest that both the eddy transport of DE and transfer of energy from MKE to EKE contribute to the seasonal EKE maxima. Significance StatementThe Earth system, including the ocean, is chaotic. Namely, the state to be realized is highly sensitive to minute perturbations, a phenomenon commonly known as the “butterfly effect.” Here, we run a sweep of ocean simulations that allow us to disentangle the oceanic expression of chaos from the oceanic response to the atmosphere. We investigate the energy pathways between the two in a physically consistent manner in the North Atlantic region. Our approach can be extended to robustly examine the temporal change of oceanic energy and heat distribution under a warming climate. 

Abstract 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 empirical orthogonal function 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°) 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. 

Abstract A wavelet‐based method is re‐introduced in an oceanographic and spectral context to estimate wavenumber spectrum and spectral flux of kinetic energy and enstrophy. We apply this to a numerical simulation of idealized, doubly periodic quasi‐geostrophic flows, that is, the flow is constrained by the Coriolis force and vertical stratification. The double periodicity allows for a straightforward Fourier analysis as the baseline method. Our wavelet spectra agree well with the canonical Fourier approach but with the additional strengths of negating the necessity for the data to be periodic and being able to extract local anisotropies in the flow. Caution is warranted, however, when computing higher‐order quantities, such as spectral flux. 

Abstract The thickness‐weighted average (TWA) framework, which treats the residual‐mean flow as the prognostic variable, provides a clear theoretical formulation of the eddy feedback onto the residual‐mean flow. The averaging operator involved in the TWA framework, although in theory being an ensemble mean, in practice has often been approximated by a temporal mean. Here, we analyze an ensemble of North Atlantic simulations at mesoscale‐permitting resolution (1/12°). We therefore recognize means and eddies in terms of ensemble means and fluctuations about those means. The ensemble dimension being orthogonal to the temporal and spatial dimensions negates the necessity for an arbitrary temporal or spatial scale in defining the eddies. Eddy‐mean flow feedbacks are encapsulated in the Eliassen‐Palm (E‐P) flux tensor and its convergence indicates that eddy momentum fluxes dominate in the separated Gulf Stream. The eddies can be interpreted to contribute to the zonal meandering of the Gulf Stream and a northward migration of it in the meridional direction. Downstream of the separated Gulf Stream in the North Atlantic Current region, the interfacial form stress convergence becomes leading order in the E‐P flux convergence.