*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** 880 m (shown in Figure 1). Figure 2 shows the research vessel's track and the navigation

the ISWs.

**3. Results**

#### *3.1. Vertical Profiles of Velocity and Echo Amplitude* speed from 23:48 UTC on 21 May to 03:00 UTC on 22 May. During the above time slot, the

*3.1. Vertical Profiles of Velocity and Echo Amplitude*

*J. Mar. Sci. Eng.* **2021**, *9*, x FOR PEER REVIEW 3 of 10

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

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

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. 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.

**Figure 2.** (**a**) Vessel's track; (**b**) vessel's navigation speed. The red and the blue lines correspond to the time of the leading wave and the trailing wave, respectively. The pentagrams indicate the beginning and the ending of the time of the waves. The green arrows indicate the vessel's direction. **Figure 2.** (**a**) Vessel's track; (**b**) vessel's navigation speed. The red and the blue lines correspond to the time of the leading wave and the trailing wave, respectively. The pentagrams indicate the beginning and the ending of the time of the waves. The green arrows indicate the vessel's direction. The blank from 00:48 UTC to 01:26 UTC corresponds to the ADCP being switched off.

The blank from 00:48 UTC to 01:26 UTC corresponds to the ADCP being switched off. 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) 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].

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).

lines. 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 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).

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. 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.

**Figure 4.** Current velocity profiles of the trailing wave. (**a**) Zonal current velocity; (**b**) vertical current velocity.

#### *3.2. Analysis of Phase Speed* 3.2.1. Solution of the Korteweg-De Vries (KdV) Theory

*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 stratifica-

*J. Mar. Sci. Eng.* **2021**, *9*, x FOR PEER REVIEW 5 of 10

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 N<sup>2</sup> indicates that the strongest stratification was at a depth of 37.5 m. tion 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 N<sup>2</sup> indicates that the strongest stratification was at a depth of 37.5 m.

**Figure 5.** The background physical properties of the HYbrid Coordinate Ocean Model (HYCOM) product. (**a**–**e**) Temperature, salinity, density calculated, background current, and Brunt–Väisälä frequency N<sup>2</sup> . **Figure 5.** The background physical properties of the HYbrid Coordinate Ocean Model (HYCOM) product. (**a**–**e**) Temperature, salinity, density calculated, background current, and Brunt–Väisälä frequency N<sup>2</sup> .

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

$$c\frac{\partial \eta}{\partial t} + c\_0 \left(\frac{\partial \eta}{\partial \mathbf{x}} + \alpha \eta \frac{\partial \eta}{\partial \mathbf{x}} + \beta \frac{\partial^3 \eta}{\partial \mathbf{x}^3}\right) = 0 \tag{1}$$

In Equation (1), where <sup>0</sup> is the linear wave speed and is the vertical displacement of the ISW. The parameters 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]. In Equation (1), where *c*<sup>0</sup> is the linear wave speed and *η* is the vertical displacement of the ISW. The parameters *α* and *β* 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). The environmental parameters can be calculated by as the Equations (2) and (3).

$$\kappa = \frac{3}{2} \frac{\int\_{-H}^{0} \rho\_0(z) \left(\frac{df\_n}{dz}\right)^3 dz}{\int\_{-H}^{0} \rho\_0(z) \left(\frac{df\_n}{dz}\right)^2 dz} \tag{2}$$

$$\beta = \frac{1}{2} \frac{\int\_{-H}^{0} \rho\_0(z) (f\_n)^2 dz}{\int\_{-H}^{0} \rho\_0(z) \left(\frac{df\_n}{dz}\right)^2 dz} \tag{3}$$

where <sup>0</sup> is the density of the depth z, and where is the vertical structure of vertical displacement corresponding to a particular mode , which can be solved by the boundary condition problem [20]. where *ρ*<sup>0</sup> is the density of the depth *z*, and where *f<sup>n</sup>* is the vertical structure of vertical displacement corresponding to a particular mode *n*, which can be solved by the boundary condition problem [20].

$$\frac{d}{dz}[\rho\_0(z)\frac{df\_n}{dz}] + \rho\_0(z)\frac{N^2(z)}{c\_n^2}f\_n = 0\tag{4}$$

$$f\_n(z) = 0, \; z = 0 \tag{5}$$

*fn*(*z*) = 0, *z* = −*H* (6)

where *N<sup>2</sup>* is the Brunt–Väisälä frequency, where *H* is the bottom depth. The solution to the KdV equation is

$$
\eta(\mathbf{x}, t) = \eta\_0 \text{sech}^2 \left( \frac{\mathbf{x} - vt}{\Delta} \right) \tag{7}
$$

where *η*<sup>0</sup> is the wave amplitude, where ∆ = q12*β αη*0 is the characteristic width, and the phase speed *c<sup>p</sup>* = *c*<sup>0</sup> 1 + <sup>1</sup> 3 *αη*0 .

According to the formulas above, the calculated nonlinear parameter *α* is approximately <sup>−</sup>5.42 <sup>×</sup> <sup>10</sup>−<sup>4</sup> s −1 , and the calculated dissipation parameter *<sup>β</sup>* is 4.74 <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> s −1 . The negative sign of the nonlinear parameter *α* suggests it is a depression wave [21]. The calculated characteristic width of the wave ∆ is 3289.4 m, and the calculated phase speed *c<sup>p</sup>* is 1.76 m/s.
