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Figure1. (a) Map of the major currents in the northwestern Pacific (NWP), ECS and South China Sea (SCS). The TWC and Kuroshio Current (KC) are indicated by the red arrow and curve (solid thick line). The blue line is the 200-m contour of topography from the General Bathymetric Chart of the Oceans (GEBCO). The black frame in (a) is the study area shown in (b). The AVISO climatological mean (1993-2012) absolute dynamic topography contours of 0.9 m, 1.0 m and 1.1 m are indicated by solid black lines. The colored background is the bathymetry from GEBCO. The interval of the topography is 100 m. The magenta dots represent the hydrological stations. A02 and A06 with magenta squares are 25-h repeated stations. The microstructure stations are denoted by triangles.Observations in the northwestern part of the ECS——namely, the Yellow Sea (Lozovatsky et al., 2008; Liu et al., 2009), northern ECS (Lee et al., 2006; Lozovatsky et al., 2012, Lozovatsky et al., 2015), and shelf break (Matsuno et al., 2005; Zhou et al., 2005)——have indicated that the turbulent kinetic energy (TKE) dissipation rate ε varies in the range of 10-9-10-5 W kg-1, corresponding to a diapycnal diffusivity $\kappa$ of 10-6-10-2 m2 s-1. However, measurements of turbulence are absent in the NTI. Using ship-based observations from late June to early July in the summer of 2006, this paper presents the first observations of turbulent mixing associated with the surface and internal tides in the NTI.
The rest of this paper is organized as follows: In section 2, the data and methods are briefly introduced. In section 3, the ε and $\kappa$ in the NTI are statistically analyzed based on observations. Internal tides and the associated turbulent mixing are discussed in section 4. Section 5 is used to explain the enhancement of turbulence on the shelf of the NTI. The Ekman dynamics are also documented in this section. In section 6, the tidal modulation of water masses in the NTI are discussed. A summary and conclusion are given in section 7.
2.1. Data collection
A cruise survey along two cross-shelf sections A and B in the NTI was conducted by R/V Dong Fang Hong 2 in the summer of 2006 (Fig. 1 and Table 1). The cruise started from station A01 on 28 June and ended at station B01 on 3 July. Combined conductivity-temperature-depth (CTD) and lowered acoustic Doppler current profilers (LADCP) measurements were carried out at 18 sites along transects A and B. Following the CTD/LADCP measurements, the Turbulence Ocean Microstructure Acquisition Profiler (TurboMAP-II, Alec Inc., Japan) was deployed to collect turbulence measurements. Stations A01-A05 and B01-B09 were on the shelf, while stations A06-A08 and B10 were on the slope, where the water depth is greater than 200 m. A total of 48 profiles of CTD and LADCP deployments at two cross sections were obtained. Stations A02 (anchored) and A06 (not anchored) were two 25-h-duration repeat stations. The time interval of each CTD/LADCP casting at A02 and A06 was 1.5 h and 2 h, respectively. At S06, the vessel was not anchored because the water depth exceeded 1000 m, but the vessel returned to the designated location after each deployment.A downward-looking 300-kHz ADCP was mounted on the CTD rosette package. The vertical bin size was set to 8 m and the sampling frequency was 1 Hz. To obtain accurate current data, the falling velocity of the instrument was controlled to be no more than 0.5 m s-1. The relative horizontal velocity was measured throughout the water column with an estimated uncertainty of 1 cm s-1, and the absolute velocity was derived from the relative velocity by a linear inverse method (Visbeck, 2002). The raw LADCP data were processed using an updated MATLAB package from Martin Visbeck (personal communication, 2008). The synchronized CTD time series, GPS position and bottom track velocity data were also used to calculate the pressure, vessel velocity and absolute bottom velocity.
The free-falling TurboMAP-II measured small-scale velocity shear and temperature microstructure at a descending speed of 0.5 m s-1, as well as conductivity and pressure. The range of the measured change in velocity was from 0.001 to 0.5 m s-2, with a precision of 5%, while the precisions of the temperature and conductivity measurements were 0.01°C and 2× 104 m s-1 cm-1, respectively. The velocity microstructure shear was used to compute the ε, with a noise level of 10-10 W kg-1. The operating principle, calibration, signal handling, and limitations were described in (Wolk et al., 2002). The maximum measurement depth was set to 500 m. Five microstructure profiles were obtained at A02 (two profiles), A06 (two profiles) and A07 (one profile) in section A. In section B, nine TurboMAP-II profiles were obtained from B09 to B01 (Table 1). A more detailed description and technical report on these fine-structure profiles in the ECS can be found in the thesis of (Zhong, 2009).
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2.2. Data processing
2.2.1. Harmonic analysisIn the ECS, the principal tidal constituent is the semidiurnal M2 tide (Baines, 1982; Guo and Yanagi, 1998; Niwa and Hibiya, 2004; Garrett and Kunze, 2006). The diurnal K1 tide is also significant in this region (Zhu and Liu, 2012). To obtain the K1 and M2 tidal currents u K1, M2(z,t), harmonic analysis was applied to the observed velocity (u,v). The realistic depth at A06 exceeded 1000 m (Fig. 1b and Table 1). However, the maximum measurement depth in some profiles reached only 360 m (not anchored). Therefore, harmonic analysis was applied to the observed velocities only at depths above 360 m. Harmonic analysis does not account for incoherent internal tides (Kerry et al., 2014). The incoherent portion is negligible for a 25-h period.
2.2.2. Estimation of dissipation rate
With the assumption of isotropy, ε was computed by integrating the measured shear spectrum from TurboMAP-II: \begin{equation} \varepsilon=\dfrac{15}{2}\nu\overline{\left(\dfrac{\partial V}{\partial z}\right)^2}=\dfrac{15}{2}\nu\int_{k_1}^{k_2}\psi(k){\rm d}k , \ \ (1)\end{equation} where Ν is the coefficient of kinematic viscosity, ψ is the shear spectrum, and the overbar denotes the average depth. The small-scale velocity shear ? V/? z is estimated using Taylor's frozen assumption, \begin{equation} \dfrac{\partial V}{\partial z}=\dfrac{1}{W}\dfrac{\partial V}{\partial t} , \ \ (2)\end{equation} where V is the small-scale velocity and W is the sinking velocity of the instrument. Equation (2) was applicable when the sinking velocity W of TurboMAP-II exceeded 0.3 m s-1. On the right-hand side of Eq. (1), ψ is integrated over the wavenumber k. The wavenumber k1 in Eq. (1) was set to 1 cpm (circle per meter) and the upper limit k2 is the cutoff wavenumber that is not contaminated by high-frequency noises. For each profile, the Nasmyth spectrum (Nasmyth, 1970) was routinely used to evaluate the shapes of the measured dissipation spectra (Zhong, 2009).
Based on ε, the diffusivity $\kappa$ can be calculated by \begin{equation} \kappa=\lambda\dfrac{\varepsilon}{N^2} . \ \ (3)\end{equation} When ε/(Ν N2)>100 (Ν is the molecular viscosity), Λ=2[ε/(Ν N2)]-1/2; otherwise, Λ=0.2 (Osborn, 1980; Shih et al., 2005). Equation (3) is applicable only when the buoyancy frequency N2>0. To rule out the effects of the vessel on turbulence, we focused only on the results below the depth of 10 m.
Figure 2 shows the distribution of density, ε and $\kappa$ along transect A. The depth-mean ε and $\kappa$ at A02 were 10-6 W kg-1 and 10-2 m2 s-1, respectively. The ε showed a significant bottom enhancement at A02, with a maximum value of 3.9× 10-5 W kg-1. Although there was strong stratification at A06 and A07, large ε and $\kappa$ values were observed in the pycnocline at A06, and the enhanced ε at A07 appeared at depths of 150 to 250 m. Along transect B, a surface mixed layer of ～15 m was observed (Fig. 3). An enlarged ε often occurred in the upper 40 m from B01 to B07 (Fig. 3a). Below 40 m, there was also sporadic strong turbulence. At B01, the turbulence was enhanced in the bottom mixed layer (below 20 m). As a result, very large $\kappa$ (>10-2 m2 s-1) was observed therein (Fig. 3b). At B08 and B09, close to the continental slope, large ε and $\kappa$ were observed near the pycnocline.
Figure2. The sectional density fields in section A incorporated with the ε [log10$\varepsilon$; (a); black curve] and vertical turbulent mixing [log10$\kappa$; (b); black curve] at A02, A06 and A07. The interval of the density contours is 0.5 kg m-3.
Figure3. The ε [lg$\varepsilon$; (a)] and vertical turbulent mixing [lg$\kappa$; (b)] incorporated with the density (units: kg m-3; black contours) fields along transect B. The interval of the density contours is 1 kg m-3.2
4.1. Current and isopycnal observations
Figures 4a and d show the profiles of time-mean velocities, $\bar{u}(h)$ and $\bar{v}(h)$, at A02 and A06, respectively. The TWC persists almost throughout the year with a transport of ～ 1.5 Sv, providing a source- and sink-driven dynamic for the warm current in the South China Sea (Su and Wang, 1987; Su et al., 1994; Yang, 2007; Yang et al., 2008). At A02, the TWC was observed as flowing northeast at a maximum velocity of 0.4 m s-1 (Fig. 4a). The northward component $\bar{v}$ remained at 0.2 m s-1 throughout the water column, while the eastward component $\bar{u}$ was 0.3 m s-1 in the upper 30 m but decreased to 0.1 m s-1 from 30 to 75 m. At A06, the upslope currents had longer durations than the off-shelf currents, providing a net onshore transport (Fig. 4d). A significant on-shelf Kuroshio intrusion with a dominant westward velocity component (u=0.2 m s-1) was observed from 100 m to 250 m. In the upper layer (above 100 m), the velocity was nearly northward (v=0.3 m s-1). Beneath 250 m, the zonal velocity had a strong shear.
Figure4. The time-mean zonal [$\bar{u}$(h); m s-1; red line] and meridional [$\bar{v}$(h); m s-1; blue line] currents at (a) A02 and (d) A06. The observed full (original), zonal [u(h,t); m s-1] and meridional [v(h,t); m s-1] currents at (b, c) A02 and (e, f) A06. The contour interval was set to 0.1 m s-1. The zero-contour of the velocity is highlighted by a thick black line. The times on the x-axis represent the deploying casts of CTD and LADCP. The red triangles at the bottom indicate the time of TurboMAP-II profiles.
Figure5. The zonal [u bac(h,t); m s-1] and meridional [v bac(h,t); m s-1] baroclinic currents at (a, b) A02 and (c, d) A06. The contour interval was set to 0.05 m s-1 for A02 and 0.1 m s-1 for A06. The zero-contour of the velocity is highlighted by a thick black line. The bottom red triangles indicate the time of TurboMAP-II profiles. The isopycnal variations (σ; kg m-3) are incorporated by green contours with black labels.At both A02 and A06, the periodic tidal motions were visible. Semidiurnal barotropic tides were predominant at A02, with a maximum velocity of 1 m s-1 (Figs. 4b and c). The zonal velocity was larger than the meridional component. At A06, significant current shears were observed (Figs. 4e and f), suggesting the dominance of baroclinic motions on the slope.
To distinguish internal tides from barotropic tides, the observed high-frequency velocity (u',v') was decomposed into barotropic and baroclinic components at A02 and A06: \begin{eqnarray} u'(h,t)&=&u-\bar{u}=u_{\rm bat}(t)+u_{\rm bac}(h,t) , \ \ (4)\\ v'(h,t)&=&v-\bar{v}=v_{\rm bat}(t)+v_{\rm bac}(h,t) , \ \ (5)\end{eqnarray} where u bat and v bat are the depth-mean (barotropic) velocity and u bac and v bac are the baroclinic velocity.
The baroclinic currents at A02 were relatively weak, with a maximum velocity of 0.15 m s-1 (Figs. 5a and b). The isopycnals, especially the contour of 22.5 kg m-3, showed a semidiurnal fluctuation with the largest vertical displacement of ～ 10 m, suggesting relatively weak internal tides. Large baroclinic velocities were observed at A06 (Figs. 5c and d), with a maximum velocity of 0.5 m s-1. The largest isopycnal displacement with a semidiurnal period was greater than 100 m. These observations suggested the occurrence of strong internal tides on the slope.
Harmonic analysis was applied to u' and v' to obtain a time series of the tidal currents u K1+u M2 and v K1+v M2 (Fig. 6). At A02, the tidal currents showed an anticlockwise rotation with a dominant zonal component (u). Therefore, the tidal ellipses were stretched across the isobaths. At A06, two significant features were found. First, u K1+u M2 and v K1+v M2 had comparable magnitudes. The tidal ellipses on the slope (A06) were significantly different from those on the shelf (A02). Second, the tidal currents at A06 showed an evident baroclinic mode in the vertical profile, suggesting dominant internal tides.
Figure6. The sum of the diurnal and semidiurnal currents (units: m s-1) by harmonic fit at (a, b) A02 and (c, d) A05. The contour interval is 0.1 m s-1. The zero-contour of the velocity is highlighted by a thick black line.2
4.2. Current instability
To understand how turbulence was generated, the vertical velocity shears (uz2+vz2) were calculated. Figure 7 shows shears in (u,v), $(\bar{u},\bar{v})$ (u',v') and (u K1+u M2,v K1+v M2) at A02 and A06. At A02, the high-frequency velocity shears dominated the full velocity shears from the surface to 45 m and below 70 m. From 50 m to 70 m, the shears in residual and high-frequency currents had comparable magnitudes, contributing to the full velocity shears. The high-frequency shears were primarily generated by currents K1 and M2. At A06, the shears in the upper 150 m (pycnocline) were approximately one order greater than those below 150 m. From the surface to 150 m, the total shears were dominated by the K1 and M2 current shears, while the total shears were dominated by the high-frequency shears below 150 m. The contribution of the residual current shears was negligible. In this paper, as the hourly observations in a day were not sufficient to decompose full velocity into all componential velocities with different frequencies, the high-frequency velocity shears include the shears associated with internal tides, the energy cascade through nonlinear wave-wave interaction (e.g., Xie et al., 2008), and/or some other physical mechanisms that may also play important roles in enhancing the energy dissipation.
Figure7. The logarithms of time-averaged velocity shears (units: s-2) at (a) A02 and (b) A06. The observed full velocity shears are in red, the residual mean shears are in magenta, high-frequency velocity (full-residual) shears are in black, and K1+M2 shears are in blue. The vertical means of the above velocity shears are plotted in the same color at the bottom of the figures.To link turbulence to the shear instability associated with internal tides, the Richardson number Ri=N2/[(? u/? z)2+(? v/? z)2] was computed from the LADCP-based velocity shears and CTD-based buoyancy frequency. The ε and diffusivity showed similar vertical variations at both sites (Fig. 8). At S02-2, Ri was large ( Ri>1) between the depths of 20 and 30 m, corresponding to small ε and $\kappa$ values. The Ri decreased with increasing depth, and it was smaller than 0.25 near the bottom where the ε and $\kappa$ values were enhanced. This suggested that enhanced turbulence may be generated by shear instability. At A06, peaks of larger ε and $\kappa$ values were often accompanied with minimum Ri values. When Ri was less than 0.25, ε was elevated to 10-7 W kg-1 due to potential internal wave breaking. At these depths, $\kappa$ reached 10-3 m2 s-1. Because B08 was close to the continental slope, enhanced stratified turbulence was also observed in this area, as shown in Fig. 3.
Figure8. The Richardson number Ri=N2/[(? u/? z)2+(? v/? z)2] (black), the logarithms of observed ε (W kg-1) (red) and turbulent mixing $\kappa$ (blue) in the vertical profile at (a) A02-2 and (b) A06-1. The Ri values larger than 5 were set to be 5 for visualization purposes. The TurboMAP-II was immediately deployed after the CTD/LADCP package returned. The observation time for A02-2 was 1123 UTC 29 June 2006, while it was 0837 UTC 30 June for A06-1. Note the different y-axis for the two figures.
Figure9. (a). Vertical structure of density (σ; kg m-3) averaged over 17 profiles at A02. (b). Velocity magnitude (units: m s-1) of the mean velocity of the 17 profiles in 25 h at A02 (solid blue line with circles). (c) Current direction (units: °) of the mean velocity (solid red line with circles).The bottom boundary layer (BBL) on the shelf often consists of a thick Ekman layer over a thin logarithmic layer, which has been previously observed in the northern ECS (e.g., Yoshikawa et al., 2010). Beneath 45 m, the velocity magnitude associated with the northeastward TWC decreased gradually from 0.32 m s-1 in the interior to 0.18 m s-1 near the bottom (Fig. 9b). The rotation of the mean current spirals at A02 from the depth of 45 to the bottom was approximately 27° (Fig. 9c). This seems to go against classical Ekman theory, which predicts the rotation angle of the velocity veers anticlockwise by 45° in the Northern Hemisphere from the direction of the interior geostrophic velocity (Pedlosky, 1987). However, previous observations have indicated that the anticlockwise veering over the BBL is much less than 45°, typically reaching a maximum of only 20° (Perlin et al., 2007). The rotation angle of 27° in this paper is similar to the above observations.
The mean observed diffusivity was used to calculate the viscosity based on the balance of the turbulence production and dissipation (Zhiyu LIU, personal communication, 2018). The turbulence shear production S=ρ Av[(? u/? z)2+(? v/? z)2] and buoyant production $B=\kappa\rho N^2$ are balanced by the TKE dissipation E=ρε, where Av is the viscosity. The balance is S-B=E. Using the calculation of $\kappa=\lambda\varepsilon/N^2$, where the mixing efficiency is 0.2, the buoyancy contribution was obtained as B=0.2ρε. Thus, the shear production S=ρ Av[(? u/? z)2+(? v/? z)2]=1.2ρε. That is, Av[(? u/? z)2+(? v/? z)2]=1.2ε. The vertical scale for the shears of ? u/? z and ? v/? z was approximately 0.9 m, which was determined from the spectrum analysis [see Eqs. (1) and (2)] based on standard technical procedure (Wolk et al., 2002). The observed ε and velocity shears can be used to obtain the viscosity Av. The mean viscosity was approximately 7× 10-3 m2 s-1. The observed vertical mean viscosity (7×10-3 m2 s-1) and interior velocity (0.3 m s-1) were used to calculate the classic Ekman solutions. From 50 m to 70 m, the predicted bottom Ekman currents agreed well with the observations in the velocity direction, but the magnitudes were slightly larger than observed (Fig. 10). At 75 m, the theoretical solution underestimated the real magnitude and direction. This underestimation may be attributable to the use of constant viscosity (Cushman-Roisin and Mala?i?, 1997; Perlin et al., 2005, Perlin et al., 2007). It has to be noted that the classic bottom Ekman theory was applied to this situation in which the vertical viscosity shows significant vertical and temporal variations. In theory, the bottom Ekman spiral can be modified slightly by the use of different vertical viscosity; however, the basic structure of bottom Ekman spiral does exist here. In this paper, we only depict and identify the Ekman dynamics and its dynamical connection with the local turbulent processes. The effects of different choices of viscosity on modifying the shapes of Ekman spirals are beyond the scope of this study and these discussions can be found in (Huang, 2010). On the other hand, such accumulative observations of Ekman spirals will help obtain the vertical viscosity inversely (Yoshikawa et al., 2010).
Figure10. Observed velocity vectors (black arrows) and spirals in the BBL at A02 versus the analytical Ekman solutions (red curve with circles) using the observed magnitude of the TWC and bottom turbulent viscosity (Table 2). The numbers near the vectors and curves are the depths of the velocity. The dashed purple lines and numbers represent the velocity magnitudes. The MATLAB program of bottom Ekman solution was adapted from J. F Price's MIT-WHOI joint program class in 2009.Below 63 m, the dissipation rate at A02 showed an increase, agreeing with the law-of-the-wall theory for the estimation of the bottom dissipation rate ε b. Here, we also used this theory to estimate ε b (Trowbridge et al., 1999; Peters and Bokhorst, 2000). In this theory, the dissipation rate in the constant stress layer is related to the bottom friction velocity u*: \begin{eqnarray} \varepsilon_{\rm b}&=&u_*^3(\kappa_{\rm vk}z)^{-1} , \ \ (6)\\ u_*&=&\sqrt{\dfrac{\tau_{\rm b}}{\rho}} , \ \ (7) \end{eqnarray} where z is set to 4 m, $\kappa_{vk}$ (=0.4) is the von Kármán's constant, and τ b is the magnitude of the bottom shear stress: \begin{equation} \tau_{\rm b}=\rho c_{\rm d}|u_{\rm b}|u_{\rm b} , \end{equation} where u b is the LADCP bottom track velocity and c d (=0.002) is the drag coefficient.
Figure 11 shows the near-bottom velocity and ε estimated by Eq. (6) at A02. The bottom velocities ranged from 0.1 m s-1 to 0.5 m s-1, with a semidiurnal period. The bottom dissipation rate ε b varied from 10-7 W kg-1 at flat tide to 10-5 W kg-1 at flood or ebb tide. During the TurboMAP-II deployments, the bottom currents were larger and ε b=10-5 W kg-1 (Fig. 11b), which was consistent with the direct microstructure observations at 73 m (Fig. 8a).
Figure11. (a) The near-bottom currents from the bottom track of LADCP (at 75 m) during 28-29 June. (b) The estimated near-bottom ε [ log10ε b; units: W kg-1)] based on Eqs. (6) and (7). The bottom triangles indicate the times of the TurboMAP-II profiles.The T-S property at both A06 and A02 had a tidal period modulation, indicating the role of the rotating surface tides (Fig. 12a). At flood tide, A02 featured high T and S, with an opposite situation at ebb tide (Figs. 13a and c). However, the effect of tidal advections on the T-S diagram was weak above 10 m and below 35 m. During the upslope transport (Figs. 13b and c), the T-S relationship at A06 was similar to that of KSW, while it approached the T-S characteristics of the SW during the downslope transport. However the effect of tidal advection on the T-S characteristics at A06 was confined to the upper 120 m (Fig. 13c).
Figure12. The T-S diagrams for (a) cross-section A and (b) cross-section B, with the colors labeled on the top of the curves. The water masses of KBW, KSW and SW are indicated by dark blue, purple and dark red frames, respectively.
Figure13. Comparisons of the T-S diagram at A02 and A06 with different directions of tidal currents. Red (black) curves and arrows in (a) and (c) represent the T-S properties and the offshore (onshore) direction currents at A02. Magenta (blue) curves and arrows in (b) and (c) represent the T-S property and the offshore (onshore) direction currents at A06. Panel (b) is the same as (a) but for A06. Orange circles and labels in (a) and (b) represent the velocity magnitude. The observation times of these profiles are labeled in (c).