 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.
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).
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 −⟨p′w′⟩, 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).
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., ∇h ⋅ u). 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 u′2 + υ′2 is much larger than those of u′2 − υ′2 and u′υ′ 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.
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.
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.
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.
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.
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