A Strong Internal Solitary Wave with Extreme Velocity Captured Northeast of Dong-Sha Atoll in the Northern South China Sea

Abstract

Internal solitary waves (ISWs) in the South China Sea (SCS) have received considerable attention. This paper reports on a strong ISW captured northeast of Dong-Sha Atoll on 22 May 2011 by shipboard Acoustic Doppler Current Profiler (ADCP), which had the largest velocity among the ISWs so far reported in the global ocean. The peak westward velocity (u) was 2.94 m/s, and the peak downward velocity (w) was 0.63 m/s, indicating a first baroclinic mode depression wave. The amplitude of ISW inferred from ADCP backscatter was about 97 m. 2.2 h later, a trailing wave was captured with a peak westward velocity and downward velocity of 2.24 m/s and 0.42 m/s, respectively, surprisingly large for a trailing wave, suggesting that the ISW is type-A wave. The estimated baroclinic current induced by the leading ISW was much larger than the barotropic current. The Korteweg-De Vries (KdV) theoretical phase speed and the phase speed inferred from the satellite images were 1.76 m/s and 1.59 m/s, respectively. The peak horizontal velocity exceeded the phase speed, suggesting the ISW was close to or already in the process of breaking and may have formed a trapped core.

1. Introduction

Internal solitary waves (ISWs) are ubiquitous in some marginal seas, especially in the South China Sea (SCS) [1]. They are supposedly generated near the Batan Islands of Luzon Strait and propagate northwestward in the deep basin with long crest lengths ranging from about 100 to 250 km [2,3], then shoal onto the continental shelf and finally dissipate on the plateau [4].

ISWs have rapid spatial evolution in shallow water [5], and they have been extensively studied near Dong-Sha Atoll by in situ measurements, remote sensing, and numerical simulations. Strong ISWs have been observed near Dong-Sha Atoll by moorings and shipboard surveys with amplitudes ranging from 70 to 173 m and peak westward velocities from 0.73 to 2.4 m/s [4,5,6,7,8,9,10,11,12].

However, one ISW with a peak westward current velocity of 2.94 m/s northeast of Dong-Sha Atoll is presented in this paper, with the largest ISW velocity ever observed in the global ocean.

This paper is organized as follows. Section 2 gives a general representation of the data. The description of measurements and the phase speed analysis are provided in Section 3. The discussion follows in Section 4, which includes the impact of the barotropic tide, the trapped core, and the breaking stage. Finally, a conclusion is given in Section 5.

2. Materials

2.1. Field Measurements

The shipboard observations were obtained near the continental shelf break to the northeast of Dong-Sha Atoll, during 21–22 May 2011 (Figure 1). The research vessel collected temperature, conductivity, and depth (CTD) measurements with a Sea-Bird SBE-911 and velocity, echo amplitude with a hull-mounted 75 kHz Teledyne RDI Acoustic Doppler Current Profiler (ADCP). The ADCP vertical resolution was 16 m over a depth range from 25 m to about 650 m. The temporal resolution was 2 s, recording ensemble averages every minute, suitable to sample the ISW with the period in the order of 10 min. Several ISWs were captured during this cruise. This paper focuses on an ISW with an extreme velocity captured on 22 May that was selected for extensive discussion.

2.2. HYCOM Reanalysis Products

The background stratification was derived from a HYbrid Coordinate Ocean Model (HYCOM) of temperature and salinity with a temporal resolution of 3 h and a spatial resolution of 0.08°. The variables are interpolated onto 41 layers at depths between 0 and 5000 m. The model assimilates altimeter observations and in situ sea surface temperature, as well as vertical temperature and salinity profiles from Argo floats, expendable bathythermographs (XBTs), and moored buoys, by Navy Coupled Ocean Data Assimilation (NCODA) system [13,14]. The model data was used to estimate stratification before the ISW event.

2.3. Satellite Data

Remote sensing data such as Synthetic Aperture Radar (SAR) and Advanced Synthetic Aperture Radar (ASAR) has been widely used to study ISWs [15]. Depression ISWs can be identified on SAR images as a bright band in front followed by a dark band on SAR images, and vice-versa for elevation ISWs [16].

European Space Agency Environment satellite (Envisat) images were used to investigate sea surface signatures of ISWs near Dong-Sha Atoll in the northern SCS. The Envisat is an advanced polar-orbiting Earth observation satellite with ASAR active between 1 March 2002 and 8 April 2012, with a spatial resolution of about 30 m, sufficient to resolve the ISWs.

3. Results

3.1. Vertical Profiles of Velocity and Echo Amplitude

On 22 May 2011, an unusual ISW with extreme velocity was captured between 00:00 and 00:45 UTC in northern SCS to the northeast of the Dong-Sha Atoll, where the depth is 880 m (shown in Figure 1). Figure 2 shows the research vessel’s track and the navigation speed from 23:48 UTC on 21 May to 03:00 UTC on 22 May. During the above time slot, the vessel drifted from (117.795° E, 21.146° N) to (117.753° E, 21.154° N) when the ISW passed by (red line in Figure 2a). Then the vessel moved back to the primary site near (117.795° E, 21.146° N) (black line in Figure 2a) and captured a trailing wave about 2.2 h later than the leading wave. Before the trailing wave arrived, the vessel was drifting (blue line in Figure 2a). The ADCP was switched off between 00:48 and 01:26 UTC, so the ship’s track and speed in this period are not shown. The averaged drifting speed and the maximum drifting speed induced by the leading wave were 1.62 m/s and 2.53 m/s, respectively. For the trailing wave, the corresponding speeds were 1.51 m/s and 1.96 m/s, which were uncommonly large.

The mean ADCP velocity data 30 min prior to the ISW arrival is used as the background current, not influenced by the ISW yet. The velocity profile of the ISW was calculated by subtracting the background current. Figure 3 shows current velocity and echo amplitude timeseries, as a function of depth from 23:17 to 00:48 UTC. Notable horizontal current velocities were observed near the surface, with a peak westward velocity (u) of 2.94 m/s, where the depth was 89 m (Figure 3a). There were strong downward (upward) currents (w) at the leading (trailing) edge, and the peak velocity was 0.63 m/s (Figure 3b) extended in the whole water column. The northward velocity (v) was small and not the focus of this paper. One instance of significant horizontal velocity shear was recorded (Figure 3a), suggesting this ISW was a first baroclinic mode depression wave [2].

The echo amplitude from ADCP closely tracks isopycnals inferred from seawater density and biomass on a large scale, which can be qualitatively used for visualizing the internal waves [4,17]. The maximum vertical excursion of echo amplitude reached 97 m, located at a depth of 185 m, suggesting the amplitude of ISW was 97 m (Figure 3c).

Figure 4 shows the trailing wave current velocity timeseries. The signal around 01:50 UTC was induced by a sudden deceleration of the ship (Figure 2b). The trailing wave had a peak westward velocity of 2.24 m/s at a depth of 73 m and peak downward velocity of 0.42 m/s; surprisingly large for a trailing wave.

3.2. Analysis of Phase Speed

3.2.1. Solution of the Korteweg-De Vries (KdV) Theory

Since no CTD cast was deployed near the location of ISW, the background stratification was calculated from HYCOM data at 00:00 UTC (Figure 5). The temperature profile shows a main thermocline between 35 and 300 m, below a mixed layer with a depth-independent temperature of 26.2 °C. The background current shows there was a slightly westward flow with a mean speed of 0.06 m/s. The calculated Brunt–Väisälä frequency N² indicates that the strongest stratification was at a depth of 37.5 m.

The wave is fitted to the KdV equation in a stratified fluid, which is generally used to describe characteristics of ISW [18].

$$\frac{\partial \eta }{\partial t}+c_0\left(\frac{\partial \eta }{\partial x}+\alpha \eta \frac{\partial \eta }{\partial x}+\beta \frac{{\partial }^3\eta }{\partial x^3}\right)=0$$

(1)

In Equation (1), where $c_0$ is the linear wave speed and $\eta$ is the vertical displacement of the ISW. The parameters $\alpha$ and $\beta$ are the nonlinear parameter and dissipation parameter, respectively. These two coefficients are also called “environmental parameters” as they contribute to conditions such as stratification and water depth [19].

The environmental parameters can be calculated by as the Equations (2) and (3).

$$\alpha =\frac{3}{2}\frac{{{\displaystyle \int }}_{-H}^0{\rho }_0\left(z\right){(\frac{d{f}_n}{dz})}^{3}dz}{{{\displaystyle \int }}_{-H}^0{\rho }_0\left(z\right){(\frac{d{f}_n}{dz})}^{2}dz}$$

(2)

$$\beta =\frac{1}{2}\frac{{{\displaystyle \int }}_{-H}^0{\rho }_0\left(z\right){\left(f_n\right)}^{2}dz}{{{\displaystyle \int }}_{-H}^0{\rho }_0\left(z\right){(\frac{d{f}_n}{dz})}^{2}dz}$$

(3)

where ${\rho }_0$ is the density of the depth z, and where $f_n$ is the vertical structure of vertical displacement corresponding to a particular mode $n$, which can be solved by the boundary condition problem [20].

$$\frac{d}{dz}[{\rho }_0\left(z\right)\frac{d{f}_n}{dz}]+{\rho }_0\left(z\right)\frac{N^2\left(z\right)}{c_n^2}{f}_n=0$$

(4)

$$f_n\left(z\right)=0, z=0$$

(5)

$$f_n\left(z\right)=0, z=-H$$

(6)

where N² is the Brunt–Väisälä frequency, where H is the bottom depth.

The solution to the KdV equation is

$$\eta \left(x,t\right)={\eta }_{0}sec{h}^2\left(\frac{x-vt}{\Delta }\right)$$

(7)

where ${\eta }_0$ is the wave amplitude, where $\Delta =\sqrt{\frac{12\beta }{\alpha {\eta }_0}}$ is the characteristic width, and the phase speed $c_p=c_0\left(1+\frac{1}{3}\alpha {\eta }_0\right).$

According to the formulas above, the calculated nonlinear parameter $\alpha$ is approximately −5.42 × 10⁻⁴ s⁻¹, and the calculated dissipation parameter $\beta$ is 4.74 × 10⁴ m³ s⁻¹. The negative sign of the nonlinear parameter $\alpha$ suggests it is a depression wave [21]. The calculated characteristic width of the wave $\Delta$ is 3289.4 m, and the calculated phase speed $c_p$ is 1.76 m/s.

3.2.2. Estimation by Satellite Image

Fortunately, we got one ASAR image during the cruise. The phase speed was also estimated from the satellite image for comparison. Figure 6 shows an ASAR image acquired by the Envisat satellite at 02:17 UTC on 23 May 2011, capturing the same ISW 26.3 h after it was detected by the vessel. The image shows several bright–dark bands corresponding to wave crests–troughs near Dong-sha Atoll, indicating the first baroclinic mode depression waves. The wave we discussed above was a leading wave, and the trailing wave was also detected (Section 3). The ISW wave packet can be classified as an A-type wave.

The distance between the wave crest (shown in Figure 6) and the ship ADCP measurements location was about 150 km. Considering the distance and time difference, the mean phase speed of the ISW was around 1.59 m/s, which is only 0.17 m/s slower than the theoretical result of the KdV solution. The difference can be attributed to the accuracy of HYCOM data products in the SCS, and also may relate to the variations of bathymetry over a distance of 150 km and the background current.

4. Discussion

4.1. Influence of Barotropic Tide

The barotropic tide velocity can reach in the order of 10 cm/s in the northern SCS [22], which may contribute to the horizontal velocity in ADCP measurements. When considering the influence of the barotropic tide on the observed ISW, the barotropic tide should be calculated first. With long-term and all-depth observation records, the internal wave signal could be separated via filter analysis from tidal and inertial signals [2,23,24] to investigate the influence of the barotropic tide on the observed ISW. However, the vessel cannot provide full-depth current data due to ADCP measurement limitations. Instead, here we considered two other methods to subtract the velocity of the barotropic tide.

4.1.1. Modal Decomposition to Reconstruct the Barotropic Current

According to [25], full-depth barotropic currents and baroclinic currents from limited mooring observations can be obtained by combining harmonic analysis and modal decomposition. Harmonic analysis is used to calculate harmonic constants of the major constituents and predict the time series of each major tidal constituent. Modal decomposition is carried out to obtain full-depth tidal currents of each mode by using the least-squares method [26]. It was found that when more than three vertical modes were considered in the calculation, the prescribed tidal currents could be reconstructed accurately [25].

As the time series of shipboard ADCP measurement was not long enough to be frequency filtered, processes at frequencies other than barotropic tide and baroclinic tide were ignored. Thus, we focused on the modal decomposition, only taking into account the first three vertical modes. The calculation did not go into detail here.

The first three vertical modes were taken into account. The reconstructed barotropic westward velocity (u) was 2 cm/s, and the southward velocity (v) was 6.34 cm/s. Both were insignificant compared to the large velocity induced by ISW.

4.1.2. Estimation of Barotropic Current Using Numerical Modelling

Numerical modeling can also be used to infer the tidal signal [27]. Here we use the Tidal Model Driver (TMD) toolbox to predict the barotropic tidal constituent height and amplitude [28].

At 00:00 UTC on 22 May, the prediction of westward barotropic tidal velocity (u) was 6.36 cm/s, and the southward velocity (v) was 3.12 cm/s, which are similar to the results mentioned above.

In conclusion, the barotropic tidal velocity at the site where the ISW was observed likely has little influence on the current field.

4.2. The Trapped Core and Breaking Stage

The trapped core is defined as the particle, which was trapped in the wave and carried along at constant propagating speed [29] and occurs when the water velocity exceeds the propagation speed of the wave [30]. It is formed when ISWs shoal from deep to shallow water. As the ISW reaches its breaking limit, it forms a subsurface trapped core [31]. A trapped core was identified in the measured ISW zonal velocity (inside the white line representing the ISW phase speed in Figure 3a). The upper portion of the trapped core was beyond the shipboard ADCP range.

The breaking stage can be defined according to [32] by comparing the peak current velocity $u_{max}$ and phase speed $c$. When $u_{max}>0.8 c$ in a continuously stratified fluid, the ISW would break. The ISW presented in this paper had values of $u_{max}=2.93 \mathrm{m}/\mathrm{s}$ and $c=1.76 \mathrm{m}/\mathrm{s}$, with peak current velocity much larger. Obviously, the peak current velocity was much larger than the estimated phase speed. The ISW was close to or already in the process of breaking.

The above results are consistent with those in [5], which present 41 ISWs captured in April 1999 and 2000 on the continental slope of the northern South China Sea during the Asian Seas International Acoustics Experiment (ASIAEX) [5]. One ISW among them was similar to our observations, with the largest westward current exceeding 2.4 m/s right near our research area (details shown in

Table 1. Observations in this study and in [5].

	Location	Depth	Peak Western Current Velocity	Depth of Nodal Point	Breaking Stage
This study	(117.80° E, 21.14° N)	880 m	22 May 2011	2.94 m/s	Between 297 m and 329 m
Results in [5]	(117.22° E, 21.05° N)	426 m	9 April 2000	Missing data, but exceeding 2.4 m/s	Between 210 m and 323 m

). This suggests that when one ISW approaches the breaking stage, its velocity could be significantly larger than before.

5. Conclusions

In this paper, an ISW with extreme current velocity northeast of Dong-Sha Atoll is reported and discussed, whose velocity is the largest among the ISWs ever observed in the global ocean. The peak westward velocity (u) was 2.94 m/s, and the peak downward velocity (w) was 0.63 m/s, respectively. The amplitude of ISW was about 97 m, propagating as a mode 1 depression wave. A strong trailing wave was captured 2.2 h later and suggested the ISW was an A-type wave. The barotropic tide had little influence on the current field of the ISW, which indicated that the velocity induced by the ISW was extremely large indeed. The KdV theoretical phase speed and the estimated phase speed by the satellite image were 1.76 m/s and 1.59 m/s, respectively. By comparing the peak current velocity $u_{max}$ and phase speed $c$, it is inferred that the ISW reported in our paper was close to or already in the process of breaking and may have developed a trapped core.

In the deep basin of northern SCS, a strong ISW was reported with an amplitude of 240 m and a peak westward current velocity of 2.55 m/s [33], with a larger amplitude but lower peak velocity than the one discussed in this paper. However, the ISW reported in [33] was captured in the deep basin of northern SCS where the depth was 3847 m, rather than in the vicinity of Dong-sha Atoll.

ISWs with such a large velocity are rare, with previous observations near Dong-Sha Atoll reporting amplitudes ranging from 70 to 106 m and peak westward velocities from 0.73 to 2.4 m/s. In the vicinity of Dong-sha Atoll, 41 ISWs were identified with moorings, among which only one ISW with a large peak westward current exceeding 2.4 m/s was captured, whose characteristics were similar to the ISW discussed in this paper [5]. Both ISWs in the two studies were near breaking. Thus, the ISW discussed in this paper has the largest velocity so far reported in the global ocean.

According to [11], ISWs in a marginal convectively unstable state (which leads to a trapped core) can contribute to turbulence mixing with long distances, along with the propagation. We supposed that the turbulence mixing would appear if the breaking state continued, but further observations are needed to prove it.