Portal de Periódicos da CAPES

Turbulent diapycnal mixing in the subtropical northwestern Pacific: Spatial-seasonal variations and role of eddies

2011; American Geophysical Union; Volume: 116; Issue: C10 Linguagem: Inglês

10.1029/2011jc007142

2156-2202

Zhao Jing, Lixin Wu, Lei Li, Chengyan Liu, Xi Liang, Zhaohui Chen, Dunxin Hu, Qing‐Yu Liu,

Climate variability and models

Journal of Geophysical Research: OceansVolume 116, Issue C10 Free Access Turbulent diapycnal mixing in the subtropical northwestern Pacific: Spatial-seasonal variations and role of eddies Zhao Jing, Zhao Jing [email protected] Physical Oceanography Laboratory, Ocean University of China, Qingdao, ChinaSearch for more papers by this authorLixin Wu, Lixin Wu Physical Oceanography Laboratory, Ocean University of China, Qingdao, ChinaSearch for more papers by this authorLei Li, Lei Li Physical Oceanography Laboratory, Ocean University of China, Qingdao, ChinaSearch for more papers by this authorChengyan Liu, Chengyan Liu Physical Oceanography Laboratory, Ocean University of China, Qingdao, ChinaSearch for more papers by this authorXi Liang, Xi Liang Physical Oceanography Laboratory, Ocean University of China, Qingdao, ChinaSearch for more papers by this authorZhaohui Chen, Zhaohui Chen Physical Oceanography Laboratory, Ocean University of China, Qingdao, ChinaSearch for more papers by this authorDunxin Hu, Dunxin Hu Key Laboratory of Ocean Circulation and Wave, Chinese Academy of Sciences, Qingdao, ChinaSearch for more papers by this authorQingyu Liu, Qingyu Liu Physical Oceanography Laboratory, Ocean University of China, Qingdao, ChinaSearch for more papers by this author Zhao Jing, Zhao Jing [email protected] Physical Oceanography Laboratory, Ocean University of China, Qingdao, ChinaSearch for more papers by this authorLixin Wu, Lixin Wu Physical Oceanography Laboratory, Ocean University of China, Qingdao, ChinaSearch for more papers by this authorLei Li, Lei Li Physical Oceanography Laboratory, Ocean University of China, Qingdao, ChinaSearch for more papers by this authorChengyan Liu, Chengyan Liu Physical Oceanography Laboratory, Ocean University of China, Qingdao, ChinaSearch for more papers by this authorXi Liang, Xi Liang Physical Oceanography Laboratory, Ocean University of China, Qingdao, ChinaSearch for more papers by this authorZhaohui Chen, Zhaohui Chen Physical Oceanography Laboratory, Ocean University of China, Qingdao, ChinaSearch for more papers by this authorDunxin Hu, Dunxin Hu Key Laboratory of Ocean Circulation and Wave, Chinese Academy of Sciences, Qingdao, ChinaSearch for more papers by this authorQingyu Liu, Qingyu Liu Physical Oceanography Laboratory, Ocean University of China, Qingdao, ChinaSearch for more papers by this author First published: 19 October 2011 https://doi.org/10.1029/2011JC007142Citations: 29AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Abstract [1] Both spatial and seasonal variation of turbulent diapycnal mixing in the subtropical northwestern Pacific are evaluated by employing a fine-scale parameterization method based on profiles of potential density, which are obtained from CTD measurements during our recent hydrographic surveys implemented by the China National Key Basic Research Project from 2008 to 2010 and the World Ocean Circulation Experiment. Over smooth seafloor, the value of diffusivity away from the boundary is comparable with the values observed in the stratified midlatitude ocean interior, i.e., O (10−5 m2 s−1). On the other hand, enhanced diapycnal mixing, i.e., O (10−4 m2 s−1) or larger has been found over rough topography such as the Central Basin Trough, Okidaito Ridge, the origin of the Kuroshio Current, and especially Luzon Strait, which might result from dissipation of baroclinic energy generated when barotropic tides rub over rough topography. Over flat bathymetry, mixing is probably stirred by the wind work on near inertial motions in the upper 600 m and enhanced downward propagating energy has been found in the presence of anticyclonic eddies, which points to the important role of anticyclonic eddies in enhancing the diapycnal mixing at greater depth. The diffusivity also displays a distinct seasonal variation with strong (weak) mixing corresponding to strong (weak) wind-input energy in winter (summer), which, however, is only confined to upper 600 m. This is different from the midlatitude northwestern Pacific, where seasonality of diffusivity can be found at 1500-m depth. Key Points Seasonality of diapycnal mixing stirred by wind-input near inertial energy Enhanced downward-propagating energy in the presence of anticyclonic eddies Enhanced diapycnal mixing over rough bathymetry 1. Introduction [2] Turbulent diapycnal mixing in the ocean controls the transport of heat, modifies water masses, and maintains ocean stratification. Understanding the spatial and temporal variation of diapycnal diffusivity is important for improving the representation and prediction of large-scale ocean circulation and climate with numerical models [Saenko and Merryfield, 2005; Wunsch and Ferrari, 2004]. With the traditional one-dimensional advection–diffusion model, Munk [1966] argued that an average vertical diffusivity K of O (10−4 m2 s−1) is required to maintain the observed abyssal stratification. However, the last three decades of microstructure measurements have indicated a much smaller diapycnal diffusivity value, i.e., O (10−5 m2 s−1), in the stratified midlatitude ocean interior away from boundaries [Gregg, 1987; Polzin et al., 1997; Kunze et al., 2006]. Several possible mechanisms have been proposed to resolve this discrepancy, varying from enhanced mixing over rough topography to wind-driven diapycnal fluxes in the Southern Ocean [Toggweiler and Samuels, 1998]. In the past 20 years, elevated diapycnal diffusivities, i.e., O (10−4 m2 s−1) or larger have been found to occur over rough bathymetry such as ridges [Althaus et al., 2003; Klymak et al., 2006], seamounts [Kunze and Toole, 1997; Lueck and Mudge, 1997], canyons [St. Laurent et al., 2001; Carter and Gregg, 2002], as well as hydraulically controlled passages [Roemmich et al., 1996; Polzin, 1996; Ferron et al., 1998]. [3] Much of the oceanic mixing away from boundaries occurs through internal wave breaking. Energy input by tides and wind primarily furnishes the internal wavefield [Wunsch and Ferrari, 2004]. Internal tides are generated where the barotropic tide flows over rough bathymetry. While a small fraction of the resultant energy goes into high modes that can dissipate locally, the bulk will radiate at low vertical modes [St. Laurent et al., 2002; St. Laurent and Garrett, 2002], and it remains unknown where this part of energy dissipates. Besides, the internal lee waves can also be generated as geostrophic flows impinge on rough topography [Polzin, 1999; Polzin, 2004], which might play a very important role in maintaining the enhanced mixing founded in the Southern Ocean [Naveira Garabato et al., 2003]. Though the elevated diapycnal mixing above rough bathymetry has been well demonstrated by the previous observations, it is still poorly understood how far the enhanced mixing is able to extend and this might vary from one site to another due to the different topographic roughness as well as the strength of bottom flow [Polzin, 2004]. [4] On the other hand, the energy flux input from the wind to near inertial motions in the upper ocean mixed layer is another main source to sustain the turbulent diapycnal mixing [Alford, 2003]. However, it has been argued whether a substantial part of wind-input energy can propagate downward to sustain the subsurface and deep ocean mixing [Wunsch and Ferrari, 2004]. By using a numerical model, Zhai et al. [2005] demonstrated that the leakage of near-inertial energy out of the surface layer is strongly enhanced in the presence of the eddies, with the anticyclonic eddies acting as a conduit to the deep ocean. Nevertheless, it remains uncertain to what extent the anticyclonic eddies could modulate the diapycnal mixing under surface layer and more observations are still needed. [5] It is conceivable that seasonal and interannual variations of the wind stress and mesoscale eddies may lead to similar variations in turbulent diapycnal mixing throughout the upper ocean globally. Although the low-frequency variations of turbulent diapycnal mixing so far are still poorly understood, they are critically important for improving models' ability in evaluation and prediction of changes of large-scale ocean circulation [e.g., Richards et al., 2009]. [6] The subtropical northwestern Pacific contains a full spectrum of bathymetric features and a wide range of ocean conditions. The seafloor is almost flat and featureless in the Philippine Basin with much rougher topography around Philippine Islands, Benham Plateau, Central Basin Trough, Okidaito Ridge, and especially Luzon Strait (Figure 1). Besides, the tidal dissipation here is also considerably variable with the energy dissipation at Luzon Strait orders of magnitude larger than that in the remaining places [Egbert and Ray, 2000; Tian et al., 2009]. Therefore, the subtropical northwestern Pacific serves as a miniature of the global ocean to some extent and a thorough knowledge of diapycnal mixing here would be very useful to expand our understanding of the global mixing. In addition, recent analysis of historical hydrographic data collected to the south of Japan Island reveals that seasonality of diapycnal mixing penetrates to great depth, pointing to the important role of wind-input near inertial energy in furnishing the subsurface and deep-ocean mixing [Jing and Wu, 2010]. However, whether this holds throughout the world ocean remains uncertain due to the limited data sets. Therefore, it would be very helpful to analyze the seasonal variation here and make a comparison with previous study. Figure 1Open in figure viewerPowerPoint (a) WOCE Section P08N (pink dashed), PR20 (gray dashed), and PR21 (green dashed) along with the bathymetry in the subtropical northwestern Pacific (unit: m). The abbreviation "KO" represents the origin of the Kuroshio Current. (b) The hydrographic sections of our recent four surveys along with the map of topographic roughness: the blue solid represents the repeated sections which have been observed during each cruise, and the gray solid represents the ones only observed during Cruise 4. The color bar represents log10 (Roughness) in m2, and the arrow points to the critical value distinguishing the smooth bathymetry from rough topography. [7] In this paper we apply a fine-scale parameterization developed by Kunze et al. [2006] to CTD profiles collected here by our recent hydrographic surveys and the World Ocean Circulation Experiment (WOCE) to analyze both the spatial and seasonal variation of turbulent diapycnal mixing and the controlling mechanisms. [8] The paper is organized as follows. Data and methodology are given in section 2. Results and analysis are presented in section 3. The validation of the estimates by a fine-scale parameterization method is tested in section 4. Finally, the paper is concluded with a summary and some discussions are included in section 5. 2. Data and Methodology Data [9] Since October 2008, we have so far carried out four cruises to a number of sites in the subtropical northwestern Pacific (Figure 1b and Table 1). Data were collected using a Seabird 9–11 Plus CTD and a Seabird 9–17 Plus with sensors sampling at 24 Hz. The accuracy of conductivity and temperature are 0.0003 S m−1 (corresponding to an accuracy of about 0.003 psu for salinity) and 0.001°C, respectively. The CTD is lowered at a rate of 0.5 m s−1 and only the data collected during downcasts are used here. Temperature and conductivity values were aligned in time to correct for sensor-response-lag effects according to the Instruction Manual supplied by SeaBird Electronics, Inc. Then the data were averaged to half-second (2 Hz) values to reduce random noise, which results in an approximate 0.25-m vertical resolution. During four cruises, there were 101 profiles collected in the Luzon Strait and subtropical northwestern Pacific (Table 1). On the other hand, the CTD measurements from WOCE Section P08N, PR20, and PR21 are also employed here (Figure 1a). These profiles have 2-m vertical resolution. Uncertainties are 0.0005°C for temperature and 0.002 psu for salinity [Kunze et al., 2006]. The data spanned from year 1990 to year 1996. Only the profiles located within the latitude band 0–25°N are used here, which results in 155 profiles in total (Table 2). Table 1. Start Time, End Time, and the Number of Profiles Collected in Different Regions During Each Cruise Cruise 1 Cruise 2 Cruise 3 Cruise 4 Total Luzon Straita 6 11 4 8 29 KOb 3 5 6 14 28 Smooth 0 0 0 19 19 Othersc 0 1 1 23 25 Start time 20080917d 20090709 20091203 20101115 End time 20080928 20090729 20091220 20110105 a Luzon Strait is defined as region 120°E–122°E, 18°N–22°N. b The abbreviation "KO" represents the origin of Kuroshio Current, which is defined as region 122°E–124°E, 18°N. c "Others" means the profiles located over rough bathymetry but not located at Luzon Strait and in the origin of Kuroshio Current. d The digits "20080917" means 17 September 2008. Table 2. The Number of WOCE Profiles Collected in Different Regions P08N PR20 PR21 Total Luzon Strait 0 21 22 43 KO 0 0 0 0 Smooth 39 40 0 79 Others 16 17 0 33 [10] Besides, we also use the 6-h sea surface wind stress in the same period from NCAR/NCEP Reanalysis [Kalnay et al., 1996] and the merged satellite altimetry sea surface height anomaly data provided by AVISO with a 1-day temporal resolution as well as a 1.3° longitude Mercator spatial grid. [11] Finally the ETOPO2v2 (2-Minute Gridded Global Relief Data) are used to evaluate the topographic roughness var(h) in a 1/3° × 1/3° domain square, where h represents the topographic height [Kunze et al., 2006]. Here the smooth bathymetry is defined as regions with the roughness value less than 5 × 104 m2, and the rough topography as that with value larger than 5 × 104 m2. The critical value is chosen by visually inspecting Figures 1b and 4c, and a minor change of this value does not result in any substantial difference for the results here. Fine-Scale Parameterization Method [12] Based on the idea that weakly nonlinear interactions between a well-developed sea of internal waves act to steadily transport energy from the large (vertical) scales at which it is generated and propagates, to the small scales at which waves break due to shear or convective instabilities, the diapycnal diffusivity can be expressed in terms of fine-scale strain as [Kunze et al., 2006] where K0 = 0.5 × 10−5 m2 s−1, GM〈ξz2〉 is strain variance from the Garrett-Munk model spectrum [Gregg and Kunze, 1991] treated in the same way as the observed strain variance 〈ξz2〉: f30 = f(30°), N0 = 5.2 × 10−3 rad s−1, and Rω represents shear/strain variance ratio, which is fixed at 7 in this paper. [13] Internal wave strain is estimated from buoyancy frequency ξz = (N2(z) − 2)/2, where N2(z) is computed from the vertical difference of potential density and mean stratification, and 2 is based on quadratic fits to each profile segment [Polzin et al., 1995]. Then Fourier transforming gives the spectral representation ϕ(k), and a spectral correction is employed to compensate the attenuation at higher wave numbers due to the difference operator used to calculate strain [Polzin et al., 2002]. Strain variance 〈ξz2〉 is determined by integrating ϕ(k) from a minimum vertical wave number kmin out to a maximum wave number kmax [Kunze et al., 2006] so that The GM strain variance is computed over the same wave number band so that where E0 = 6.3 × 10−5 is the dimensionless energy level, b = 1300 m the scale depth of the thermocline, j* = 3 the reference mode number and k* = (π · j* · N)/(b · N0) the reference wave number with N0 = 5.2 × 10−3 rad s−1 [Gregg and Kunze, 1991]. [14] The dissipation rate can be expressed in the form of where Γ is mixing efficiency and typically taken to be 0.2 [Osborn, 1980]. In this paper, the vertically integrated dissipation rate from depth D1 to depth D2 represents ρ · ɛ · dz, where ρ is the density of seawater. [15] As profiles of horizontal velocity are not available, it is difficult to estimate Rω. Based on 3500 lowered ADCP/CTD profiles from the Indian, Pacific, North Atlantic, and Southern Oceans, Kunze et al. [2006] found that for N > 4.5 × 10−4 s−1 the measured shear/strain variance ratio Rω = 7 ± 3 is a little over twice the canonical GM value of 3 in diverse situations. Here, a fixed value, i.e., Rω = 7 is used, which might lead to uncertainties probably about a factor of 2 by invoking the equation (3). As the fine-scale parameterization was only able to reproduce microstructure diffusivities to within a factor of 2 [Polzin et al., 1995], the total uncertainties inherent in our results would probably be within a factor of 4. [16] Finally, all the profiles are broken into 300-m segments to evaluate the strain spectra and then the segment-averaged diffusivity. In the upper ocean the strain spectrum may be contaminated due to great depth variability in the background stratification, which means that the method is not applicable in the presence of sharp pycnoclines. Therefore, the shallowest segment, i.e., 0–300 m, is discarded by following Kunze et al. [2006]. At deeper segment, i.e., 300–600 m over smooth bathymetry, the excessive redness of the spectra due to strong depth changes in the background stratification is almost confined to the lowest resolved wave numbers, i.e., 0.04 rad m−1 (Figure 2a) and thus the contamination is negligible. Figure 2Open in figure viewerPowerPoint The averaged vertical wave number spectra for strain over smooth bathymetry (a) at the uppermost segment and (b) at the lowermost two segments. (c) The vertical wave number spectra for strain (color solid) binned with respect to the GM-normalized strain variance (legend to right) and the GM model strain spectrum (gray dashed). Vertical dashed lines denote the lower integration limit for strain variance. Note that the linear scale for both x and y axes is used in Figures 2a and 2b but the logarithmic scale is used in Figure 2c. [17] The strain spectra might also be contaminated by density noise, and the contamination would be more serious in the region with weak background stratification and low strain variance. Typically, spectra of raw quantities should be red, flattening out at some high wave number where noise becomes significant. Since strain is a gradient quantity, its spectra will be flatter and noise will appear blue. Below 3000 m over smooth topography where the background stratification is extremely weak, the spectra appear blue throughout the whole wave band (Figure 2b). Therefore, the strain variance evaluated in these regions is not reliable and should be treated cautiously. [18] Figure 2c displays vertical wave number spectra for strain in the upper 3000 m binned with respect to GM-normalized strain variance These have GM-normalized strain variances ranging from 0.5 to 1 to 5–10 with about 90% of the segments having larger than 1. Therefore, the strain spectral level is generally higher than that of GM model. For low variances, the strain spectra tend to be flat or slightly blue at mid-wave numbers (λ = 10–150 m) and as strain variances increase, the mid-wave number spectral level rises and becomes flatter. [19] By employing a Lillefors test [Lilliefors, 1967], we find the estimated values of K and ɛ among all the profiles tend to be more close to a lognormal distribution compared with a normal distribution. So all the average values relevant to K and ɛ are computed as the geometric mean rather than the arithmetic mean in this paper. Thorpe-Scale Method [20] The dissipation rate for a single density overturn event is [Thorpe, 1977] where a = 0.8 is a constant of proportionality [Dillon, 1982], N buoyancy frequency, and LT the Thorpe scale which is a measure of the vertical length scale of density overturns that, in a stratified fluid, are associated with gravitational instabilities. [21] Potential density is used for the overturn analysis. Here, σθ, σ2 and σ4 are used for the water column shallow than 1000 m, between 1000 m and 3000 m, and below 3000 m, respectively. For each turbulent overturn (here overturn is defined by following Dillon [1984]), LT is calculated as the RMS vertical displacement required to reorder the observed potential density profile into a gravitationally stable one [Thorpe, 1977], and N is evaluated from the gradient of reordered profile within the vertical boundaries of each overturn to avoid overestimation [Finnigan et al., 2002]. [22] The segment-mean dissipation rate is evaluated following Finnigan et al. [2002] in the form of Here D = 300 m represents the total depth of the segment and Li is the thickness for a single overturn. It should be noted that the Thorpe-scale method is not applicable to the WOCE data because of the limit of the vertical resolution of the data (2 m). [23] Both spatial resolution of the measurements and noise of the instruments may impose constraints on the overturn detection [Galbraith and Kelley, 1996]. Because in situ noise levels may exceed manufacturer statements for a variety of reasons, here a run length criterion is used to detect inversions created by noise, and then RMS noise level was estimated from Thorpe fluctuations of these noisy inversions [Galbraith and Kelley, 1996]. We employ this criterion to all the overturns detected in the profiles collected during our 4 cruises. The cutoff run length is about 8 for the data analyzed in this paper. We evaluate the RMS noise level for each overturn with run length less than the cutoff value. About 90 percent of these noise-induced overturns have a RMS noise level less than 0.5 × 10−3 kg m−3, which is therefore set to be the noise level in our analysis. Using the overturn size criteria of Galbraith and Kelley [1996] yields the minimum detectable overturn size for our data: In this paper, overturns with size less than either Lz or Lρ are treated as artifacts and are discarded. [24] Besides, though temperature and conductivity values are aligned in time to correct for sensor-response-lag effects according to the Instruction Manual, it might not be able to eliminate salinity spikes or T/S mismatches exhaustively in the real ocean. Here, the R0 criterion proposed by Gargett and Garner [2008] is employed to eliminate the artificial overturns produced by salinity spikes. [25] Figure 3 shows the number of overturns that occurs in each 300-m vertical segment over smooth bathymetry and at Luzon Strait respectively. Over smooth bathymetry, the number of overturns is about 7 in the uppermost two segments and then decreases rapidly with the increasing depth. Between 900 m and 3000 m, the number gradually drops from 4 to 1 (Figure 3). A similar decrease in overturn occurrence with depth can be also observed at Luzon Strait but the number of occurrence is much larger. The average drops from about 20 in the shallowest segment to less than 5 below 1500 m (Figure 3). Figure 3Open in figure viewerPowerPoint Averaged number of overturns per 300-m segment (NOT) over smooth topography (blue solid), and at Luzon strait where the bottom is much rougher (red solid). 3. Results and Analysis Spatial Distribution [26] The diapycnal diffusivity in the northwestern Pacific displays great spatial variability (Figures 4 and 5). Figures 4a and 4b show the background stratification and diffusivity along the meridional section 130°E. The background stratification strengthens slightly with the increasing latitude in the upper ocean but has nearly no meridional variation below 1000 m. On the other hand, the diffusivity does not show similar spatial distribution with background stratification. It can be seen from Figure 4b that over smooth bathymetry, the value of diffusivity away from the boundary is about O (10−5 m2 s−1), comparable with the values observed in the stratified midlatitude ocean interior. However, enhanced diapycnal mixing, i.e., O (10−4 m2 s−1) extends to around 1500 m above the seafloor in the vicinity of the Central Basin Trough and Okidaito Ridge where the bathymetry is much rougher (Figure 4c). Similar cases can also be found at the origin of the Kuroshio Current and at Luzon Strait where the seafloor is rough (Figures 5a and 5b) and elevated mixing is throughout the whole water column. To further analyze the relation of diapycnal mixing with topography, we compute the vertical wave number spectra for strain averaged among all the profiles over smooth and rough bathymetry, respectively. It can be seen from Figure 5c that the strain spectral level over rough bathymetry is about twofold of that over smooth topography between the lowest resolved wave number and 0.03 cpm, and at higher wave numbers the discrepancy becomes somewhat smaller. Figure 4Open in figure viewerPowerPoint Spatial distribution along the meridional section 130°N: (a) for the time-mean background stratification log10 (N2) in s−2, (b) for the time-mean diapycnal diffusivity log10 (K) in m2 s−1 and (c) for the bottom roughness in m2. The blue dashed line in Figure 4c represents the cutoff between rough and smooth. Figure 5Open in figure viewerPowerPoint The averaged vertical profiles of diffusivity in m2 s−1 (gray solid) (a) in the origin of Kuroshio Current and (b) at Luzon Strait. The blue dashed line represents the mean value averaged among all the profiles located over smooth bathymetry. (c) The vertical wave number spectra for strain averaged among all the profiles over smooth bathymetry (blue solid) and among all the profiles over rough bathymetry (red solid). The gray dashed line represents the GM model spectrum, and the vertical dashed line demarks the lower integration limit for strain variance. [27] The much stronger mixing detected is probably due to the dissipation of baroclinic energy generated when barotropic tides rub over rough topography [St. Laurent et al., 2002]. However, it should be noted that though the roughness values, i.e., O (105 m2) are comparable in these regions, the value of diffusivity in Luzon Strait, i.e., O (10−3 m2 s−1) is an order of magnitude larger than that at the origin of the Kuroshio Current, Central Basin Trough and Okidaito Ridge. This discrepancy might result from a much larger baroclinic energy flux in Luzon Strait [Egbert and Ray, 2000; Tian et al., 2009]. Wind-Driven Mixing in the Upper Ocean and Seasonality [28] Though the enhanced mixing over rough bathymetry here is possibly sustained by the tidal input energy, it remains uncertain what dominates the diapycnal mixing in the upper ocean over smooth topography. Away from the direct influence of boundary processes, most of the ocean mixing is driven by breaking internal gravity waves, with the wind work on near inertial motions being one of the major energy sources for the internal wavefield in the upper ocean [Wunsch and Ferrari, 2004]. Figure 6 shows the background stratification, i.e., 2, and dissipation rate averaged among all the 98 profiles over smooth topography. The most striking feature is the depletion of ɛ below 600 m. The dissipation rate in the uppermost segment is 3.7 × 10−9 m2 s−3, about four times of that in the following one, i.e., 1.0 × 10−9 m2 s−3. As the discrepancy of 2 between these two segments is only about a factor of 2, such depletion cannot simply result from the stronger background stratification in the uppermost segment. Instead, it probably implies an energy source located at the sea surface. Therefore, it is conceivable to expect that the wind-input energy plays an important role in furnishing the diapycnal mixing in the upper ocean, especially for the segment 300–600 m. To assess our conjecture, an energy budget is calculated as the first step. Figure 6Open in figure viewerPowerPoint Four CTD profiles with enhanced dissipation rate (m2 s−3, gray solid) and the corresponding background stratification (red solid) at (a) 16.5°N, 128°E, (b) 16.5°N, 130°E, (c) 16.5°N, 130°E, and (d) 18°N, 124.5°E. The first three profiles were collected on 26 November 2010; the final one was collected on 12 December 2009. The green and blue dashed lines represent the values of stratification and dissipation rate averaged among all the profiles over smooth bathymetry, respectively. [29] The energy flux from the wind to near inertial motions can be directly estimated using observed surface wind stress and mixed layer velocity data. However, only the former is usually available from observations. Here we use a simple slab model introduced by Pollard and Millard [1970], which allows us to compute the energy flux by only using wind stress data. The equations for the velocity components, u and v of a mixed layer are [D'Asaro, 1985] where Z = u + i · v is the mixed layer current, f is Coriolis parameter, H is the mixed-layer depth, T = (τx + i · τy)/ρ is the wind stress, and r is the frequency-dependent damping parameter [Alford, 2003] where σ represents the angular frequency, ro = 0.15 f and σc = f