1. Introduction
The available potential energy built up by large-scale wind-driven Ekman pumping of the main thermocline is believed to be released by the generation of eddies through instabilities of the mean currents (e.g., Gill et al. 1974). This process is parameterized in most coarse-resolution ocean climate models through an eddy-induced transport velocity that adiabatically flattens isopycnals (Gent and McWilliams 1990, hereafter GM). Although this hypothesized energy route has been supported by some idealized model studies (Radko and Marshall 2003, 2004), it is not clear whether results from these idealized studies (e.g., rectangular basin, flat bottom, simplified surface forcing, etc.) are applicable to the ocean, or even to realistic ocean simulations.
There is also the question of how eddy energy is dispersed in the ocean once generated. Recent eddy parameterization schemes proposed for the interior of the ocean carry the eddy energy as a prognostic variable in the model equations and have desirable features such as fluxing potential vorticity downgradient without generating spurious sources of energy (Eden and Greatbatch 2008; Marshall et al. 2012). However, the new eddy closure has also been found to be sensitive to parameterizations of the dispersion of eddy energy (Marshall and Adcroft 2010). The parameterized eddy energy will be advected by the mean flow and diffused, although it is clear from satellite observations that there is a dominant and ubiquitous westward propagation of eddy energy in the ocean interior (e.g., Chelton et al. 2007, 2011), except in the separated boundary currents.
However, an issue that has received relatively little attention to date is vertical fluxes of eddy energy. In general, the horizontal dispersion of eddy energy is likely to occur at different depths from that of the eddy energy generation. For example, in the subtropical ocean the largest lateral density gradients, and hence the eddy energy generation according to (1), are confined to surface layers; in contrast the horizontal dispersion of eddy energy, even if dominated by the first and higher baroclinic modes, will have a significant component at depth. Hence vertical eddy energy fluxes are required to connect the sources of eddy energy and its horizontal dispersion.
The aim of the present study is threefold:
examining where and how much the wind energy input to the large-scale ocean circulation is released through baroclinic instability using a realistic eddy-resolving model of the North Atlantic;
mapping the vertical eddy energy fluxes in the ocean model;
thus reconciling the mismatch between the depth of eddy energy production and the vertical structure of the horizontal dispersion of eddy energy.
2. A simple eddy energy balance


The vertical eddy energy flux
Schematic of the simple eddy energy balance proposed in section 2 for the (a) the subtropical gyre and (b) subpolar gyre. The generation of eddy energy is located near the surface in the subtropical gyre but deeper down in the subpolar gyre. To reconcile the mismatch between the depth of eddy energy production and the vertical structure of the horizontal dispersion of eddy energy, the vertical eddy energy flux is downward in the subtropical gyre and upward in the subpolar gyre.
Citation: Journal of Physical Oceanography 43, 1; 10.1175/JPO-D-12-021.1
3. The model
The ocean model used in this study is the Massachusetts Institute of Technology general circulation model (Marshall et al. 1997). The model domain extends from 14°S to 74°N and from 100°W to 20°E, with a horizontal resolution of
The model is driven by climatological monthly mean forcing obtained from National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis (Kalnay et al. 1996). Exchange with the Nordic Seas and the rest of the South Atlantic Ocean, which lie outside of the model domain, is crudely taken into account by restoring the model temperature and salinity fields near the boundaries toward the monthly mean climatological values at all depths with a restoring time scale that varies linearly from 3 days to infinity over the 4° wide buffer zones. There is no explicit treatment of sea ice. The model is first spun up for 23 years at the 1/5° resolution, and is then run for another 9 years at 1/10° resolution, during which the model variables are saved every 6 days. Results from the last 7 years are used for this study. The overbars hereafter denote the time-mean quantities averaged over the 7-yr period, and primes pertain to the eddy fields resolved by the model.
4. Results
Figure 2a shows the annual-mean barotropic transport streamfunction. The large-scale pattern compares well with that from other ocean models with similar horizontal resolutions (e.g., Smith et al. 2000; Eden et al. 2007). For example, the Gulf Stream does separate roughly at Cape Hatteras with a cyclonic recirculation to the north and an anticyclonic recirculation to the South. However, the path of the North Atlantic Current, as well as its eastward turn at the “Northwest Corner” is less well simulated by the model, a problem shared also by other models (e.g., Masumoto et al. 2004; Eden et al. 2007). As a consequence, the eddy field associated with the North Atlantic Current is shifted somewhat eastward (Fig. 3a).
(a) The annual-mean barotropic transport streamfunction (Sv) and (b) the wind power input to the North Atlantic Ocean (W m−2).
Citation: Journal of Physical Oceanography 43, 1; 10.1175/JPO-D-12-021.1
The rate of APE released by baroclinic instability (
Citation: Journal of Physical Oceanography 43, 1; 10.1175/JPO-D-12-021.1
a. Wind energy input
The rate of wind energy input at the sea surface is calculated using Wwind = τ · uo, where τ is the surface wind stress vector and uo is the total ocean surface velocity. The pattern and magnitude of the wind energy input (Fig. 2b) are similar to the previous studies (e.g., Wunsch 1998; Zhai and Greatbatch 2007; Hughes and Wilson 2008; Scott and Xu 2009). The majority of the wind energy input occurs in the tropical, western boundary, and subpolar regions, whereas there is little wind energy input in the interior of the subtropical gyre. The atmospheric winds thus seem to spin the subtropical gyre on its northern and southern edges. Roquet et al. (2011) suggest that the direct wind energy input to the ocean, Wwind, is first transported laterally by the Ekman transport before being pumped into the interior circulation; thus, the energy can be pumped into the ocean interior far from the region of direct surface wind work. Note that this interpretation is degenerate to the extent that any rotational energy flux can be added without modifying the energy budget.
One peculiar feature in Fig. 2b is a hot spot of wind energy input in the Caribbean Sea, north of Venezuela. This energy hot spot seems to be a robust feature, as it also shows up in other studies of wind energy input to the ocean (e.g., Wunsch 1998; Hughes and Wilson 2008; Scott and Xu 2009). The sensitivity of the strength of the subtropical gyre circulation to the wind energy input in the Caribbean Sea is interesting, but left for future study. Integrating over the North Atlantic Ocean, the total wind energy input is estimated to be about 0.14 TW.
In the following subsections we describe how the wind energy input leads to the generation of eddy energy at different depths (Fig. 3) and the subsequent vertical fluxes (Fig. 4), which we explain by relating to the vertical structure of the horizontal dispersion of eddy energy at three different latitudes (Figs. 5–7).
The vertical eddy energy flux (
Citation: Journal of Physical Oceanography 43, 1; 10.1175/JPO-D-12-021.1
(a) The eddy energy source (
Citation: Journal of Physical Oceanography 43, 1; 10.1175/JPO-D-12-021.1
(a) The eddy energy source (
Citation: Journal of Physical Oceanography 43, 1; 10.1175/JPO-D-12-021.1
(a) The eddy energy source (
Citation: Journal of Physical Oceanography 43, 1; 10.1175/JPO-D-12-021.1
b. Eddy energy generation
Figure 3 shows the rate at which the eddies release the APE stored in the mean stratification at different depths. The eddies are found to release the APE ubiquitously along the whole rim of the subtropical gyre, even though they are strongly western intensified. The vertical structure of eddy energy generation is, however, very different between the subtropical and subpolar gyres. In the subtropical gyre, the eddy energy generation,
Along the continental shelf break the plot of
c. Vertical eddy energy flux
Figure 4 shows the vertical eddy energy flux,
d. Balancing eddy energy sources/sinks
Figures 5c, 6c, and 7c show the balancing eddy energy sources/sinks inside the braces in Eq. (5) along 24°N, 39°N, and 59°N, respectively. These eddy energy sources/sinks are dominated by the divergence/convergence of horizontal eddy energy fluxes (there is a small contribution from the vertical advection of eddy energy; not shown). At 24°N (Fig. 5) the horizontal eddy energy fluxes are surface intensified, as one would expect if the eddies project predominately onto the baroclinic modes, but, nevertheless, with a nonnegligible component at depth consistent with both baroclinic and barotropic modes. This is consistent with the downward eddy energy fluxes found at this latitude. At 39°N (Fig. 6) in the vicinity of the separated Gulf Stream, the balancing eddy energy sources/sinks have substantial magnitude at depth with downward vertical eddy energy fluxes again required to connect the shallow eddy energy sources with the deeper horizontal eddy energy dispersion. In contrast, at 59°N (Fig. 7) in the subpolar gyre a more complicated picture is found, but the balancing eddy energy sources/sinks are generally more surface intensified than the deep energy sources, explaining the upward vertical eddy energy fluxes at this latitude. Thus, our model diagnostics support the simple conceptual picture presented in Fig. 1 for the eddy energy balance in the interior of the subtropical and subpolar gyres.
5. Concluding remarks
The eddy energy balance in the North Atlantic subtropical and subpolar gyres has been investigated using an eddy-resolving ocean model, with a particular focus on the eddy energy generation and vertical eddy energy fluxes. The major results of the present study are as follows.
The majority of the wind energy input to the large-scale ocean circulation is released by the generation of eddies through baroclinic instability.
The eddy energy generation is located near the surface in the subtropical gyre but deeper down in the subpolar gyre.
To reconcile the mismatch between the depth of eddy energy production and the vertical structure of the horizontal dispersion of eddy energy, the vertical eddy energy flux is downward in the subtropical gyre and upward in the subpolar gyre.
Acknowledgments
XZ thanks Dave Munday for many helpful discussions about the MITgcm. Financial support was provided by the U.K. Natural Environment Research Council. The numerical calculations were performed at the Oxford Supercomputing Centre (OSC). We thank two anonymous reviewers for their many constructive suggestions that led to a much improved manuscript.
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The eddy energy equation can be written in a more conventional way:
Note that the vertical eddy energy flux is different from the vertical eddy heat flux