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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 Parameterization of mesoscale eddies in coarse resolution ocean models is necessary to include the effect of eddies on the large‐scale oceanic circulation. We propose to use a multiple‐scale Quasi‐Geostrophic (MSQG) model to capture the eddy dynamics that develop in response to a prescribed large‐scale flow. The MSQG model consists in extending the traditional quasi geostrophic (QG) dynamics to include the effects of a variable Coriolis parameter and variable background stratification. Solutions to this MSQG equation are computed numerically and compared to a full primitive equation model. The large‐scale flow field permits baroclinically unstable QG waves to grow. These instabilities saturate due to non‐linearities and a filtering method is applied to remove large‐scale structures that develop due to the upscale cascade. The resulting eddy field represents a dynamically consistent response to the prescribed background flow, and can be used to rectify the large‐scale dynamics. Comparisons between Gent‐McWilliams eddy parameterization and the present solutions show large regions of agreement, while also indicating areas where the eddies feed back onto the large scale in a manner that the Gent‐McWilliams parameterization cannot capture. Also of interest is the time variability of the eddy feedback which can be used to build stochastic eddy parameterizations. 

Abstract The potential role of the New England seamount chain (NESC) on the Gulf Stream pathway and variability has been long recognized, and the series of numerical experiments presented in this paper further emphasize the importance of properly resolving the NESC when modeling the Gulf Stream. The NESC has a strong impact on the Gulf Stream pathway and variability, as demonstrated by comparison experiments with and without the NESC. With the NESC removed from the model bathymetry, the Gulf Stream remains a stable coherent jet much farther east than in the experiment with the NESC. The NESC is the leading factor destabilizing the Gulf Stream and, when it is not properly resolved by the model’s grid, its impact on the Gulf Stream’s pathway and variability is surprisingly large. A high-resolution bathymetry, which better resolves the New England seamounts (i.e., narrower and rising higher in the water column), leads to a tighter Gulf Stream mean path that better agrees with the observed path and a sea surface height variability distribution that is in excellent agreement with the observations. 

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 We describe a form of Atlantic Meridional Overturning Circulation (AMOC) variability that we believe has not previously appeared in observations or models. It is found in an ensemble of eddy‐resolving North Atlantic simulations that the AMOC frequently reverses in sign at ∼35°N with gyre‐wide anomalies in size and that reach throughout the water column. The duration of each reversal is roughly 1 month. The reversals are part of the annual AMOC cycle occurring in boreal winter, although not all years feature an actual reversal in sign. The occurrence of the reversals appears in our ensemble mean, suggesting it is a forced feature of the circulation. A partial explanation is found in an Ekman response to wind stress anomalies. Model ensemble simulations run with different combinations of climatological and realistic forcings argue that it is the atmospheric forcing specifically that results in the reversals, despite the signals extending into the deep ocean. 

Abstract We introduce a pseudo‐spectral algorithm that includes full compressible dynamics with the intent of simulating near‐incompressible fluids, CaTSM (Compressible and Thermodynamically consistent Spectral Model). A semi‐implicit scheme is used to model acoustic waves in order to evolve the system efficiently for such fluids. We demonstrate the convergence properties of this numerical code for the case of a shock tube and for Rayleigh‐Taylor instability. A linear equation of state is also presented, which relates the specific volume of the fluid linearly to the potential temperature, salinity, and pressure. This permits the results to be easily compared to a Boussinesq framework in order to assess whether the Boussinesq approximation adequately represents the relevant exchange of energy to the problem of interest. One such application is included, that of the development of a single salt finger, and it is shown that the energetic behavior of the system is comparable to the typical canonical development of the problem for oceanographic parameters. However, for more compressible systems, the results change substantially even for low‐Mach number flows. 

Abstract Accurate representation of air‐sea interaction is crucial to numerical prediction of the ocean, weather, and climate. Sea surface temperature (SST) gradients and surface currents in the oceanic mesoscale regime are known to have significant influence on air‐sea fluxes of momentum. Studies based on high‐resolution numerical models and observations reveal that SST gradients and surface currents in the submesoscale regime are much stronger than those in the mesoscale. However, the feedback between the submesoscale processes and the air‐sea turbulent fluxes is not well understood. To quantitatively assess the responses between air‐sea flux of momentum and submesoscale processes, a non‐hydrostatic ocean model is implemented in this study. The inclusion of SST gradients and surface currents in air‐sea bulk fluxes are argued to be significant for modeling accurate wind stress in the submesoscale regime. Taking both into account, this study shows that the linear relationship between wind stress curl/divergence and crosswind/downwind SST gradients existing in the mesoscale regime is not obvious in the submesoscale. Instead, a linear relationship between wind stress curl/divergence and surface current curl/divergence is revealed in the submesoscale. Furthermore, the magnitude of wind stress curl introduced by submesoscale processes is much greater than that presented by mesoscale processes. Another key finding is that tracer subduction and potential vorticity distribution in the submesoscale is susceptible to submesoscale‐modified air‐sea turbulent momentum flux. This study serves as a starting point in investigating the feedbacks between atmospheric and oceanic submesoscale processes. 

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 Circulation in the Southern Ocean is unique. The strong wind stress forcing and buoyancy fluxes, in concert with the lack of continental boundaries, conspire to drive the Antarctic Circumpolar Current replete with an intense eddy field. The effect of Southern Ocean eddies on the ocean circulation is significant—they modulate the momentum balance of the zonal flow, and the meridional transport of tracers and mass. The strength of the eddy field is controlled by a combination of forcing (primarily thought to be wind stress) and intrinsic, chaotic, variability associated with the turbulent flow field itself. Here, we present results from an eddy‐permitting ensemble of ocean model simulations to investigate the relative contribution of forced and intrinsic processes in governing the variability of Southern Ocean eddy kinetic energy. We find that variations of the eddy field are mostly random, even on longer (interannual) timescales. Where correlations between the wind stress forcing and the eddy field exist, these interactions are dominated by two distinct timescales—a fast baroclinic instability response; and a multi‐year process owing to feedback between bathymetry and the mean flow. These results suggest that understanding Southern Ocean eddy dynamics and its larger‐scale impacts requires an ensemble approach to eliminate intrinsic variability, and therefore may not yield robust conclusions from observations alone.