a. Model simulation

The ocean simulation presented here uses the Parallel Ocean Program (POP), version 2 (Smith et al. 2010) in an eddy-resolving oceanic tripole grid (poles in North America and Asia) with 62 vertical levels (10-m resolution above 160 m and gradually increasing to 250 m toward the sea floor) and a nominal horizontal resolution of 0.1° (11 km at low latitudes and 2.5 km at high latitudes), which is sufficient to resolve the most energetic scales of mesoscale variability and can even capture some submesoscale processes (Uchida et al. 2017). The model topography was adapted from ETOPO2 and partial bottom cells (Adcroft et al. 1997; Pacanowski and Gnanadesikan 1998) were implemented to improve topographic interaction with flows. A second-order centered difference advection scheme for both horizontal momentum and tracers is used in POP. The nonlocal K-profile parameterization (KPP) scheme (Large et al. 1994) was applied to parameterize the surface mixed layer and interior vertical mixing processes. Horizontal mixing by subgrid scales was parameterized using biharmonic operators. The viscosity and diffusivity values vary spatially with the cube of the local grid spacing and have equatorial values of 2.7 × 10¹⁰ and 3 × 10⁹ m⁴ s⁻¹, respectively.

The model configuration was similar to that used in Bryan and Bachman (2015) except that it employed a different forcing profile. The model used in this paper was forced by the Japanese 55-year Reanalysis (JRA55) data (Kobayashi et al. 2015). The JRA55 dataset, conducted by the Japan Meteorological Agency (JMA), is composed of atmospheric reanalysis and remote sensing products and based on JMA’s operational global data assimilation–forecast system. Observations used in the JRA dataset primarily come from ERA-40 and other observational products archived by the JMA. This dataset originally uses a reduced TL319 (∼55 km) grid and is interpolated onto the normal TL319 grid for forcing ocean models at 3-h intervals (Tsujino et al. 2018). The ocean is forced by the fluxes of momentum, heat, and freshwater. The momentum fluxes are computed with the bulk formula that relates the fluxes to wind speed and drag coefficient. The freshwater fluxes include evaporation, precipitation, and river runoff. The heat fluxes are composed of fluxes at the ocean–atmosphere surface and ocean–ice surface, as well as heat transport due to runoff. At the air–sea interface, the heat flux is a combination of shortwave, longwave, and turbulent latent and sensible heat fluxes. Detailed formulations to calculate the surface fluxes in JRA55 data are thoroughly summarized in Tsujino et al. (2018) in their section 2. The model simulation used in this work spans the period 1958–2018 and is initialized at rest with temperature and salinity distributions from the World Ocean Atlas 2013 (Boyer et al. 2013). Our analysis in this study is based on this interannually forced model output from 1999 to 2018 (model period of year 42 to year 61) with heat and salinity budget terms (i.e., heat fluxes u_hT, wT) accumulated and saved every 5-day besides standard model output.

b. Observational datasets

Three observational datasets are used to produce Fig. 1: sea surface height (SSH) and geostrophic velocity, SST, and surface net heat flux (NHF). The SSH and geostrophic velocity dataset is provided by the Archiving, Validation and Interpretation of Satellite Oceanographic (AVISO) and is available daily from 1992 on a 0.25° × 0.25° grid. The data used are for the temporal period from January 1993 to December 2017. The SST dataset is on a 0.25° × 0.25° grid of version 2 of the Optimum Interpolation SST product (OISSTv2) (Reynolds et al. 2007) provided by the National Oceanic and Atmospheric Administration (NOAA). The same period as the SSH dataset is used for the SST. The NHF data, which have the same horizontal resolution as SSH and SST, are from monthly mean product of J-OFURO3, a third-generation dataset developed by the Japanese Ocean Flux Datasets with Use of Remote sensing Observations (J-OFURO) and includes shortwave, longwave, and turbulent latent and sensible heat fluxes (Tomita et al. 2019).

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Surface estimates of divergent ${\text{BC}}_T^{\text{div}}$ and T-OMEA with satellite observations and forced POP model. (a),(c) The surface T-EPE conversion ($-{\overline{u_h^{\mathbf{\prime }}{T}^{\prime }}}^{\text{div}}\cdot \nabla \overline{T}$) from observations and the model, respectively. The EPE dissipation through air–sea interaction ($\overline{T^{\prime }{Q}^{\prime }}/{\rho }_o{C}_p$) is computed based on (b) J-OFURO3 and (d) the model (adapted from Bishop et al. 2020). Gray contours are mean SSH with a contour interval of 20 cm.

Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-22-0029.1

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c. T-variance equation

Different processes driving the T-variance variation are described in the underbraces. The tendency of T-variance over time, TEND, is on the left-hand side of Eq. (1). On the right-hand side, for brevity, we group the horizontal and vertical advection of mean and eddy flow into the three-dimensional vector operator $v\cdot \nabla =(\overline{u_h}+u_h^{\mathbf{\prime }})\cdot {\nabla }_h+(\overline{w}+w^{\prime })\partial /\partial z$, and denote it as ADV. Baroclinic conversions from MPE to EPE associated with temperature variability (BC_T) are represented by the horizontal eddy heat flux acting on the mean thermal gradient. The following conversion into EKE through baroclinic instability from the thermal contribution is termed as PKC_T in the T-variance equation. The vertical mixing, denoted as VMIX, includes the vertical diffusion of T-variance, the countergradient KPP flux, and heating from penetrating solar radiation. HDIFF refers to horizontal diffusion. Detailed derivations of Eq. (1) are given in appendix A.

All underbraced terms in Eq. (5) will be diagnosed in the analysis that follows.

a. Model diagnosis of conversions and sinks of T-EPE

The mesoscale variability in 1/10° POP model on a tripolar grid has been validated in a variety of studies, such as by estimating eddy heat fluxes in the Eastern Pacific (Abernathey and Wortham 2015) and the Kuroshio Extension (Bishop and Bryan 2013) and diagnosing the salinity budget (Bryan and Bachman 2015; Johnson et al. 2016) and heat budget in the tropical Pacific (Deppenmeier et al. 2021). All these studies have demonstrated the consistency between the model and available observations. More recently, global comparisons of basic climate variables from four different ocean models (including 1/10° POP used in our work) with the same configuration were given by Chassignet et al. (2020), who assessed ocean eddy kinetic energy, temperature variance, heat transport and other variables associated with ocean variability in the models by comparison with a variety of observations. Because the main focus of this work is on the ocean EPE budget, in this section we will only show the comparison of energy conversion/generation terms associated with potential energy that can be estimated with available satellite observations.

The surface eddy horizontal heat flux associated with geostrophic currents can be estimated with SSH and SST observations (Abernathey and Wortham 2015; Guo and Bishop 2022). The model’s performance on simulating eddy heat transport can be evaluated by comparing the surface estimates of the downgradient eddy heat fluxes with observations, as shown in Figs. 1a and 1c, which plot the global surface ${\text{BC}}_T^{\text{div}}$ obtained from the observations and model, respectively. The surface estimates indicate prominent poleward eddy heat transport around the midlatitude western boundary currents and the Antarctic Circumpolar Current. Such a surface pattern suggests that energy flows from MPE to EPE (positive ${\text{BC}}_T^{\text{div}}$) in the most baroclinically unstable jets, as would be expected due to baroclinic instability. In addition to the midlatitudes, a hotspot along the equatorial Pacific can be observed in both the observations and model; this hotspot may arise from tropical instability waves with a period of about 30 days (Jayne and Marotzke 2002). In general, the model shows good agreement with observations regarding the geographic distributions of this surface divergent baroclinic energy conversion. In terms of the magnitude, the surface ${\text{BC}}_T^{\text{div}}$ in the model has a relatively higher mean value of 5.8 × 10⁻⁸ °C² s⁻¹ compared with the observed value of 5.0 × 10⁻⁸ °C² s⁻¹ within 60°S–60°N. Notably, when using altimetry data, only geostrophic circulation is included in the eddy flux estimates.

In a process adapted from Bishop et al. (2020), we computed the covariance of net heat flux anomaly and SST anomaly to measure the thermal exchange that occurs through ocean mesoscale air–sea interactions (T-OMEA). The global distributions of this quantity obtained from observations and the model are shown in Figs. 1b and 1d, respectively. The T-OMEA feedback acts as a global T-EPE sink (Bishop et al. 2020) in both the observations and model. This effect is much stronger in the model, with a global mean value of −1.8 × 10⁻⁸ °C² m s⁻¹ compared with the observed value of −1.0 × 10⁻⁸ °C² m s⁻¹. In both the observations and model, the close correspondence of EPE destruction through T-OMEA to the conversion of EPE from MPE via ${\text{BC}}_T^{\text{div}}$ on the surface suggests that some amount of EPE that should be available for conversion into EKE would be dissipated by diabatic processes such as air–sea interactions. A detailed discussion on this effect is provided in section 3d. Overall, the surface energy conversion from MPE to EPE and the EPE sink from air–sea interactions induced by temperature variability in the forced model are comparable to those found in the observations. However, the extent of EPE dissipation resulting from diabatic processes is undetermined by observations and can only be evaluated with numerical models.

b. Global budget

To examine the significance of different dynamical processes driving T-EPE variation, we diagnose each term listed in Eq. (5) with the forced POP model. The depth-integrated budget terms are shown in Fig. 2, and their corresponding zonal distributions are given in Fig. 3 after integrals are applied along zonal sections. Each term is computed explicitly, and we successfully close the budget with a trivial residual in Eq. (5) using 5-day model outputs (see Figs. 2h and 3). On the left-hand side of Eq. (5), the tendency of T-EPE is negligible over a 20-yr period (Fig. 2a), and this term barely contributes to the budget in all zonal sections (Fig. 3). Figure 2b shows the total T-EPE advection by both the mean and eddy velocities. The spatial distributions display zonally propagating patterns with series of positive and negative eddy-like structures that can cancel each other out to a large extent in the zonal direction; in these distributions, the global zonal values oscillate around the zero-line at different latitudinal sections (Fig. 3). The two components (rotational and divergent) of baroclinic conversion (BC_T) are shown in Figs. 2c and 2d, respectively. The original distribution of BC_T before partitioning has a wavelike structure, a similar pattern to that shown in the advection term, with positive and negative values alternatively occurring due to the meandering characteristics of oceanic zonal jets. This spatial structure is caused by the rotational eddy heat flux and is most prominent in regions of zonally meandering currents (Jayne and Marotzke 2002), as shown in Fig. 2c. However, the rotational component does not truly contribute to the global budget with the actual dynamics in its divergent counterpart. ${\text{BC}}_T^{\text{div}}$ exhibits a smooth distribution, with generally positive values in all regions, indicative of the conversion from MPE to EPE. The EKE generation through baroclinic instability is quantified in the PKC_T term, and the vertically integrated distribution of this process is shown in Fig. 2e. Globally, this upgradient vertical eddy heat flux shares a similar geographic distribution with the downgradient horizontal flux, and the spatial patterns of both of these quantities suggest strong eddy activity in the midlatitude western boundary currents and the Antarctic Circumpolar Current (Fig. 3). In addition, vertical diffusion plays a role as an energy sink and can greatly modulate energy conversions in the most energetic regions (Fig. 2f). The most prominent vertical dissipation occurs in the midlatitudes and tropics, where the strongest energy conversions (as in Figs. 2d, 2e, and 3) exist. This vertical mixing dominates the total diffusion in the horizontal and vertical directions (Figs. 2f,g), although a small amount of T-EPE can also be destroyed through horizontal mixing (Fig. 3).

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Horizontal distributions of depth-integrated budget terms from ocean surface to bottom in Eq. (5) from the 20-yr forced POP simulation (°C² m s⁻¹). Gray contours are mean SSH with a contour interval of 20 cm.

Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-22-0029.1

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The distributions of zonally and vertically integrated terms in Eq. (5). The thick solid lines indicate the distributions after applying a smoothing operator (1D Gaussian filter with length of 1°) to the original distributions (thin dashed lines).

Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-22-0029.1

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A representation of the global vertical structure of each term in the T-EPE equation, obtained by zonally integrating over all longitudes, is indicated in Fig. 4, showing how different dynamical processes regulate the T-EPE variability in the water column. With relatively steady turbulence over 20 years, the TEND values are quite small at all depth levels. The ADV and ${\text{BC}}_T^{\text{rot}}$ terms have similar vertical distributions but opposite signs in most areas (Figs. 4b,c). These two terms can eventually compensate for each other to a large extent and do not largely contribute to EPE changes globally. The large internal cancellation between advection of EPE and rotational baroclinic conversion is achieved with two conditions, as discussed in Marshall and Shutts (1981). First, the rotational flux, which is associated with the spatial growth and decay of eddies, circulates around the temperature variance. This relationship is verified in the Kuroshio Extension (Bishop et al. 2013) and Gulf Stream (Cronin and Watts 1996) with full-depth in situ observations, and in the global mixed layer with surface satellite observations and a high-resolution climate simulation (Guo and Bishop 2022). Second, the mean velocity follows the mean temperature contours, as demonstrated in Marshall and Shutts (1981), and it infers that there is a linear relationship between the geostrophic streamfunction and temperature field (Killworth 1992; Cronin and Watts 1996; Bishop et al. 2013). With these two conditions, it is straightforward to show that ${\text{BC}}_T^{\text{rot}}$ is approximately balanced by ADV as derived in Marshall and Shutts (1981) in their section 3. The necessarity of partitioning the baroclinic conversion into rotational and divergent components is also discussed in Chen et al. (2014); Kang and Curchitser (2015) with a different interpretation from the perspective of regional eddy–mean flow interactions. Their work, which only estimated ocean internal energy transfers between potential and kinetic reservoirs for both mean and eddy circulations instead of fully closing energy budgets, shows that the “nonlocal” processes (i.e., advection, air–sea interactions) play a nontrivial role in eddy–mean flow energy conversions in typical baroclinically unstable regions, such as the Kuroshio, Gulf Stream, and Southern Ocean (Chen et al. 2014). The ${\text{BC}}_T^{\text{rot}}$ computed in our work is part of these nonlocal processes, which is nonnegligible in regional energy budgets (Cronin and Watts 1996; Bishop et al. 2013; Zhai and Greatbatch 2006). Regarding the most significant generation of T-EPE, a global cross section of the downgradient divergent eddy heat flux from POP model is shown in Fig. 4d. The ${\text{BC}}_T^{\text{div}}$ term exhibits surface-intensified vertical distributions in the midlatitudes and reaches a maximum in the subsurface in low-latitude regions. Figure 4e shows the vertical distribution of PKC_T, which is associated with the upgradient vertical flux. The strong eddy energy conversions can penetrate as deep as 800 m in the midlatitudes and occurs in regions with large thermal gradients (as indicated by closeness of the contour lines in Fig. 4). In addition to its horizontal distribution, ${\text{BC}}_T^{\text{div}}$ is also spatially coherent with the PKC_T in the vertical except for a very weak vertical heat flux in the mixed layer (Fig. 4e). The weaker energy conversion between T-EPE and EKE on the ocean surface correspond to surface-intensified vertical mixing, as shown in Fig. 4f. The VMIX term reveals that the EPE dissipation that occurs through vertical thermal diffusion is mostly confined to the upper ocean, where the heat exchange between the atmosphere and ocean eddies plays an important role (Ma et al. 2016; Bishop et al. 2020). The horizontal diffusion process (Fig. 4g) is shown to be less significant than the vertical mixing term, and the HDIFF only exhibits large values in a narrow zonal band in the midlatitudes in the upper 200 m. In general, the main balance in Eq. (5) occurs among ${\text{BC}}_T^{\text{div}}$, PKC_T, and VMIX, as shown in Figs. 4d–f, with relatively small contributions from other processes.

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Global cross sections of zonally integrated terms in Eq. (5) (°C² m s⁻¹). The contour lines are mean temperature with a contour interval of 3°C.

Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-22-0029.1

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c. Regional variability

The local T-EPE budget terms for the Gulf Stream are shown in Fig. 5. Based on the vertically integrated spatial distributions of the terms in Eq. (5), the significant processes driving the local rate of change in T-EPE are ADV, ${\text{BC}}_T^{\text{rot}},\hspace{0.17em}{\text{BC}}_T^{\text{div}}$, PKC_T, and VMIX, each of which has a clear spatial structure. Among these terms, the wavelike pattern is most prominent in the ${\text{BC}}_T^{\text{rot}}$ term, which is spatially related to the ADV term. As proposed in Marshall and Shutts (1981), the rotational eddy heat flux is indicative of the spatial growth and decay of eddies and balances the mean advection of T-variance when the advection by the eddy velocity is neglected. In Figs. 5b and 5c, the signal of this relationship, as described in Marshall and Shutts (1981), is shown for the Gulf Stream; however, the ${\text{BC}}_T^{\text{rot}}$ term does not balance the mean advection precisely, as the triple correlation term (eddy advection) may also play a role in regions where the Rossby number is not small. In an adiabatic scenario, a nearly one-to-one balance between ${\text{BC}}_T^{\text{div}}$ and PKC_T was inferred in Marshall and Shutts (1981). As shown in the Gulf Stream, the local ${\text{BC}}_T^{\text{div}}$ is spatially coherent with PKC_T, and both are aligned with the mean SSH gradient (Figs. 5d,e). The different signs of ${\text{BC}}_T^{\text{div}}$ and PKC_T indicate that horizontal eddy heat fluxes act to weaken the background temperature gradient and that the vertical thermal structure can be restratified through vertical eddy fluxes. Although their spatial patterns share many similarities, the magnitude of ${\text{BC}}_T^{\text{div}}$ is larger than that of PKC_T in some areas. In addition, this magnitude mismatch can be largely explained by the strong diabatic mixing occurring along the jets (Figs. 5f,g). Compared with the horizontal diffusion term HDIFF, the vertical mixing VMIX plays a larger role in energy dissipation along the western boundary currents as found in the Kuroshio Extension (not shown) and Gulf Stream (Fig. 5). In these regions, the distributions of VMIX mostly concentrate on the poleward side of the western boundary currents, as shown in the example given in Fig. 5f. Bishop et al. (2020) also captured these characteristics in their estimates of mesoscale air–sea interactions using the covariance of anomalous SST and net heat fluxes obtained from satellite observations. This pattern potentially implies that the warm eddies on the colder side of the zonal currents release larger amounts of potential energy when exposed to the much colder and drier overlying atmosphere (Yang et al. 2019). Moreover, the spatial patterns of VMIX are generally associated with the ${\text{BC}}_T^{\text{div}}$, with larger energy conversions corresponding to stronger energy dissipation. For example, in the Gulf Stream, ${\text{BC}}_T^{\text{div}}$ and VMIX share two regional hotspots: one is located near the large meander after the Gulf Stream separates off Cape Hatteras and extends to the region off Cape Cod (Fig. 5d); the other is further downstream on the eastern boundary of the domain shown in Fig. 5. The horizontal spatial coherence among ${\text{BC}}_T^{\text{div}}$, PKC_T, and VMIX suggests a nearly three-way balance in modulating local T-EPE variations.

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Regional maps of depth-integrated budget terms in the Gulf Stream (°C² m s⁻¹). The gray contour lines indicate mean SSH, with a contour interval of 20 cm.

Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-22-0029.1

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In Fig. 6, we show the regional T-EPE budgets for the Southern Ocean. The horizontal structures of the depth-integrated terms are generally located along the Antarctic Circumpolar Current path, as indicated by the large SSH gradient, and the western boundary currents and their extensions dominate the majority of the T-EPE sources and sinks. Similar to the conditions seen in the Gulf Stream, ADV and ${\text{BC}}_T^{\text{rot}}$ are spatially correlated with each other and barely contribute to the integrated energy. The aforementioned three-way balance appears in the Southern Hemisphere as well, with the energy conversions (Figs. 6d,e) in the most turbulent regions modulated by the VMIX term (Fig. 6f). The strongest energy dissipation through vertical mixing is seen in the Agulhas Return Current and Brazil–Malvinas Confluence, where the most prominent energy conversions occur.

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As in Fig. 5, but for the Southern Ocean (°C² m s⁻¹).

Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-22-0029.1

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d. Role of air–sea interaction

We have shown above that vertical mixing plays a significant role in regulating the baroclinic pathway based on a global T-EPE diagnosis. Notably, in Eq. (5), the VMIX term includes all processes that together contribute to the vertical dissipation of T-EPE in the model prognostics. Here we further decompose this term into three components related to air–sea interactions (VMIX_a-s), diffusive mixing (VMIX_diff) and countergradient fluxes in KPP scheme (VMIX_kpp). These three components are partitioned as

$\text{VMIX}=\underset{{\text{VMIX}}_{\mathrm{as}}}{\underbrace{\overline{T^{\prime }\hspace{0.17em}\frac{\partial }{\partial z}\left(\frac{Q^{\prime }}{{\rho }_o{C}_p}\right)}}}+\underset{{\text{VMIX}}_{\text{diff}}}{\underbrace{\overline{T^{\prime }\hspace{0.17em}\frac{\partial }{\partial z}\left(\kappa \hspace{0.17em}\frac{\partial T^{\prime }}{\partial z}\right)}}}+\underset{{\text{VMIX}}_{\text{kpp}}}{\underbrace{\overline{T^{\prime }\hspace{0.17em}\frac{\partial }{\partial z}(\kappa {\Gamma }^{\prime })}}},$(7)

where Q is a combination of surface nonsolar net heat flux Q_o and the penetrative radiation Q_sw. We adopt zero surface boundary conditions for the latter two terms in Eq. (7). The total VMIX is shown on the top panel of Fig. 7a in the same form as the plot in Fig. 2f, but with a different color scale. This energy destruction through mesoscale air–sea interaction (Fig. 7b) generally dominates the global geographic patterns of VMIX, with large concentrations on the midlatitudes and tropics. The mixing associated with the vertical diffusive flux is relatively weaker than the air–sea feedback, and regional hotspots from VMIX_diff are found on the poleward side of western boundary currents and along the equator (Fig. 7c). In addition, a portion of the energy dissipation is completed by the vertical nonlocal flux in the KPP scheme for the vertical turbulent heat flux. The effect of countergradient fluxes introduced by KPP in VMIX is evaluated in Fig. 7d, and the VMIX_kpp term is found to be mostly concentrated along the western boundary currents. Based on the zonal integrals of the three components shown in Fig. 8, VMIX_a-s plays the largest role in destroying T-EPE, with zonal maximums in the midlatitudes and tropics. In the Northern Hemisphere, all three components in VMIX reach local maximums near 40°N, and the zonal integrals of VMIX_diff and VMIX_kpp are slightly offset from that of VMIX_a-s to the north and south, respectively. Near the equator, the VMIX_diff term is the strongest quantity compared with the contributions from air–sea interactions and countergradient fluxes from KPP. In the Southern Hemisphere, the VMIX_diff term induces the smallest portion of T-EPE sink around 40°S, with over 70% of the total destruction coming from air–sea interactions VMIX_a-s. Globally, the interior vertical mixing including both VMIX_diff and VMIX_kpp (∼0.16 TW) has a comparable magnitude with the mesoscale air–sea feedback VMIX_a-s (∼0.17 TW). The unit conversions are described in the following discussion section.

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The horizontal distributions of (a) total vertical mixing and its three components related to (b) air–sea interaction, (c) diffusive flux, and (d) countergradient flux in KPP, after vertically integrating from the surface to the bottom (°C² m s⁻¹). Gray contours are mean SSH with a contour interval of 20 cm.

Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-22-0029.1

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Zonally and vertically integrated three components in VMIX (°C² m² s⁻¹).

Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-22-0029.1

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The cross sections of vertical mixing and its three components are shown in Fig. 9. The VMIX process is mostly confined to the upper 200 m, with air–sea interactions (Fig. 9b) playing the largest role near the surface. In the midlatitudes, the surface-intensified vertical mixing is dominated by the mesoscale air–sea energy sink even though the positive VMIX_diff and VMIX_kpp near the surface compensate for part of the surface destruction. In the tropics, the T-EPE sink induced by VMIX_a-s is partly canceled out by the positive VMIX_diff, resulting in a very weak negative VMIX near the surface (Fig. 9). The opposite effect of solar penetrative flux and vertical diffusion on cross-isothermal motions is demonstrated in the near-surface equatorial Pacific (Deppenmeier et al. 2021). From the perspective of eddy energetics in this study, the mesoscale air–sea interaction acts to destruct eddy energy, while the near-surface turbulence VMIX_diff tend to oppose this effect. But the surface sink of T-EPE in VMIX_a-s exceeds the magnitude of positive VMIX_diff, leading to an overall negative signal in surface VMIX. Deeper in the surface layer the VMIX_diff and VMIX_kpp terms are the only two sources for vertical mixing except for a small contribution from solar penetrative radiation in VMIX_a-s. The impact of downward solar heat radiation flux reduces with depth and is negligible below 50 m (Fig. 9b). In the midlatitudes, the countergradient flux induced by KPP (Fig. 9d) has the largest influence on the sink of EPE below the surface and shows symmetric vertical structures between the two hemispheres. The negative sign in VMIX_kpp in the midlatitudes indicates a reduced magnitude of countergradient flux with depth in the boundary layer and the energy destruction from this effect can reach to 150 m near 40°. The mixing associated with diffusive fluxes (Fig. 9c) is predominant in the total mixing below 50 m in low-latitude regions. The large negative signal is located in the areas where isotherms are dominantly horizontal (see contours in Fig. 9c), suggesting a massive destruction of eddy energy by vertical turbulence in the tropics. The large vertical motions across the nearly horizontal isotherms are found to be primarily driven by vertical diffusion processes, favoring water mass transformation in the tropical Pacific (Deppenmeier et al. 2021). Although the air–sea feedback is only concentrated near the surface, it comprises 52% of the total VMIX globally. If the energy dissipation that occurs through horizontal diffusion is also taken into account, the air–sea interactions induced by mesoscale structures contribute 39% of the global T-EPE destruction, which is close to a regional value (36%) in the Kuroshio Extension obtained from a coupled simulation by Yang et al. (2019). Note that we used an ocean-only model in this work, and there is no actual feedback from the ocean to the atmosphere. To make sure the air–sea interaction term in the forced simulation is reasonable, we compared VMIX_a-s in this work to that from a high-resolution coupled simulation of the Community Earth System Model (CESM), which used the exact same ocean model as described in Small et al. (2014). The sink of T-EPE by mesoscale air–sea interaction is quite comparable in the ocean simulation used in this work to that in the coupled simulation with regard to both spatial distributions and global integrations (not shown).

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Cross sections of zonally integrated (a) total vertical mixing and the contributions from (b) air–sea interaction, (c) diffusive flux, and (d) countergradient flux in KPP (°C² m s⁻¹). The contour lines are mean temperature with a contour interval of 3°C.

Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-22-0029.1

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e. Seasonality

There is evidence that the air–sea interactions at the oceanic mesoscale have pronounced seasonal signals due to strong turbulent heat fluxes that occur in the wintertime when atmospheric synoptic storms are active (Bishop et al. 2020; Yang et al. 2019; Ma et al. 2016). However, the impact of this seasonality on global eddy energetics has not yet been well addressed. Here, we examined how the seasonally varying mixing processes regulate the baroclinic energy pathway based on the T-EPE budgets. The depth-integrated distributions of the three-way balance between ${\text{BC}}_T^{\text{div}}$, PKC_T and VMIX in the upper 200 m are shown in Fig. 10 for the winter months (JFM) and summer months (JAS) along with their corresponding zonal integrals. Globally, nearly identical spatial patterns are observed in ${\text{BC}}_T^{\text{div}}$ for both seasons, and trivial differences are also found in their zonal distributions between the seasons, suggesting no obvious seasonality in the MPE-to-EPE conversions in the global ocean. Nevertheless, the subsequent conversion into EKE shows strong seasonal differences in terms of the horizontal distributions (Figs. 10c,d). In the midlatitudes, it is apparent that PKC_T is most prominent in the local summer season, implying a possible summer peak in EKE (Rieck et al. 2015). Moreover, the seasonal signal indicated by PKC_T is highly associated with the seasonality shown in VMIX (Figs. 10e,f). The weakened wintertime energy conversion in PKC_T is accompanied by the enhancement of vertical dissipation, and vice versa in summertime. Vertically, the cross sections of the zonally integrated terms are given in Fig. 11 for the two seasons. As shown in its horizontal distribution, a very weak seasonal signal is found in the vertical structure of ${\text{BC}}_T^{\text{div}}$. However, for the other two processes, PKC_T and VMIX, the vertical structures in the winter and summer are reversed between the two hemispheres. Furthermore, it is evident that the EKE conversion in the upper ocean is largely modulated by vertical mixing in different seasons. In the boreal wintertime (JFM), a deepened vertical structure of VMIX corresponds to a deeper core of PKC_T, where most of the energy above the core is destroyed through mixing. During the summertime (JAS), PKC_T reaches maximums at shallower depths due to the relatively weak mixing processes. The seasonality shown in Fig. 11 further provides evidence for the nearly three-way balance driving T-EPE variations. In addition, we compare the annual cycle of three dominant terms from the three regions shown as examples in Fig. 12. Each individual month displays a roughly equivalent contribution (8%) of ${\text{BC}}_T^{\text{div}}$ over the year, and very small amplitudes of the annual cycles are found in ${\text{BC}}_T^{\text{div}}$ in all three regions. Inversely correlated signals appear in the annual variations between the regional PKC_T and VMIX, with the high summertime PKC_T corresponding to low VMIX. It is also indicated that PKC_T lags behind VMIX by 1–2 months in these regions. This phase relationship suggests a possible adjustment period of upper-ocean baroclinic instability to seasonally varying vertical dissipation.

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Seasonality in ${\text{BC}}_T^{\text{div}}$, PKC_T and VMIX. (a),(b) Depth-integrated ${\text{BC}}_T^{\text{div}}$ in the upper 200 m in the boreal winter (JFM) and summer (JAS), respectively (°C² m s⁻¹). (c) The corresponding zonal integrals are shown (°C² m² s⁻¹). (d)–(f) As in (a)–(c), but for PKC_T. (g)–(i) As in (a)–(c), but for VMIX. The gray contour lines are mean SST in the corresponding seasons with a contour interval of 3°C.

Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-22-0029.1

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Vertical structures of the budget terms in (top) JFM and (bottom) JAS for (a),(d) ${\text{BC}}_T^{\text{div}}$; (b),(e) PKC_T; and (c),(f) VMIX (°C² m s⁻¹). The gray contour lines are mean temperature in the corresponding seasons with a contour interval of 3°C.

Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-22-0029.1

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Seasonal variations of ${\text{BC}}_T^{\text{div}}$, PKC_T, and VMIX in the (a) Kuroshio Extension, (b) Gulf Stream, and (c) Agulhas Current, as indicated by boxes in Fig. 10. The y axis represents percentage of variance explained in each individual month over the year.

Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-22-0029.1

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