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  • View in gallery

    Vertical profiles of −⟨pw′⟩ at different seasons averaged over the Kuroshio Extension (32°–42°N, 130°–170°E). The gray and black dashed lines mark the mean and maximum SBL depth for each season.

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    The spatial distribution of surface near-inertial current amplitude (m s−1) simulated in CESM: (a) October–March and (b) April–September.

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    The spatial distribution of annual mean (a) WI and (b) FSBL (mW m−2) simulated in CESM.

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    The spatial distribution of annual mean (a) δrad (defined as the ratio of local FSBL to WI) and (b) enstrophy (s−2) of BMs simulated in CESM. Regions with FSBL < 0.05 mW m−2 are masked.

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    Bin-averaged δrad (defined as the ratio of local FSBL to WI) as a function of WI (mW m−2) and enstrophy of BMs (s−2) (a) within cyclonic regions and (b) within anticyclonic regions. Bins with the sample number less than 1000 are not shown as there are insufficient samples to obtain robust statistics.

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    The spatial distribution of annual mean (a) Π, (b) Πcon, (c) Πstrain, and (d) Πshear. Unit here is mW m−2.

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    (a) Probability density function (PDF) of vertically averaged ∇hu within 150–950 m in the WBC extensions (Kuroshio Extension: 29°–42°N, 130°–170°E; Gulf Stream Extension: 29°–42°N, 78°–53°W) and the Southern Ocean (65°–40°S, 0°–360°E). (b) As in (a), but with the symmetric part of PDF subtracted. (c) NIW energy averaged within 150–950 m as a function of vertically averaged ∇hu. (d) As in (c), but with the symmetric part of NIW energy subtracted. (e) υ¯/xu¯/y averaged within 150–950 m as a function of vertically averaged ∇hu. (f) As in (e), but with the symmetric part of υ¯/xu¯/y subtracted.

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    The spatial distribution of composite mean Πstrain (mW m−2) for the periods with (a) positive and (b) negative OW parameters.

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    Vertical profiles of quasi-global integral of ε (black) and its three components εcon (orange), εstrain (red), and εshear (blue) below the SBL: (a) from the SBL base to 500 m and (b) from 500 to 3000 m.

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    Spatial distribution of mean turbulent vertical viscosity (VVC) within the SBL in January parameterized by the (a) KPP scheme and (b) Pacanowski–Philander scheme. (c),(d) As in (a) and (b), but in July. All the values are derived from the CESM simulation.

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    The spatial distribution of δrad in January parameterized by the (a) KPP scheme and (b) Pacanowski–Philander scheme. (c),(d) As in (a) and (b), but in July. All the values are derived from the CESM simulation.

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Energy Flux into Near-Inertial Internal Waves below the Surface Boundary Layer in the Global Ocean

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  • 1 aKey Laboratory of Physical Oceanography and Frontiers Science Center for Deep Ocean Multispheres and Earth System, Ocean University of China, Qingdao, China
  • | 2 bPilot National Laboratory for Marine Science and Technology (Qingdao), Qingdao, China
  • | 3 cInternational Laboratory for High-Resolution Earth System Prediction, Texas A&M University, College Station, Texas
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Abstract

Near-inertial internal waves (NIWs) are thought to play an important role in powering the turbulent diapycnal mixing in the ocean interior. Nevertheless, the energy flux into NIWs below the surface boundary layer (SBL) in the global ocean is still poorly understood. This key problem is addressed in this study based on a Community Earth System Model (CESM) simulation with a horizontal resolution of ~0.1° for its oceanic component and ~0.25° for its atmospheric component. The CESM shows good skill in simulating NIWs globally, reproducing the observed magnitude and spatial pattern of surface NIW currents and wind power on NIWs (WI). The simulated downward flux of NIW energy (FSBL) at the SBL base is positive everywhere. Its quasi-global integral (excluding the region within 5°S–5°N) is 0.13 TW, about one-third the value of WI. The ratio of local FSBL to WI varies substantially over the space. It exhibits an increasing trend with the enstrophy of balanced motions (BMs) and a decreasing trend with WI. The kinetic energy transfer from model-resolved BMs to NIWs is positive from the SBL base to 600 m but becomes negative farther downward. The quasi-global integral of energy transfer below the SBL base is two orders of magnitude smaller than that of FSBL, suggesting the resolved BMs in the CESM simulations making negligible contributions to power NIWs in the ocean interior.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Shengpeng Wang, wangshengpeng@ouc.edu.cn

Abstract

Near-inertial internal waves (NIWs) are thought to play an important role in powering the turbulent diapycnal mixing in the ocean interior. Nevertheless, the energy flux into NIWs below the surface boundary layer (SBL) in the global ocean is still poorly understood. This key problem is addressed in this study based on a Community Earth System Model (CESM) simulation with a horizontal resolution of ~0.1° for its oceanic component and ~0.25° for its atmospheric component. The CESM shows good skill in simulating NIWs globally, reproducing the observed magnitude and spatial pattern of surface NIW currents and wind power on NIWs (WI). The simulated downward flux of NIW energy (FSBL) at the SBL base is positive everywhere. Its quasi-global integral (excluding the region within 5°S–5°N) is 0.13 TW, about one-third the value of WI. The ratio of local FSBL to WI varies substantially over the space. It exhibits an increasing trend with the enstrophy of balanced motions (BMs) and a decreasing trend with WI. The kinetic energy transfer from model-resolved BMs to NIWs is positive from the SBL base to 600 m but becomes negative farther downward. The quasi-global integral of energy transfer below the SBL base is two orders of magnitude smaller than that of FSBL, suggesting the resolved BMs in the CESM simulations making negligible contributions to power NIWs in the ocean interior.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Shengpeng Wang, wangshengpeng@ouc.edu.cn

1. Introduction

The global ocean conveyor belt is a constantly circulating system of ocean currents that transport water and redistribute heat and carbon around the world. Its variability influences the global ocean heat uptake and biological carbon storage, playing a fundamental role in climate change (Broecker 1991; Mikaloff Fletcher et al. 2006; Khatiwala et al. 2009; Marshall and Speer 2012; Oka and Niwa 2013). To maintain the large-scale oceanic conveyor belt and the existing structure of marine stratification, an energy source of 2 TW is needed to furnish the turbulent diapycnal mixing below the main thermocline in the open ocean (Munk and Wunsch 1998; Wunsch and Ferrari 2004; St. Laurent and Simmons 2006). Away from boundaries, turbulent diapycnal mixing is dominated by the breaking of internal waves. Internal tides and lee waves generated through the interactions of barotropic tides and balanced motions (BMs) with the topography are estimated to account for about 1 and 0.2 TW, respectively (Munk and Wunsch 1998; Egbert and Ray 2001; Jayne and St. Laurent 2001; Wunsch and Ferrari 2004; Nikurashin and Ferrari, 2011). It is conjectured that the remaining energy source might be attributed to the near-inertial internal waves (NIWs) (Whalen et al. 2020).

As a natural resonance on a rotating planet, NIWs are efficiently excited by fluctuating wind stress at similar frequencies. The wind power on NIWs (WI) is previously estimated to range from 0.3 to 1.4 TW based on numerical models (Watanabe and Hibiya 2002; Alford 2003; Jiang et al. 2005; Furuichi et al. 2008; Simmons and Alford 2012; Rimac et al. 2013), whereas the recent observation (Liu et al. 2019) refine the range as 0.3–0.6 TW and ascribe the higher values in numerical simulations to the overlook of ocean current’s imprint on wind stress. Much of the NIW energy input by WI is dissipated in the surface boundary layer (SBL) as a result of strong shear instability (Greatbatch 1984; Price et al. 1986; Plueddemann and Farrar 2006; Jochum et al. 2013) with the remaining amount radiating into the ocean interior to furnish the turbulent diapycnal mixing there. Theoretical analyses suggest that radiation of NIW energy from the SBL into the ocean interior is strongly enhanced when the vertical vorticity of BMs is spatially inhomogeneous, with anticyclonic eddies acting as an energy conduit to the deep ocean (Kunze 1985; Young and Jelloul 1997; Balmforth et al. 1998). This is confirmed by recent observations. For instance, based on mooring observations in the Kuroshio Extension region, Jing and Wu (2014) reported that the downward flux of NIW energy into the ocean interior accounts for 45%–62% of WI during the passage of an anticyclonic eddy, whereas this value is less than 33% in the northeast Pacific where BMs are much weaker (Alford et al. 2012). In addition, ship-based surveys in a dipole vortex in the Iceland Basin revealed that the downward-radiation beam of NIW energy can reach depths greater than 200 m on the anticyclonic side in the Iceland Basin (Thomas et al. 2020).

BMs do not only facilitate downward radiation of NIWs but are also their potential energy sources. Several mechanisms have been proposed for the permanent energy exchange between NIWs and BMs, including wave breaking near critical layers (Bretherton 1966), relaxation effects through nonlinear wave–wave interactions (Müller 1976), conservation of wave angular momentum (Weller 1982), wave capture (Bühler and McIntyre 2005), spontaneous generation (Vanneste 2013), and stimulated generation (Xie and Vanneste 2015; Rocha et al. 2018) in recent research. Limited observations reveal the permanent energy transfer from BMs to NIWs through the horizontal strain field of BMs but the energy transfer rates differ substantially among studies (Frankignoul 1976; Frankignoul and Joyce 1979; Ruddick and Joyce 1979; Polzin 2010; Jing et al. 2018; Cusack et al. 2020). Observational evaluation of energy transfer due to the vertical shear of BMs is more uncertain partially because the vertical velocity associated with NIWs cannot be directly measured but is inferred from the potential density or temperature equation under the adiabatic assumption (Polzin 2010).

The energy flux into NIWs below the SBL in the global ocean is still poorly quantified. In particular, there is still lack of comprehensive knowledge of global distributions of downward flux of NIW energy at the SBL base and energy transfer from BMs to NIWs below the SBL as well as their relative importance. The existing observations are too sparse to provide reliable estimates and will probably remain so in the next decade. Numerical modeling provides a feasible tool for addressing this important issue. In fact, numerous numerical studies have been carried out to evaluate the downward flux of NIW energy into the ocean interior. But these studies are either based on the idealized numerical settings or focus on a particular region, making them incapable of representing the global integral. The only exception is Rimac et al. (2016) who used a global 0.1° ocean general circulation model (OGCM) and reported that 11% of WI leaves the SBL to the ocean below. This estimate is, however, subject to some uncertainties given that it is derived from the model output of two months and might be significantly affected by the seasonality. As to the energy exchange between NIWs and BMs, there have been no attempts at global scales to the best of our knowledge, although regional or idealized simulations studies are extensive (e.g., Gertz and Straub 2009; Polzin 2010; Nagai et al. 2015; Whitt and Thomas 2015; Xie and Vanneste 2015; Barkan et al. 2017; Jing et al. 2018).

In this study, we estimate the energy flux into NIWs below the SBL in the global ocean using a high-resolution Community Earth System Model (CESM) resolving BMs down to several tens of kilometers and with 3-hourly model output lasting for one year. The paper is organized as follows. Section 2 details the model configurations and methods for computing the energy flux into NIWs below the SBL. Results are presented in section 3. Limitations of the climate simulation are discussed in section 4 followed by conclusions in section 5.

2. Data and methods

a. Model configurations

An eddy-resolving climate simulation is completed using the Community Earth System Model (CESM) version 1.3 (Hurrell et al. 2013). This model includes the Community Atmosphere Model version 5 (CAM5) with a spectral element dynamical core as the atmospheric component and the Parallel Ocean Program version 2 (POP2) as the oceanic component. A detailed model description is given by Meehl et al. (2019). As the latest version of the atmosphere model series, the CAM5 is based on a global cubed-sphere grid at horizontal resolution of about 0.25° with 30 pressure levels in the vertical direction. This is sufficiently fine to resolve atmospheric mesoscale variabilities that contribute substantially to WI (Rimac et al. 2013; Jing et al. 2016). POP2 is a finite-difference code on an Arakawa-B grid (velocities are specified at tracer cell corners) with a horizontal resolution of 0.1° (decreasing from 11 km at the equator to 2.5 km at high latitudes) and 62 z levels in the vertical with increasing grid space from 5 m near the sea surface to 250 m near the bottom. Subgrid-scale horizontal mixing is parameterized using biharmonic operators for momentum and tracers. The hyper viscosity and diffusivity values vary spatially with the cube of the average grid length for a given cell (see Maltrud et al. 1998) and have equatorial values, −2.4 × 1010 and −3.0 × 1010 m4 s−1, respectively. Vertical mixing coefficients for momentum and tracers are obtained from the K-profile parameterization (KPP; Large et al. 1994).

The ocean and atmosphere components of CESM are connected by a coupling software framework which allows frequent mass, momentum, and energy exchanges at the interface. For every half hour, POP2 offers SST and surface velocity to CAM5 and obtains momentum flux, heat flux and equivalent “salt flux” (calculated based on freshwater flux) from CAM5 on the basis of surface flux scheme developed by Large and Yeager (2009). The land and sea ice models run at the same resolution and grid as the atmosphere and ocean models, respectively.

The ocean component of CESM is initialized with the January-mean climatological potential temperature and salinity from the World Ocean Atlas (WOA). The climate forcing is set as the present-day condition and repeated every year. After a spinup of 10 years, the global kinetic energy in the upper 1000 m exhibits no obvious tendency, suggesting a quasi-equilibrium state for BMs and NIWs. The model integration is then continued for one more year, outputting the 3-hourly averaged ocean velocity, temperature, salinity, wind stress, surface air pressure, and SBL depth (based on the KPP scheme) plus other standard variables. Such high-frequency output is sufficient to resolve NIWs globally and will be used to estimate the energy flux into NIWs below the SBL. In this study, regions within 5° of the equator are excluded from our analysis as the smallness of Coriolis frequency (f) there conflates NIWs with other kinds of waves (e.g., tropical instability waves) in the frequency domain.

b. Computation of wind power on NIWs (WI)

The value of WI is computed as
WI=τu,
where τ = (τx, τy) is the surface wind stress and u = (u, υ) is the surface horizontal current, and the prime represents the perturbations in the near-inertial band (0.75–1.25f).

c. Computation of NIW energy flux from the SBL into the ocean interior

The seasonal mean NIW energy flux from the SBL to the ocean interior can be computed as
FSBL=pw|z=hs,
where p is the dynamic pressure, w is the vertical velocity, hs is the SBL depth, and angle brackets denote the seasonal average. The projection of horizontal NIW energy flux on the slope of the SBL base is neglected in Eq. (2) as existing literature (Rimac et al. 2016) suggests that it contributes less than 1% to the NIW energy flux leaving the SBL. The annual mean FSBL is obtained by averaging the values over four seasons. Finally, a 2° × 2° running mean is applied to the annual mean FSBL to remove gridscale noise.

The value of w is available from model output, while the value of p is derived based on the temperature, salinity, sea surface height, and surface air pressure data according to the hydrostatic balance. For each season, the value of hs is set as the maximum of the 3-hourly SBL depth records within that season. We use the maximum instead of the mean value because the former is closer to the peaking depth of −⟨pw′⟩, whereas using the latter to compute FSBL significantly underestimates the NIW energy flux into the ocean interior (see Fig. 1 for an instance in the Kuroshio Extension).

Fig. 1.
Fig. 1.

Vertical profiles of −⟨pw′⟩ at different seasons averaged over the Kuroshio Extension (32°–42°N, 130°–170°E). The gray and black dashed lines mark the mean and maximum SBL depth for each season.

Citation: Journal of Physical Oceanography 51, 7; 10.1175/JPO-D-20-0276.1

d. Computation of kinetic energy transfer from BMs to NIWs below the SBL

The seasonal mean kinetic energy transfer rate from BMs to NIWs is defined as (Müller 1976; Polzin 2010):
ε=εcon+εstrain+εshear
with
εcon=ρ012(u2+υ2)hu
εstrain=ρ012(u2υ2)(u¯xυ¯y)+uυ(υ¯x+u¯y)
εshear=ρ0(uwu¯z+υwυ¯z)
where ∇h = (∂/∂x + ∂/∂y) and u = (u, υ) is the surface horizontal current, the overbars represent BMs isolated using a low-pass (<0.75f) filter.

The term εcon represents the energy transfer through the horizontal convergence/divergence of BMs (i.e., ∇hu). Although BMs are, to a large extent, geostrophically balanced so that their induced horizontal convergence/divergence is weak, contribution of εcon to ε is not necessarily negligible as the magnitude of u2 + υ2 is much larger than those of u2υ2 and uυ′ according to the polarization relation of NIWs. The term εstrain represents the energy transfer through the horizontal strain of BMs, while the term εshear corresponds to the energy transfer through the vertical shear of BMs.

Finally, the vertically integrated kinetic energy transfer rate below the SBL can be computed as
Π=hbhs(εcon+εstrain+εshear)dz,
where the SBL depth hs is defined in the same way as in section 2c and z = −hb is the lower bound of the integration. Depending on topographic slopes, hb is taken as either the ocean bottom or one level above the bottom. Contributions from εcon, εstrain, and εshear are denoted as Πcon, Πstrain, and Πshear, respectively. Again, a 2° × 2° running mean is applied to Π and its three components to remove gridscale noise.

3. Results

a. NIWs simulated by CESM

Before analyzing the energy flux into NIWs below the SBL, we first evaluate the performance of CESM in simulating NIWs. The surface near-inertial currents simulated by CESM show good agreement with the observation (Chaigneau et al. 2008; Elipot and Lumpkin 2008). For example, over the Northern (Southern) Hemisphere, the simulated mean amplitude is 10.1 (9.5) × 10−2 m s−1, comparable to 10.0 (9.0) × 10−2 m s−1 obtained from surface drifters (Chaigneau et al. 2008). Energetic NIWs occur in the 30°–60° latitude band for both hemispheres and exhibit pronounced enhancement under the midlatitude storm tracks (Fig. 2). There are also strong NIWs in the northeastern equatorial Pacific and along the trajectories of tropical cyclones (Fig. 2b) during April–September in the Northern Hemisphere. The seasonal cycle of simulated surface near-inertial currents is also consistent with estimates from observations. Both exhibit the largest magnitude during October–March in the Northern Hemisphere (Fig. 2a). In the Southern Hemisphere, seasonal variability is weaker, except in the southern Indian Ocean basin.

Fig. 2.
Fig. 2.

The spatial distribution of surface near-inertial current amplitude (m s−1) simulated in CESM: (a) October–March and (b) April–September.

Citation: Journal of Physical Oceanography 51, 7; 10.1175/JPO-D-20-0276.1

We next compare the annual mean WI in the CESM simulation (Fig. 3a) and observations. Consistent with the recent observation based on surface drifters and satellite-measured surface winds (Liu et al. 2019), strong wind power input occurs in the western boundary current (WBC) extensions and southern ocean as a result of energetic winter storms. In addition to these regions, the simulated WI exhibits local enhancement along the trajectories of tropical cyclones, which is absent in the observed WI. The difference does not imply the deficiency of CESM simulation but is likely to be attributed to the sampling inadequacies in the observations. The quasi-global integral of the simulated WI amounts to 0.44 TW. This value lies within the range of the observed value, i.e., 0.3–0.6 TW, providing further evidence for the credibility of the CESM simulation.

Fig. 3.
Fig. 3.

The spatial distribution of annual mean (a) WI and (b) FSBL (mW m−2) simulated in CESM.

Citation: Journal of Physical Oceanography 51, 7; 10.1175/JPO-D-20-0276.1

b. Downward flux of NIW energy from the SBL to the ocean interior

The annual mean FSBL is positive definite almost everywhere (Fig. 3b), suggesting universal downward flux of NIW energy from the SBL to the ocean interior. The quasi-global integral of FSBL is 0.13 TW, accounting for 29.6% of WI. The value of FSBL exhibits pronounced spatial variability. This is partially due to the inhomogeneity in WI and also implies the varying downward flux of NIW energy radiation efficiency in space. The radiation efficiency can be measured as the ratio of FSBL to WI (denoted by δrad henceforth):
δrad=FSBLWI.

Figure 4a displays the spatial distribution of δrad, excluding regions with FSBL less than 0.05 mW m−2 where the downward flux of NIW energy from the SBL to the ocean interior is negligible. There is local enhancement of δrad in the WBC extensions and Antarctic Circumpolar Current region with energetic BMs (Fig. 4b). The value of δrad in these regions can locally reach 50%–60%, larger than the global mean value but comparable to that derived from the mooring observation in the Kuroshio Extension (Jing and Wu 2014). Moreover, the values of δrad at midlatitudes tend to be smaller than those at low latitudes except along the trajectories of tropical cyclones, implying a negative correlation between δrad and WI.

Fig. 4.
Fig. 4.

The spatial distribution of annual mean (a) δrad (defined as the ratio of local FSBL to WI) and (b) enstrophy (s−2) of BMs simulated in CESM. Regions with FSBL < 0.05 mW m−2 are masked.

Citation: Journal of Physical Oceanography 51, 7; 10.1175/JPO-D-20-0276.1

A composite analysis is performed to further reveal the effects of BMs and WI on δrad. To do so, we first bin FSBL according to the annual mean enstrophy of BMs and WI, and then divide it by WI to compute the bin-averaged δrad. Given the differed roles of cyclonic and anticyclonic eddies in the downward radiation of NIW energy (Lee and Niiler 1998; Zhai et al. 2005; Alford et al. 2012; Whalen et al. 2018; Asselin et al. 2020; Thomas et al. 2020), the analysis is performed in the cyclonic and anticyclonic eddies separately. As shown in Fig. 5, the value of δrad decreases monotonically with WI both in cyclonic and anticyclonic eddies. This negative correlation between δrad and WI is likely to result from the effects of NIWs on turbulent vertical mixing within the SBL. The dissipation of NIW energy within the SBL (denoted as D) is equal to the product of near-inertial shear variance and turbulent vertical viscosity that itself increases with the near-inertial shear variance. Assuming that the near-inertial shear variance is proportional to WI, D will grow superlinearly as WI increases. Neglecting the horizontal radiation and tendency of NIW energy, δrad can be approximated as 1 − D/WI, a decreasing function of WI.

Fig. 5.
Fig. 5.

Bin-averaged δrad (defined as the ratio of local FSBL to WI) as a function of WI (mW m−2) and enstrophy of BMs (s−2) (a) within cyclonic regions and (b) within anticyclonic regions. Bins with the sample number less than 1000 are not shown as there are insufficient samples to obtain robust statistics.

Citation: Journal of Physical Oceanography 51, 7; 10.1175/JPO-D-20-0276.1

The dependence of δrad (defined as the ratio of local FSBL to WI) on the enstrophy of BMs is more complicated, exhibiting different features between the cyclonic and anticyclonic eddies. The value of δrad is systemically larger in the anticyclonic than cyclonic eddies. In addition, δrad increases monotonically with the enstrophy of BMs in the anticyclonic eddies (Fig. 5b) but less so in the cyclonic ones (Fig. 5a). This confirms the crucial role of anticyclonic eddies as the NIW energy conduit to the deep ocean, which is consistent with existing theoretical studies and observational estimates (Balmforth et al. 1998; Klein and Smith 2001; Klein et al. 2004; Rainville and Pinkel 2004; Jing and Wu 2014; Thomas et al. 2020).

In addition to the pronounced spatial variability, FSBL exhibits evident seasonality (Table 1). The quasi-global integral of FSBL reaches maximum (0.16 TW) and minimum (0.1 TW) in winter and spring/summer, respectively. Such a seasonal cycle is similar to that of WI, suggesting that the seasonality of FSBL is mainly attributed to WI. Indeed, the value of δrad varies less than 15% among different seasons.

Table 1.

Seasonal variation of the quasi-global integral of FSBL, WI, and the corresponding δrad simulated in CESM. The second and third rows list the months used to compute the seasonal mean values for the Northern Hemisphere (NH) and Southern Hemisphere (SH), respectively.

Table 1.

c. Energy transfer from BMs to NIWs below the SBL

In this subsection, we analyze the energy transfer from BMs to NIWs below the SBL. The annual mean Π is generally positive at midlatitudes but is dominated by negative values in the low-latitude regions (Fig. 6a). Correspondingly, the quasi-global integral of Π is close to zero (−2.8 × 10−4 TW). Even in the WBC extensions where the forward energy transfer from BMs to NIWs is most pronounced, the magnitude of Π is more than an order of magnitude smaller than that of FSBL. Therefore, the energy source for NIWs in the ocean interior is dominated by the downward flux of NIW energy at the SBL base with the energy transfer from BMs making negligible contribution.

Fig. 6.
Fig. 6.

The spatial distribution of annual mean (a) Π, (b) Πcon, (c) Πstrain, and (d) Πshear. Unit here is mW m−2.

Citation: Journal of Physical Oceanography 51, 7; 10.1175/JPO-D-20-0276.1

Decomposition of Π into Πcon, Πstrain, and Πshear suggests that all the three components play an important role in shaping the spatial pattern of Π (Figs. 6b–d). The most notable feature for Πcon is the large negative values along the trajectories of tropical cyclones (Fig. 6b), which is attributed to the horizontal divergent flows associated with the wind-induced upwelling. This strong inverse energy transfer (i.e., the energy transfer from NIWs to BMs) is largely compensated by the forward energy transfer in the WBC extensions and Southern Ocean, so that the quasi-global integral of Πcon is only slightly negative (−8 × 10−4 TW). It should be noted that in the Southern Ocean and WBC extensions, the probability density functions (PDFs) of BM-induced horizontal convergence and divergence are nearly symmetric (Figs. 7a,b). The net energy transfer associated with Πcon stems instead from a tendency for NIWs to be stronger in horizontally convergent balanced flow (Figs. 7c,d), as revealed by the bin-averaged u2 + υ2 as a function of ∇hu. As Πcon is proportional to the product of u2 + υ2 and ∇hu, forward energy transfer in convergent balanced flows surpasses the inverse energy transfer in divergent balanced flows, leading to a net forward energy transfer from BMs to NIWs. The asymmetry of u2 + υ2 between horizontal convergence and divergence of BMs could result from two factors. The first is the feedback of energy transfer on NIWs. Specifically, forward and inverse energy transfers in the convergent and divergent balanced flows act to increase and decrease NIW energy, respectively. The second is the relative dominance of horizontal convergence (divergence) in the anticyclonic (cyclonic) eddies (Figs. 7e,f), which is consistent with the composite results in previous study (Yan et al. 2016). As NIWs tend to be repelled from cyclonic eddies but concentrated in the anticyclonic eddies, this also leads to stronger NIWs in the convergent than divergent balanced flows. Which factor is more important remains unclear but deserves further analysis in the future.

Fig. 7.
Fig. 7.

(a) Probability density function (PDF) of vertically averaged ∇hu within 150–950 m in the WBC extensions (Kuroshio Extension: 29°–42°N, 130°–170°E; Gulf Stream Extension: 29°–42°N, 78°–53°W) and the Southern Ocean (65°–40°S, 0°–360°E). (b) As in (a), but with the symmetric part of PDF subtracted. (c) NIW energy averaged within 150–950 m as a function of vertically averaged ∇hu. (d) As in (c), but with the symmetric part of NIW energy subtracted. (e) υ¯/xu¯/y averaged within 150–950 m as a function of vertically averaged ∇hu. (f) As in (e), but with the symmetric part of υ¯/xu¯/y subtracted.

Citation: Journal of Physical Oceanography 51, 7; 10.1175/JPO-D-20-0276.1

The value of annual mean Πstrain is positive over most parts of the global ocean (Fig. 6c). Its quasi-global integral amounts to 0.0044 TW. Similar to Πcon, the magnitude of the annual mean Πstrain is intensified in the WBC extensions and Southern Ocean as well as along the trajectories of tropical cyclones where strong NIWs and horizontal strain of BMs coexist. Consistent with the observational results (Polzin 2010; Jing et al. 2018), we find the energy transfer through Πstrain is mainly accounted for by the wave capture mechanism. In this mechanism, the relation between the evolution of internal waves and geostrophic flows is determined by the Okubo–Weiss (OW) parameter (Provenzale 1999). When the OW parameter is negative, the horizontal wave vector rotates and its magnitude oscillates. Then geostrophic flows have no permanent influences on internal waves. However, azimuth of horizontal wave vector asymptotically points to a direction determined by the geostrophic velocity gradient alone when the OW parameter is positive. In that direction, the magnitude of wavenumber exhibits exponential growth with time (Jing et al. 2018). As the group velocity of internal waves decreases with increasing wavenumber magnitude (Bühler and McIntyre 2005), internal waves will be eventually captured by the geostrophic flow.

Figures 8a and 8b display the composite mean Πstrain for the periods with positive OW parameter when the wave capture can take place and negative OW parameter when the wave capture is inhibited, respectively. The spatial pattern of the former is highly correlated to that of annual mean Πstrain with a correlation coefficient of 0.92, whereas this value reduces to 0.44 for the latter. Moreover, the quasi-global integral of composite mean Πstrain for the positive OW parameter period amounts to 0.0052 TW. In contrast, the value is only 0.0025 TW for the negative OW parameter period, confirming the important role of wave capture mechanism in the energy transfer from BMs to NIWs.

Fig. 8.
Fig. 8.

The spatial distribution of composite mean Πstrain (mW m−2) for the periods with (a) positive and (b) negative OW parameters.

Citation: Journal of Physical Oceanography 51, 7; 10.1175/JPO-D-20-0276.1

The annual mean Πshear exhibits significant spatial variability (Fig. 6d). It is noisy in the WBC extensions and Southern Ocean even after the 2° × 2° running mean, with the spatial mean value over these regions close to zero. Spatially coherent positive Πshear resides in the subtropical gyre interior of the Southern Hemisphere. But this forward energy transfer through Πshear is overwhelmed by the inverse energy transfer in the north and south equatorial currents. The quasi-global integral of annual mean Πshear is −0.0039 TW, almost cancelling the forward energy transfer though Πstrain. Notably, the magnitude of Πshear does not vanish in the abyss (Fig. 9). The quasi-global integral of εshear exhibits a positive peak around 200 m (Fig. 9a) and a negative peak around 900 m, respectively (Fig. 9b). This is in contrast to εcon and εstrain of which the magnitudes attenuate rapidly with the increasing depth. Due to the dipolar structure of εshear in the vertical direction, the quasi-global integral of ε is positive from the SBL base to 600 m and becomes negative farther downward. Therefore, energy is transferred from BMs to NIWs in the upper ocean but this energy is returned back to BMs in the abyss, consistent with the recent observation derived from mooring and microstructure measurements in the Southern Ocean (Cusack et al. 2020) and numerical simulations (Taylor and Straub 2016, 2020).

Fig. 9.
Fig. 9.

Vertical profiles of quasi-global integral of ε (black) and its three components εcon (orange), εstrain (red), and εshear (blue) below the SBL: (a) from the SBL base to 500 m and (b) from 500 to 3000 m.

Citation: Journal of Physical Oceanography 51, 7; 10.1175/JPO-D-20-0276.1

4. Discussion

Simulation results from the high-resolution CESM suggest that about one-third of WI can survive from the dissipation in the SBL and radiate into the ocean interior to power the turbulent diapycnal mixing. This ratio value is considerably larger than the recent estimate (i.e., 11%) derived from the ocean-alone simulation with comparable horizontal resolution (Rimac et al. 2016). It should be noted that δrad derived by Rimac et al. (2016) is based on the simulation results in two particular months (January and July), whereas computation in this study is performed over one entire year. Furthermore, the definition of the SBL base used by Rimac et al. (2016) differs from ours. However, we find that these differences cannot account for the differed δrad between Rimac et al. (2016) and this study, because recomputing δrad for the same period and with the same definition of SBL as used by Rimac et al. (2016) does not result in any substantial changes (not shown). Therefore, the discrepancy in δrad is likely to result from the differed model configurations between Rimac et al. (2016) and this study. One important difference is that Rimac et al. (2016) adopted the Pacanowski–Philander (PP) turbulent vertical mixing scheme (Pacanowski and Philander 1981), whereas the KPP scheme is used in our simulation. To examine the effect of different turbulent vertical mixing schemes on δrad, we repeat our CESM simulation adopting the PP scheme with all the other model configurations unchanged. Due to the limited computing resources, the CESM simulation adopting the PP scheme is only integrated for 2 months (July and January) as in the simulation conducted by Rimac et al. (2016). It is found that the parameterized turbulent vertical viscosity by the PP scheme within the SBL is systematically larger than that by the KPP scheme (Fig. 10). This leads to stronger NIW energy dissipation within the SBL, making less NIW energy available to radiate downward into the ocean interior (Fig. 11). In the simulation adopting the KPP scheme, the quasi-global integral of FSBL in January (July) accounts for 30.5% (31.8%) of WI, whereas the value is reduced to 17.2% (16.3%) in the simulation with the PP scheme. It is difficult to justify which mixing scheme is more reasonable. Therefore, both the values of δrad estimated by Rimac et al. (2016) and this study should be treated with caution.

Fig. 10.
Fig. 10.

Spatial distribution of mean turbulent vertical viscosity (VVC) within the SBL in January parameterized by the (a) KPP scheme and (b) Pacanowski–Philander scheme. (c),(d) As in (a) and (b), but in July. All the values are derived from the CESM simulation.

Citation: Journal of Physical Oceanography 51, 7; 10.1175/JPO-D-20-0276.1

Fig. 11.
Fig. 11.

The spatial distribution of δrad in January parameterized by the (a) KPP scheme and (b) Pacanowski–Philander scheme. (c),(d) As in (a) and (b), but in July. All the values are derived from the CESM simulation.

Citation: Journal of Physical Oceanography 51, 7; 10.1175/JPO-D-20-0276.1

It should be noted that the value of δrad in the CESM simulation with the PP scheme is still evidently larger than 11% obtained by Rimac et al. (2016). We suspect that it might be partially due to the excessive damping of BMs by their induced surface heat and momentum flux (wind stress) anomalies in an ocean-alone simulation as the overlying atmosphere is not allowed to make adjustment to these anomalous fluxes (Renault et al. 2016; Yang et al. 2018). This might lead to weaker BMs in Rimac et al.’s (2016) simulation than ours, reducing the efficiency of downward NIW energy radiation at the SBL base.

There is also a caveat for the reliability of simulated energy change between BMs and NIWs by CESM. In particular, the horizontal resolution of the CESM in this study is insufficient to resolve BMs at submesoscales that produce stronger strain, shear, and convergence/divergence than mesoscale BMs. Existing literature suggests these submesoscale BMs are more efficient than mesoscale BMs in exchanging their energy with NIWs (D’Asaro et al. 2011; Whitt and Thomas 2013; Nagai et al. 2015; Whitt et al. 2018). However, the submesoscale BMs are mainly confined to the SBL (Boccaletti et al. 2007; Fox-Kemper et al. 2008; Mensa et al. 2013; Gula et al. 2014; McWilliams 2016) although recent studies reported that they could occasionally penetrate into the thermocline (Erickson and Thompson 2018; Yu et al. 2019; Siegelman 2020; Siegelman et al. 2020). It remains unclear whether these submesoscale BMs play an important role in powering the NIWs in the ocean interior. Nevertheless, this study suggests that the energy transfer from mesoscale BMs to NIWs makes negligible contribution at least in terms of global mean.

5. Conclusions

In this study, we estimate the global energy flux into NIWs below the SBL based on a high-resolution CESM. Its ocean component has a horizontal resolution of ~0.1°, which is fine enough to resolve balanced motions at mesoscales. The atmosphere component has a horizontal resolution of ~0.25°, which can resolve atmospheric fronts and tropical cyclones that contribute substantially to the wind stress variability around the inertial frequency. The major conclusions are as follows.

The CESM simulates the NIWs in the global ocean reasonably well. The simulated quasi-global integral of wind power on NIWs (WI) amounts to 0.44 TW, consistent with the recent observational estimate derived from surface drifters and satellite wind measurements.

The downward flux of NIW energy at the SBL base (FSBL) is positive definite, exhibiting enhancement in the WBC extensions and Southern Ocean as well as along the trajectory of tropical cyclones. Its quasi-global integral is 0.13 TW, accounting for 29.6% of WI.

The ratio (δrad) of local FSBL to WI varies substantially over the space, ranging from 20% to 65%. It exhibits an increasing trend with the enstrophy of BMs and a decreasing trend with WI.

The kinetic energy exchange between BMs and NIWs is depth dependent. Energy is transferred from BMs to NIWs from the SBL base to 600 m but this energy is transferred back farther downward. Correspondingly, the quasi-global integral of energy transfer below the SBL is only −2.8 × 10−4 TW, more than two orders of magnitude smaller than that of FSBL.

This study suggests that an energy flux of 0.13 TW is into the NIWs in the ocean interior. This energy flux is comparable to that (~0.2 TW) into the lee waves (Nikurashin and Ferrari 2011) and not negligible compared to that (1 TW) into the internal tides (Munk and Wunsch 1998; Egbert and Ray 2001; Jayne and St. Laurent 2001). Therefore, NIWs may play an important role in powering the turbulent diapycnal mixing in the ocean interior. Currently, parameterization of NIW-induced turbulent diapycnal mixing remains to be challenging (MacKinnon et al. 2017). A particular difficulty is the specification of δrad. While the existing parameterizations typically adopt a constant value for δrad (Danabasoglu et al. 2012; Jochum et al. 2013; Olbers and Eden 2013), this study reveals pronounced spatial variability of δrad. The spatial variability of δrad is to some extent accounted for by the dependence of δrad on WI and enstrophy/vorticity of BMs. Hopefully, such dependence could provide guidance for developing more reliable parameterizations of NIW-induced turbulent diapycnal mixing.

Acknowledgments

This research is supported by National Science Foundation of China (41822601, 41776006), Fundamental Research Funds for the Central Universities (201762013, 202072009, 202113002, 202172001), and Taishan Scholar Funds (tsqn201909052, tsqn201812022). The model simulation and many of the computations were executed at the High Performance Computing Center of Pilot National Laboratory for Marine Science and Technology (Qingdao). We would like to acknowledge supports from the International Laboratory for High-Resolution Earth System Prediction, a collaboration by Pilot National Laboratory for Marine Science and Technology, Texas A&M University, and the U.S. National Center for Atmospheric Research.

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