Response of Near-Inertial Shear to Wind Stress Curl and Sea Level

Near-inertial waves (NIWs) contain a pronounced portion of shear energy in the internal wave field and is of great importance to deep ocean mixing. However, accurate simulation of NIWs remains a challenge. Here we analyzed 3-year long mooring observation of velocity profiles over 80–800 m to study the responses of near-inertial downward shear to varying wind stress curls and sea level anomalies (SLAs). It is demonstrated that moderate (even weak) cyclone makes more contributions to enhanced shear below the pycnocline than very strong cyclone. Because very strong curl can stall the downward propagation of large shear. The large positive and negative SLAs cause the accumulation of large shear in the lower and upper parts of the pycnocline through inducing downwelling and upwelling motions, respectively. Time variation of near-inertial shear was strongly influenced by cases of large curls and interannual variation of SLA, and thus did not follow the seasonal variation of wind stress. Our analyses suggest that matched fields of wind stress curl and SLA, and well representing the ocean response to moderate cyclone are needed in simulating the role of NIWs on mixing.

wavenumber domains, suggesting the co-occurrence of upward and downward energy propagations, respectively. In comparing with near-inertial energy in negative and positive wavenumbers and in different depths observed by upward-and downward-looking ADCPs, the former situations were larger than the latter one. This suggests that downward propagation (energy propagation, same hereinafter) and shallower layers contained more near-inertial energy than upward propagation and deeper layers, respectively. In addition, the spectra also show peaks at semi-diurnal (m 2 ) and diurnal (k 1 ) tidal frequencies, and some subharmonic frequencies (e.g., m 2 ± f, k 1 + f). Frequencies of m 2 and k 1 in velocity spectra (Fig. 3a,c) have larger energy than that in the shear spectra (Fig. 3b,d), indicating that semi-diurnal and diurnal tidal energy are dominated by low-mode motions. The appearances of m 2 ± f and k 1 + f peaks can be attributed to nonlinear wave-wave interaction [12][13][14][15][16] or vertical heaving of the near-inertial shear by tidal motions [17][18][19] . We also evaluate the model capability of simulating the NIWs. The wavenumber-frequency spectra of daily shear obtained from Hybrid Coordinate Ocean Model (HYCOM)   Wavenumber-frequency spectra of WKB-scaled rotary velocities and shears. Spectra in (a) and (c) are derived from hourly velocities observed by one upward-looking and one downward-looking ADCPs, spanning over 80-400 m and 500-800 m, respectively. Panels (b) and (d) are the same as panels (a) and (c), but for hourly shears. Panels (e) and (f) are the same as panel (b), but for daily shear from HYCOM and mooring observation, respectively. In all spectra, the period of data is from 1 October 2016 to 10 November 2016, f, m 2 , and k 1 denote inertial, semi-diurnal, and diurnal frequencies, and CW and CCW represent clockwise and counter-clockwise rotations. Figures are plotted using MATLAB R2015b (http://www.mathworks.com/).
The two-fold processes are associated with the change of stratification profile during the strong curl passing the mooring site. According to previous observational studies 24,25 , the strong positive wind stress curl can cause shallower pycnocline, and increase in N 2 in the pycnocline and decreases in N 2 below the pycnocline through inducing upwelling motion. Decrease in N 2 below the pycnocline leads to smaller vertical internal wave flux (F E ), meaning the confining of downward shear [26][27][28] . This can be understood as follows. F E can be obtained by calculating internal wave-induced velocity-pressure perturbations correlation or by multiplying vertical group velocity (C gz ) and energy density (Methods). First, internal wave-induced pressure perturbation is positively correlated with N 26 , and thus decreasing N 2 below the pycnocline corresponds to smaller F E . Second, based on the definition of C gz , decreasing N 2 leads to smaller C gz and resultant F E . The variation of C gz can be seen from Fig. 5. With increasing curl from Case 7 to Case 30, the slant angle of shear phase with respect to vertical direction is reduced, corresponding to decreasing C gz . Furthermore, shallower pycnocline and enhanced N 2 within it induced by strong curl are combined to make the intensified shear only accumulating in the shallower depth. This scenario may imply that it is the moderate intensity of wind stress curl that can make more contributions to the deep ocean mixing. Scenario 2 is constructed to evaluate the impact of SLA on time-depth variation of downward shear (Fig. 6). Four cases are contained in this scenario. The first two cases are under comparable forcing wind stress curls, but with inverse SLAs. The latter two cases resemble the first two, but their curls are negative. The difference of downward shear between the positive and negative SLA cases is striking. For the negative SLA cases (Cases 19 and 18), the strong shear with absolute value larger than 4 × 10 −3 s −1 is confined at the depth above 120 m. For the positive SLA case (Cases 39 and 38), the shear with similar intensity can extend into the depth of 220 m. The positive SLA usually corresponds to downwelling motion, leading to increases in the depths of the base of the mixed layer and pycnocline, and the pycnocline thickness [20][21][22]28 . The deepening of the base of the mixed layer means the generation depth of downward shear deeper. Furthermore, the deepening and thickening of pycnocline facilitate the downward propagation flux of internal waves. The situation is reversed during the period of negative SLA. The negative SLA corresponds to shallower generation depth and smaller vertical flux of internal waves. The above studies revealed that the intensity and propagation depth of enhanced shear are related to wind stress curl and SLA. However, these results are only presented as the "scenario" style, and still needs supports from significant statistics. We next do the scatter and ensemble mean analyses using all available wind-induced NIW cases. There is a total of 42 cases, the detailed information of which are given in Table 1. Each case contains 121-529 hourly shear profiles and corresponds to one forcing curl and one influencing SLA on the start day. Persisting periods of triggered shear during 42 cases add up to 587 days, accounting for approximate 50% of the whole measurement period. Note that Case 11 is strongly influenced by the fast-moving strong cyclone (Fig. 5), although its forcing curl is negative due to insufficient time-space resolution, and we thus set the curl to its absolute value. We also try to use 6-hourly wind data (e.g., Cross-Calibrated Multi-Platform (CCMP) gridded surface vector winds) that with the same spatial resolution (0.25°) as ASCAT. Their results show that strong wind stress curls are underestimated as compared to those from ASCAT, although there is improvement in time resolution (figure not shown).
Corresponding to the Scenario 1, we first separate all 42 cases into some typical ensembles of forcing wind stress curls. Forcing curls are divided into three ensembles, including the very strong ensemble with positive curl much larger than 15 × 10 −7 N m −3 , the moderate ensemble with positive curl over 8 × 10 −7 -15 × 10 −7 N m −3 , and the weak ensemble with curl over −8 × 10 −7 -8 × 10 −7 N m −3 . The strong and moderate negative curl ensembles are not involved in this study. Because there are only two negative curl cases with intensity larger than 8 × 10 −7 N m −3 and we are uncertain that these two negative curls are caused by fast-moving cyclone due to insufficient time-space evolution or by the real anticyclone. The very strong, moderate, and weak ensembles contain 4 cases and 1852 shear profiles, 6 cases and 1422 shear profiles, and 30 cases and 10134 shear profiles, respectively. Figure 7a shows curl ensemble-mean of hourly shear energy profiles. At the depth above 170 m (upper dashed box in Fig. 7a), shear intensity is positively correlated with the level of forcing curl, and mean shear energy of the strong curl ensemble is larger than those of moderate and weak curl ensembles. At the depth over 190-330 m (lower dashed box in Fig. 7a), the mean shear energy of the moderate curl ensemble becomes most energetic, and is 4 times larger than that of strong curl ensemble. Such difference in shear energy may correspond to diapycnal diffusivity difference of one order of magnitude based on their relationships already established in other open ocean areas 29,30 . Based on 42 cases and their 14130 hourly shear profiles, we next do the scatter plots of forcing curl versus case mean (large color dots) and profile mean (small gray dots) shear energy in (80-170 m) and below (190-330 m) the pycnocline, with color depicting the corresponding  (Fig. 7c,d). At the depth over 80-170 m, there is an increasing trend of shear energy with increasing absolute value of forcing curl. The correlation can reach 0.76 if we exclude the cases which are strongly influenced by large positive and negative SLAs (dots with red and blue colors). In the weak curl range, Cases 6, 33, 36, and 37 appeared to be influenced by fast-moving large curl fields, which however cannot be fully resolved by daily wind data. Thus, their forcing curls tend to be smaller than the real values. At the depth over 190-330 m, almost all profile mean shear energy is reduced with the significant decrease in the strong curl range. The case mean and profile mean shear energy of very strong curls notably decrease by approximate 87%. This decreasing amplitude of strong curls are 40% and 49% higher than those of moderate and weak curls, respectively. The increasing trend of shear energy with forcing curl in the shallower depth is changed to the parabolic trend here, showing the peak shear energy in the moderate curl range.
Corresponding to the Scenario 2, we also first separate all 42 cases into some typical ensembles of SLAs.  (Fig. 7b), the difference of shear energy above 240 m is striking. At the depth above 110 m (upper dashed box in Fig. 7b), shear energy of the negative SLA ensemble is larger than that of the positive SLA ensemble. At the depth between 110 m and 240 m (lower dashed box in Fig. 7b)), the situation is reversed, and the mean shear energy of the positive SLA ensemble is 4 times larger than that of the negative SLA ensemble. Based on 42 cases and their 14130 shear profiles, we next do the scatter plots of SLA versus case mean (large color dots) and profile mean (small gray dots) shear energy over the upper (80-110 m) and lower (110-240 m) parts of pycnocline, with color depicting the corresponding forcing curl (Fig. 7e,f). At two depth ranges, energetic shear energy generally corresponds to large forcing curl, mainly located in the reference SLA ensemble. In comparing with shear energy between two depth ranges, the significant change by a factor of 2 can be found in positive and negative SLA ensembles. However, their change trends are opposite, corresponding to the increase in positive SLA ensemble and the decrease in negative SLA ensemble, respectively. Previous studies (e.g., Alford et al. 2 and Jing et al. 29 ) have revealed seasonal variations of near-inertial energy and its inducing mixing. Here, a 3-year long mooring observation provides us a good opportunity to examine the variability of near-inertial shears. Time series of mean shear energy over 80-800 m are shown in Fig. 4i Table 1. Start day, forcing wind stress curl, influencing SLA, persisting period of triggered shear, and number of hourly shear profiles for all 42 wind-induced NIW cases. * Note that Case 11 is strongly influenced by the fastmoving strong cyclone (Fig. 5), although its forcing curl is negative due to insufficient time-space resolution, and we thus set the curl to its absolute value. The forcing wind stress curl and influencing SLA are defined as their corresponding values on the start day.
Scientific RepoRtS | (2019) 9:20417 | https://doi.org/10.1038/s41598-019-56822-z www.nature.com/scientificreports www.nature.com/scientificreports/ www.nature.com/scientificreports www.nature.com/scientificreports/ line in Fig. 4c,d), and was strongly influenced by cases of large curls and interannual change of SLA. Most of the large shear occurred in the wake of strong and moderate curls. From September 2015 to May 2016, negative SLA limited the mean shear energy to low values. These features revealed from time variation further support our abovementioned findings.
In summary, the influencing factors on intensity and propagation depth of near-inertial downward shear energy are discussed and some conclusions can be reached. 1) The response of shear intensity below the pycnocline to the increasing curl is non-monotone. Because very strong curl can stall the downward propagation of strong shear through decreasing internal wave flux below the pycnocline. Hence, it is the moderate (even weak) cyclone rather than the very strong cyclone that makes more contributions to the sub-pycnocline mixing. 2) The large positive and negative SLA fields cause the accumulation of large shear in the lower and upper parts of the pycnocline through inducing downwelling and upwelling motions, respectively. These conclusions give us some hints on how to improve the capability of simulating wind-induced near-inertial energy. Inaccurate and unmatched fields of wind stress curl and SLA, and ignorance of important contributions from the moderate and weak curls will probably misestimate the role of wind-induced near-inertial waves on the pycnocline and sub-pycnocline mixing.
In this study, observed velocity profiles spanning over 80-800 m lends us the opportunity to study the responses of near-inertial shears within and below the pycnocline to different forcings. During the whole observation period, intensities of all cyclones were not strong enough to reach the criteria of typhoon; however, this instead provides us an opportunity to study how the near-inertial shears respond to common cyclones, which are widely existing but drawn fewer attentions before. Another good opportunity for this study is that the corresponding SLA fields can be nearly equally divided into positive and negative periods, and amplitudes of SLAs during two periods were almost the same. This boosts the accuracy in estimating the influence of SLA on near-inertial shear. Although some influencing factors on intensity and propagation of near-inertial shear are discussed, it is not possible here to draw the conclusion of all forcings, such as the parametric subharmonic interaction (PSI), nonlinear wave-wave interaction, and moving speed and direction of cyclone. Nevertheless, we still hope that this study can deepen our knowledge of controlling mechanisms of downward near-inertial shear, and thus improve the capability of simulating NIWs (Fig. 3e,f). In the future, the structure, variability, and mechanism of upward energy propagating shear and their relationships with downward shear will be considered.

Methods
Mooring measurement and data processing. The subsurface mooring was located at 139.1°E, 11.6°N with a water depth of ~5200 m. This mooring is a part of the Scientific Observing Network of the Chinese Academy of Sciences (CASSON) in the western Pacific Ocean. The mooring was initially deployed on 14 August 2014 and recovered on 2 December 2017. On 7 November 2015 and 18 November 2016, the mooring was redeployed twice for maintenance. One upward-and one downward-looking TRDI 75 kHz ADCPs were equipped on the main float of the mooring at ~450 m. Two ADCPs measured velocity profiles over 50-1000 m with a bin size of 8 m every one hour. Data were then vertically interpolated into standard depth. Record gaps during the mooring redeployment were linearly interpolated.
In order to eliminate the change of internal waves' amplitude and vertical wavelength due to variations in the buoyancy frequency as internal waves propagate vertically, zonal and meridional velocities (u and v) were WKB scaled 31 as where N z ( ) is climatological buoyancy frequency profile computed from WOA13 temperature and salinity, and N 0 is a reference buoyancy frequency calculated from the depth mean of N z ( ) over 50-1000 m. Near-inertial velocity was obtained by applying a first-order Butterworth band-pass filter over (1 ± 0.3) f to original velocity time series. Vertical shears of zonal and meridional velocities (Su = (∂u/∂z) and Sv = (∂u/∂z)) were calculated by first-differencing velocities over 8 m interval.
The wavenumber-frequency spectrum of velocity or shear is given as where w is complex velocity (w(t, z) = u(t, z) + iv(t, z)) or shear (w(t, z) = Su(t, z) + iSv(t, z)), w * is the complex conjugate of w, which has been demeaned and detrended, ∼ w is 2D Fourier transform of w, and max w w ⁎ | × | ∼ ∼ denote the maximum of ⁎ | × | ∼ ∼ w w over time and depth 9 . In frequency-wavenumber spectrum, positive and negative frequencies correspond to counterclockwise and clockwise rotations, respectively, and positive and negative wavenumbers indicate upward and downward energy propagations, respectively. The total velocity and shear fields can be decomposed into upward and downward propagating constituents through 2D Fourier filtering 9,31 .
Internal wave energy fluxes. Internal wave energy flux (F E ) can be used to identify the vertical propagation of energy density (E), and can be written as