On Characteristics and Mixing Effects of Internal Solitary Waves in the Northern Yellow Sea as Revealed by Satellite and In Situ Observations

Abstract

This study examines the characteristics, statistics, and mixing effects of internal solitary waves (ISWs) observed in the northern Yellow Sea (YS) during the summers of 2018 and 2019. The mooring stations are located between offshore islands with rough topographic features. Throughout the observation period, the ISWs with vertical displacements of up to 10 m induced prevailing high-frequency (3–10 min period) temperature variations. Synthetic aperture radar (SAR) images showed that the observed ISWs propagate in zonal directions generated around the islands where internal-tide-generating body force is strong. The estimated ISW propagation speed ranges from 0.16 to 0.25 m s⁻¹, which agrees with the Korteweg-de Vries (KdV) model. The ISW intensity exhibits a clear spring-neap cycle corresponding to the local tidal forcing. The constant occurrence of ISWs at low tide suggests an important generation site where the ISWs are tidally generated. The ray-tracing result indicates that this generation site appears to be located at a strait between Dahao and Xiaohao islands. A generalized KdV model successively reproduces the propagation process from the generation site to the mooring station. Following the passage of ISWs, microstructure profiling observations reveal a high turbulent kinetic energy dissipation rate (10⁻⁶ W kg⁻¹). The prevalence of ISWs in the study area is believed to play a crucial role in regulating vertical heat and nutrient transport, thereby modulating the biogeochemical cycle.

1. Introduction

Internal solitary waves (ISWs) are ubiquitous in world coastal oceans; they are long-lived features and can travel tens/hundreds of kilometers before dissipating [1,2]. These waves can generate strong reverse flow across the pycnocline, which induces the intense turbulent vertical exchange of heat and nutrients, regulating the biogeochemical cycle [3,4,5]. Therefore, comprehending the characteristics, statistics, and mixing effects of ISWs is crucial to understanding how marine ecosystems behave.

ISWs can be produced by a variety of mechanisms, including the lee wave mechanism [6], a transformation of the internal tide [7,8], or resonance in the transcritical flow [9], depending on the local stratification, topographic features, and tidal amplitudes. The lee wave mechanism has traditionally been used to explain the generation of ISWs at an underwater sill or bank [6]. The isopycnal disturbance on the topography exhibits a large lee wave when the flow reaches a supercritical flow condition (the Froude number F_r = U/c₀ > 1, where U is the tidal current and c₀ is the first-mode linear internal wave phase speed). The lee wave moves upstream as the tidal flow slows, evolving into several ISWs. Therefore, locally generated ISWs are often associated with tides. Kozlov et al. found a similar distance between adjacent ISW packages in the White Sea that matched the M₂ wavelength value based on synthetic aperture radar (SAR) images [10]. According to statistical findings from years of observations in the Strait of Georgia, the ISW packets tended to appear at the specific tidal phase with similar time intervals [11], which emphasized the importance of tidal forcing in generating ISWs in the ocean.

ISWs can cause significant vertical displacements across the pycnocline and exacerbate turbulence [12,13]. In the investigation of Oregon’s continental shelf, Moum et al. revealed the evolving nature of interfaces through microstructure observations. As ISWs propagate shoreward, the interfaces may become unstable and break, creating turbulent flow [14]. Lee et al. investigated the generation and longevity of nonlinear internal waves in the northern East China Sea [4], suggesting that shear instability was the generation mechanism for the observed turbulence. The turbulent mixing can modify the transport of particulates and nutrients, influencing the distribution and recruitment of various littoral larval species [15]. These dynamical and ecological consequences provide additional motivation to investigate the causes of internal turbulent mixing and their effects on ecology and aquaculture.

The Yellow Sea (YS) is a temperate shelf sea in the northwest Pacific Ocean with a mean depth of 44 m. It connects to the East China Sea in the south and the Bohai Sea in the north. Limited observations have revealed the existence of ISWs, wind-induced near-inertial waves, and semidiurnal internal tides there [12,16,17,18,19]. Hsu et al. examined the distribution of ISWs in the YS based on SAR images onboard the satellites ERS-1 and ERS-2 [16]. They found that the ISWs were widely distributed along the coast of the YS, with the islands west of the Korea Peninsula being the local hot spots for ISWs due to their topographic features. After their generation on the west coast of the Korean Peninsula, ISWs propagated into the YS. Their phase speed increased nonlinearly with the water depth, averaging a value of approximately 0.1–0.7 m/s [20]. A recent numerical study showed that the simulated internal tides in the YS have an excellent spatial consistency with the satellite-detected ISWs because both the internal tides and ISWs are of tidal origin [21]. Moreover, Liu et al. observed that ISWs with a vertical displacement of 4–5 m had induced intensified turbulence in the pycnocline by creating small-scale shear instabilities based on microstructure observations in the local shelf break of the southern YS [12].

Only limited studies have looked into the ISWs in the northern YS. Lin et al. used numerical simulations to explore that energetic internal tides were generated near the coast around the northern YS [22], with a maximum baroclinic energy flux of 45 W/m. Although the baroclinic energy flux is much lower in the northern YS due to the shallow bathymetry, there are still significant large values at the topographic changes, which indicate the local generation of ISWs and internal tides. Alpers et al. have confirmed the presence of ISW packets in the northern YS through satellite imagery [17]. These images show the characteristics of ISWs in the northern YS, which appear frequently in the summer and seldom have wavelengths longer than 1000 m due to the shallow water. However, it is still challenging to determine the variability, property, and mixing effects of the ISWs because satellite observations alone cannot shed light on the features of ISWs in the interior of oceans. In situ observations are important methods to reveal the characteristics and mixing effects of ISWs [23,24]. Although the combination of satellite observations and in situ observations has been widely used [25,26], the characteristics of ISWs and their effects on turbulent mixing are still unclear in the northern YS due to the lack of in situ observations.

In this study, we conducted long-term high-frequency temperature observation for two mooring stations in the northern YS. SAR images and mooring observations were combined to analyze the statistical characteristics of the ISWs. The effect of ISWs on turbulent mixing was also discussed. This paper is organized as follows. Section 2 describes the observation data and methods. In Section 3, the results of the in situ hydrographic observations and satellite SAR investigations are presented. The correlation between ISWs and tide, potential generation sites, and the influence of ISWs on turbulence are discussed in Section 4. Conclusions are summarized in Section 5.

2. Materials and Methods

2.1. Mooring Observation

The data for this study were collected at two mooring stations in the northern YS from 29 June to 18 August 2018 and 5 June to 18 August 2019 (Figure 1b). The mooring stations (Stns.) A4 (39.03°N 122.98°E) and B4 (39.04°N 122.96°E) are located between two offshore islands (Zhangzi and Haiyang islands) in water with a mean depth of about 40 m. The T-chain is used to measure temperature at the mooring stations, equipped with four temperature sensors (T, ONT18S) with a frequency of 1 Hz at Stn. A4. At Stn. B4, the T-chain is equipped with two Conductivity-Temperature-Depth instruments (CTD, RBR420), two Temperature-Depth sensors (TD, RBR duet), and two temperature sensors (T, ONT18S). Temperature measurements are valid from 1.5 m to 25 m above the bottom.

Table 1. Stations, sensors, frequency, and sensor height of the mooring observations.

Stations	Depth (m)	Sensors	Sampling Period (s)	Sensor Height (m)
A4	39	T	1	1.5
		T	1	9
		T	1	17
		T	1	24.5
B4	38.8	CTD	300	1.5
		TD	10	8
		T	10	14
		T	10	18
		CTD	10	21
		TD	10	25

summarizes information on the corrected sensor depths and temporal resolution. Figure 1c depicts the instrument configuration diagram.

We calculated the vertical velocity (w) from vertically densely spaced temperature sensor data after converting the series T(z, t) to isotherm displacements $\eta$(z, t) [27]. This study selects a set of isotherms with constant mean spacing (0.5 °C). For each isotherm, w is calculated by dividing the displacement of the isotherms in adjacent time by the time interval

$$w=\frac{\eta }{t}$$

(1)

where $\eta$ is the isotherm displacements in adjacent time and t is the time interval. The velocity of each layer is acquired by linear interpolation.

2.2. VMP Observations

We deployed the Vertical Microstructure Profiler- (VMP-) at Stn. B4 on 14–15 July 2019, to investigate the role of ISWs in inducing turbulent mixing. The VMP was activated once every hour for 22 h. The VMP is outfitted with two high-resolution frequency shear probes, one high-frequency temperature probe (FP07), and one high-frequency conductivity probe (SBE7), all with sampling rates of 512 Hz. The turbulent kinetic energy dissipation rate was calculated using microstructure shear. Using the assumption of isotropic turbulence, the turbulent kinetic energy dissipation rate $\epsilon$ was calculated as follows:

$$\epsilon =\frac{15}{2}v\overline{{{\displaystyle (\frac{\partial u}{\partial z})}}^2}=\frac{15}{2}v{\displaystyle \underset{{{\displaystyle k}}_1}{\overset{{{\displaystyle k}}_2}{\int }}\varphi (k)dz}$$

(2)

where v is the kinematic molecular viscosity; $\overline{{{\displaystyle \left(\partial u/\partial z\right)}}^2}$ is the variance of the vertical shear; $\phi (k)$ is the power spectrum of velocity shear; and k₁ and k₂ are the lower and upper limits of the wavenumber for integration, respectively. The calculation of $\epsilon$ is based on the ODAS Matlab Library Manual program by Rockland Scientific International (RSI) Inc. Previous studies have extensively described the corresponding data processing theories and methods (Gregg, 1999). For details of the calculation methods, please refer to Yang et al. [28] and Xu et al. [18]. The shear spectrum is calculated over consecutive segments of 2 m with a 50% overlap. As a result, we could obtain vertical profiles of $\epsilon$ with a vertical resolution of 1 m.

2.3. SAR Images

The ISW-induced currents modify sea surface roughness, which can be imaged using satellite images via Bragg backscattering [29,30,31]. Synthetic aperture radar (SAR) has long been a principal sensor in the observation of ISWs, because of its all-day, all-weather imaging capability [32]. SAR maps the sea surface roughness through Bragg scattering from the capillary waves and short gravity waves. The relation is

$$\Lambda =\frac{\lambda }{2\sin \theta }$$

(3)

where $\Lambda$ and $\lambda$ are the wavelength of capillary waves and radar, respectively, and $\theta$ is the local incidence angle. In satellite SAR images, the ISWs typically appear as a pair of bright and dark stripes, corresponding to the rougher (convergence) and smoother (divergence) surface zones, respectively [30,32]. In this study, we used the C-band SAR of Sentinel-1 and GF-3 satellites launched by the European Space Agency on 3 April 2014 and China Aerospace Science and Technology Corporation on 10 August 2016, respectively. Both satellites can continuously image ISWs at 10 m resolution using HH-polarization. There are 59 images taken in the study area during the observation periods in 2018 and 2019, 11 of which show clear signatures of ISW packets.

2.4. The KdV Equation

The evolution of ISWs is generally influenced by topography and horizontally variable stratification [33,34]. For shallow water approximation, the KdV equation and its generalizations are widely used for the investigation of the propagation and transformation of ISWs in the shelf and coastal oceans [10,33]. To overcome the lack of direct observations of continuous stratification in the northern YS, we used the generalized Korteweg-de Vries (gKdV) equation to simulate the propagation of ISWs in the varied topography [10,35] as follows:

$$A_t+C_0\left(x\right)A_x+\alpha \left(x\right)A{A}_x+{\alpha }_1\left(x\right)A^2{A}_x+\beta \left(x\right)A_{xxx}+\left(\frac{C_0\left(x\right)}{2\gamma \left(x\right)}\right){\gamma }_{x}A-\zeta A_{xx}=0$$

(4)

where A(x, t) is the interface amplitude; C₀(x) is the linear wave speed; and parameters $\alpha \left(x\right)$, ${\alpha }_1\left(x\right)$, $\beta \left(x\right)$, $\gamma \left(x\right)$, and $\zeta$ are the coefficients for the nonlinear, higher-order nonlinear (cubic), dispersion, transformation, and dissipation effects, respectively.

The numerical model based on the gKdV equation was discretized by the Predictor-Evaluation-Corrector-Evaluation (PECE) method and iterated by the implicit corrector scheme [36], which ensures convergence and computational efficiency of the iterative process. There is a steady summer pycnocline between the surface and intermediate water masses along the ISW propagation trajectory at depths of 5–10 m. Segur and Hammack [37] and Koop and Butler [38] found that the KdV model can be simplified to a two-layer model and predicted the solitary waves with remarkable accuracy. Thus, a two-layer system of upper quasi-homogeneous and lower layers with thicknesses h₁ and h₂, respectively, can be used [10,33]:

$$C_0=\sqrt{\Delta \rho g{{\displaystyle h}}_1{{\displaystyle h}}_2/\rho \left({{\displaystyle h}}_1+{{\displaystyle h}}_2\right)}$$

(5)

$$\alpha =\left[3\left({{\displaystyle h}}_1-{{\displaystyle h}}_2\right)/2\left({{\displaystyle h}}_1{{\displaystyle h}}_2\right)\right]C_0$$

(6)

$${\alpha }_1=\left[-3\left({{\displaystyle h}}_1^2+{{\displaystyle h}}_2^2+6{{\displaystyle h}}_1{{\displaystyle h}}_2\right)/8{\left({{\displaystyle h}}_1{{\displaystyle h}}_2\right)}^2\right]C_0$$

(7)

$$\beta =\left({{\displaystyle h}}_1{{\displaystyle h}}_2/6\right)C_0$$

(8)

$$\gamma ={\left\{{{\displaystyle C}}_0\left(0\right){{\displaystyle C}}_0^{-1}\left[{{\displaystyle h}}_1^{-1}\left(0\right)+{{\displaystyle h}}_2^{-1}\left(0\right)\right]/\left[{{\displaystyle h}}_1^{-1}+{{\displaystyle h}}_2^{-1}\right]\right\}}^3$$

(9)

where g is the acceleration of gravity; ${\rho }_1$, h₁ and ${\rho }_2$, h₂ are the density and thickness of upper and lower layers, respectively.

3. Results

This section is divided into subheadings. It should provide a concise and precise description of the experimental results, their interpretation, as well as the experimental conclusions that can be drawn.

3.1. Temperature Variations

Figure 2 and Figure 3 show the temperature variation observed by the T-chain at Stns. A4 and B4, respectively. These two stations shared many characteristics due to their close distance and similar time of the year for observation. The observed temperature shows a warming trend at both stations. The temperature measured by the lowest sensors increased from 10 to 18 °C and from 8 to 20 °C at Stns. A4 and B4, respectively. The observed part of the water column is usually stratified, with the largest vertical temperature difference reaching 11.2 °C and 12.8 °C at Stns. A4 and B4, respectively. There was a significant increase in temperature throughout the water column on 13 August at Stn. B4 (Figure 3a,b). The bottom temperature changed from 15 to 19 °C, after which the temperature fluctuated and dropped gradually. The surface elevation demonstrates that semidiurnal tides dominate at both stations with a distinct spring-neap cycle (Figure 2a and Figure 3a).

One notable phenomenon observed at both stations is prevailing temperature spikes that last throughout the observation period. Close-view examples of the temperature spikes show that these spikes have frequencies ranging from 3–10 min (Figure 2c,e and Figure 3c,e). When the bottom layer is well-mixed, temperature spikes may appear only in the upper sensors (Figure 2d,f). The uppermost temperature sensor increased from 14 to 23 °C in 100 s with a period of 5 min (Figure 2c). Figure 2c,e and Figure 3c,e show that these temperature spikes are caused by the prevailing high-frequency ISWs of depression in this area. The vertical displacement of the ISWs is about 8–10 m (Figure 2c). Additionally, the leading waves have the largest vertical displacement of 13 m, corresponding to the highest temperature variation of 7 °C, as observed in Figure 3d,f. The observed prevailing ISW packets in the study area are surprising. This is because, although the previous SAR imagery studies have revealed the presence of ISW packets around offshore islands in the northern YS, this region has never been considered a hot spot for ISWs [17]. Given the prevalence of the observed ISWs, they may have significant biogeochemical implications. Next, the properties of the ISWs are examined.

3.2. Spectral Estimates

The frequency spectrum of temperature is calculated to examine the energy content as a function of frequency. The temperature in the uppermost layer is selected to calculate the frequency spectrum. Figure 4c,d depicts the frequency spectrum calculated from mooring temperature observations at Stns. A4 and B4, respectively. The frequency spectra are dominated by near-inertial/diurnal (~1 cycle per day (cpd)), semidiurnal (~2 cpd), and higher tidal harmonics at both stations. The strongest peak corresponds to the frequency of the M₂ tide. The spectra generally decrease with increasing frequency, except where there seems to exist a spectral bump at ~144 to 480 cpd (a period of ~3 to 10 min). Figure 2 and Figure 3 depict that the spectral bump is associated with the high-frequency temperature variations.

The high-frequency region of the spectra was then examined to obtain a better look at the spectral bump. In order to examine the temporal variation of the high-frequency motions, we calculated the frequency spectrum for each day by dividing the temperature variation into daily segments. Figure 4a,b shows that high spectral energy appears between 3 and 10 min periods, which corresponds to the spectral bump. The spectral bump almost lasts throughout the observation period. This is consistent with the observed frequent temperature spikes, indicating that ISWs are common in the study area.

3.3. Close View of the ISWs

The SAR images and mooring observations are combined to examine the properties of ISWs. For example, we selected two typical SAR images (10 m resolution, HH-polarization) with clear ISWs acquired on 11 July and 8 August 2019. The in situ mooring observations are analyzed alongside the SAR images to provide additional information about propagation details. Figure 5d depicts the capture of two ISW packets (ISW A and ISW B) at 3.4 and 7.9 km from Stn. B4. ISW A arrives at Stn. B4 approximately 4 h after the imaging time, causing significant temperature variations. Within 3 min, the temperature measured by the uppermost sensor rises from 13 to 22 °C. Close inspection reveals that ISW A has a vertical displacement of 10 m and a period of about 10 min (Figure 5c). The ISW propagation speed is estimated to be 0.25 m s⁻¹ based on relative packet positions and arrival times. ISW B originates on Haiyang Island and has a propagation speed of 0.16 m s⁻¹.

The other SAR image was acquired on 8 August 2019, at 17:46, capturing at least four ISW packets (Figure 6d). Three of the four packets propagate from west to east in a similar direction. ISW C first passes through the mooring station, causing high-frequency temperature variations for 28 min. This ISW has an amplitude of approximately 9 m and a period of 7 min (Figure 6c). The propagation speed of ISW C is estimated to be 0.21 m s⁻¹. The propagation speeds of ISWs A and B are estimated to be 0.21 and 0.17 m s⁻¹, respectively, based on the distance revealed by SAR images and arrival time. Wavelengths appear to be variable during the propagation of the ISW. ISW A has the largest wavelength at about 500 m, and ISWs B and C have relatively small wavelengths of less than 200 m. In the same ISW packet, the wavelengths of ISWs are also different. As shown in ISW B and ISW C in Figure 6, the wavelengths are significantly larger in the southern part of the waves.

The linear phase speed at any frequency depends on the vertical density profile of the water column, based on the KdV equation for internal waves [39]. The two-layer model, consisting of the upper layer with thickness h₁ and density ${{\displaystyle \rho }}_1$, and the lower layer with thickness h₂ = H − h₁ and density ${{\displaystyle {\rho }_2>\rho }}_1$, is widely considered for the simulation of internal waves [40,41]. In this case, assuming the ISWs are of the KdV type, the speeds of propagation of ISWs are generally calculated from Equation (10):

$$\mathrm{c}=\sqrt{\frac{g\left({{\displaystyle \rho }}_2-{{\displaystyle \rho }}_1\right){{\displaystyle h}}_1{{\displaystyle h}}_2}{{{\displaystyle \rho }}_2{{\displaystyle h}}_1+{{\displaystyle \rho }}_1{{\displaystyle h}}_2}}+\frac{\alpha {{\displaystyle \eta }}_0}{3}$$

(10)

where g is the acceleration due to gravity; ${\eta }_0$ is the vertical displacement of ISWs; ${{\displaystyle \rho }}_1$ and ${{\displaystyle \rho }}_2$ are the upper layer and lower layer density; h₁ and h₂ are the upper layer and lower layer thickness, respectively. The parameter α is calculated using Equation (5). At the mooring station, the phase speed calculated according to Equation (10) is about 0.25 m s⁻¹, consistent with estimates from satellite observations.

4. Discussion

4.1. Statistics of ISWs

Mooring observations indicate that ISWs are prevailing phenomena in our study area that exist throughout the observation period in summer. We performed a statistical analysis on the time of appearance of ISWs to the tidal phases to investigate their characteristics and generation mechanisms. Wave packets were defined as ISWs with vertical displacements greater than 5 m. At Stns. A4 and B4, a total of 125 and 277 ISW packets were observed, respectively. The surface elevation shows a clear spring-neap cycle at both stations (Figure 2a and Figure 3a). The occurrence of ISWs is binned by their time relative to the nearest maximum of the fortnightly cycle of tidal magnitudes and by their time relative to the low tide. At Stn. A4, more ISWs seem to be observed during spring tide than during neap tide (Figure 7c). However, ISWs do not appear more frequently at Stn. B4 during spring tide (Figure 7f), showing no obvious correlation with tidal amplitude. The one-hour and one-day root-mean-square (RMS) vertical velocity $({{\displaystyle \sigma }}_w)$ are then calculated (Figure 7b,e). The $({{\displaystyle \sigma }}_w)$ shows a clear fortnightly cycle which agrees well with the variation of RMS tidal amplitude $({{\displaystyle \sigma }}_H)$.

Variations in both the occurrence frequency and intensity of the ISWs can affect the $({{\displaystyle \sigma }}_w)$. Previous research found that the likelihood of ISW packets peaked around the strongest tides in the spring-neap tide [11,17,42]. However, the likelihood of ISWs shows no apparent correlation with the spring-neap tide in the present study (Figure 7c,f). Thus, we suggest that the fortnightly variations of $({{\displaystyle \sigma }}_w)$ are responsible for modulating the ISW intensity by the spring-neap tide.

The occurrence of the ISW packet was examined by comparing it with the flood-ebb cycle of the local tides. At both stations, we first calculated the average value of the surface elevation for 25 h, showing a clear dominant semidiurnal cycle (Figure 8). The occurrence of ISWs was classified according to the local tidal phases. Figure 8 shows that most ISWs are observed at both stations during low tides. This relationship appears to be stronger at Stn. B4. In other regions, the occurrence of ISWs at a particular tidal phase has been interpreted as evidence that their generation mechanisms are connected to tidal phases [11]. This strengthens the case that tides cause the observed ISWs.

Figure 9 depicts a typical example of the phase-locked ISW packets at Stn. B4. ISW packets always occurred approximately one hour later than the previous day (marked by red arrows). Although the ISW packets appear at irregular times of the day, they occur at every low-tide phase. Furthermore, the intensity of ISWs occurring during spring tides (19–22 July) tends to be greater than during neap tides (12–18 July), consistent with the statistical results. The occurrence of ISWs at the fixed low-tide phase suggests that tide-topography interactions generate ISWs.

4.2. Generation Sites of ISWs

Next, we investigated the generation and propagation of ISWs. Figure 10a depicts an ISW distribution map of the northern YS based on the SAR images collected during the observation period. ISWs propagate in various directions, implying multiple generation sites. Specifically, the observed ISWs at the mooring station are generated at the rough topography around the island rather than being locally generated. Many ISWs propagating eastwards seem to originate from Zhangzi Island. A small number of westward-propagating ISWs also appear, which seem to have been generated around Haiyang Island.

In order to investigate the generation sites of the ISWs, we examined the distribution of internal-tide-generating body force in the northern YS (Figure 10). The depth-integrated internal-tide-generating body force is calculated as follows (Baines, 1982):

$$F=\frac{1}{\omega }\frac{1}{H^2}{\displaystyle {\int }_H^0{N}^2}\left(z\right)z\mathrm{d}z\cdot \sqrt{{(Q_x\frac{\mathrm{d}H}{\mathrm{d}x})}^2+{(Q_y\frac{\mathrm{d}H}{\mathrm{dy}})}^2}$$

(11)

where $\omega$ is the M₂ tidal frequency; H is the water depth; N²(z) is the squared buoyancy frequency; Q_x and Q_y are the zonal and meridional components of the tidal transport calculated by (Q_x, Q_y) = (uH, vH); u and v are the zonal and meridional components of the barotropic tidal current; and $\frac{\mathrm{d}H}{\mathrm{d}x}$ and $\frac{\mathrm{d}H}{\mathrm{d}y}$ are the zonal and meridional bottom slopes. The bottom topography is based on the 0.25′ grid general bathymetric chart of the oceans (GEBCO_2019) provided by the Intergovernmental Oceanographic Commission (IOC) and the International Hydrographic Organization (IHO). The OSU Tidal Prediction Software (OTPS) forecasts the zonal and meridional components of tidal velocity. Potential hot spots of internal wave generation sites around the world ocean have been examined using the spatial distribution of the F [43,44,45]. F > 0.25 m² s⁻² is usually regarded as the critical value for the generation of ISWs [44,46]. Figure 10a depicts that large F tends to be located around islands with striking topographic features.

That energetic internal tides were generated close to the offshore islands around the northern YS is consistent with recent numerical simulations [22]. Both SAR images and calculated F indicate that the ISWs are generated at these offshore islands and then propagate to the mooring stations.

Statistical analysis showed that the ISWs are related to tidal phases, with most ISWs occurring during low tide (Figure 8 and Figure 9). As a result, even though the SAR images show multiple ISW generation sites around the islands, there should be a major ISW generation site with tidally-generated ISWs reaching the mooring station periodically. Figure 9 depicts an example of ISWs fixed to local low tides, implying that they are generated tidally at a fixed location. The data from SAR images are then combined with in situ observations and the KdV model to provide additional insights into the generation and propagation details.

The ray-tracing method was used to find the major generation sites of ISWs in the northern YS [47,48,49]. Assuming that the ISWs propagate with a circular wave crest, the generation site of ISWs is defined as the intersection of two perpendicular lines across the wave crest. Figure 11a depicts an ISW packet captured on 11 July 2019, corresponding to the first ISW packet that appeared at low tide in Figure 9. The observed ISW packet from satellite images traces the generation site S1 to the straits between Dahao and Xiaohao islands, approximately 10.1 km from Stn. B4 (Figure 10b and Figure 11a). The generalized KdV model was then used to simulate the propagation of ISWs. The density is referred from the WOA18 database, showing that the upper and lower layer densities in the study area are approximately 1023 and 1024 kg m⁻³, respectively. We then simulated the propagation of ISWs with the generalized KdV model. The real topography from GEBCO was used for simulation. The density was referred to in the WOA18 database, showing that the upper and lower layer densities are about 1023 and 1024 kg m⁻³ in the study area. The depth of pycnocline is 5 m. After that, Equation (4) is numerically solved on a regular grid with $\Delta x$ = 10 m, $\Delta t$ = 10 s, the viscosity coefficient $\zeta$ = 0.0025 m² s⁻² [10], and a total integration time of 20 h. At x = 0 km, a train of two consecutive waves with vertical displacements of −5 and −4 m appears.

Figure 11b shows that the ISW packet undergoes several changes as they propagate seaward from S1. Their vertical displacements are significantly reduced, and they become broader and flatter. The ISW packet reaches the position corresponding to the SAR image after ~8.2 h of propagation from S1 (Figure 11a). The propagation from S1 to B4 takes about 12 h in total, with a mean propagating speed of ~0.25 m s⁻¹, consistent with the velocity estimated from the SAR image and mooring observations (Figure 5d). Figure 11c shows the barotropic tide at S1 when ISWs are generated. At low tide, when the direction of tidal velocities is toward the northeast, ISWs are generated in the straits between the islands. Although the site between the islands was estimated to be a critical ISW generation site, ISWs coming from different directions and at different times indicate the existence of other source regions. Furthermore, although we have shown that the ISWs are tidally generated at rough topography, the exact generation mechanism of the ISWs also awaits further investigation in the future based on numerical simulations. Nevertheless, the prevalence and properties of ISWs originating from offshore islands in the northern YS are documented for the first time based on comprehensive in situ observations and SAR images.

4.3. Influences of ISWs on Internal Turbulence

Turbulent mixing in shelf seas is a critical process that controls diapycnal nutrient transport, and it plays a vital role in biological production and carbon cycles [50,51]. The one-day VMP observations enable us to investigate the impact of ISWs on internal turbulence. Figure 12b shows the time-depth evolution of the observed $\epsilon$ and temperature. Previous studies showed that the energy input, conversion, and radiation rates increase monotonically with $\epsilon$ [52]. The largest $\epsilon$ (~10⁻⁶ W kg⁻¹) occurred in the well-mixed bottom boundary layer (BBL). One of the most noticeable features here is the presence of two peaks near the pycnocline. At the 4th hour after 13:00 on 14 July 2019, the $\epsilon$ reached the first peak with a maximum value of 10⁻⁷ W kg⁻¹. About eleven hours later, the $\epsilon$ reached the other peak with a larger value of 10⁻⁶ W kg⁻¹.

It is widely believed that turbulence in the surface boundary layer (SBL) in shelf seas can be strongly influenced by wind forcing. In order to investigate the impact of wind on the two $\epsilon$ peaks, we investigated the variation of wind speed at 10 m above the sea surface from the fifth generation European Centre for Medium-Range Weather Forecasts (ECMWF)’s atmospheric reanalysis of the global climate (ERA5). Figure 12a presents that the wind speed is less than 5 m s⁻¹ during the observation period, suggesting that the wind may not be the cause of turbulence. Surface buoyancy fluxes do not dramatically change when $\epsilon$ is intensified, which shows that changes in surface buoyancy fluxes do not cause internal turbulence. Kay and Jay found that substantial internal turbulence occurred even during periods of weak near-bed shear [53], suggesting that internal processes must contribute significantly to the internal turbulence. Figure 12c depicts the variations in internal temperature and turbulence. The temperature variations show a semidiurnal period, consistent with the M₂ tide. Around four hours (17:00 14 July 2019) and thirteen hours (02:00 15 July 2019) after the beginning of the observations, the temperature shows continuous high-frequency variations. Furthermore, we selected the depths of the ${\sigma }_{\theta }$ = 22.5 and 20.9 kg m⁻³ isopycnals to represent the lower and upper boundaries of the pycnocline, respectively (as shown by the white contours in Figure 12b). The two $\epsilon$ peaks in the pycnocline correspond to the high-frequency temperature variations (Figure 12c). The average $\epsilon$ in the pycnocline also shows a similar trend as the one-day RMS vertical velocity (Figure 12d). The largest root-mean-square vertical velocity appears at 15 h, corresponding to the long-lasting strong turbulence from 15 to 17 h. Although their largest peaks do not exactly coincide with each other, we suggest that the sustaining strong turbulence is related to the high-frequency temperature variation event which has induced a long-lasting influence. We therefore suggest that ISWs cause the observed internal turbulence.

The present observations demonstrate that ISWs are quite prevalent in the study area, originating at rough topographic features near the offshore island. The one-day VMP observation shows how passing ISWs can significantly alter internal turbulence in the northern YS. Moreover, the frequent turbulent mixing induced by ISWs can increase vertical nutrient supply and influence the local biogeochemical cycle [54,55,56]. Furthermore, the areas around the Changshan Islands are crucial aquaculture regions in China [57,58]. The presence of ISWs, which cause increased vertical flux and high-frequency temperature variations during warm seasons, may have significant ecological consequences that must be investigated.

5. Conclusions

The properties, generation mechanisms, statistics, and mixing effects of ISWs are investigated using mooring observations and SAR images from the northern YS. According to the spectral analysis, previous ISWs induced numerous high-frequency temperature spikes with periods ranging from 3 to 10 min. These ISWs are mainly depression type, with vertical displacements of up to 10 m. Dramatic vertical displacements can lead to nearly 9 °C temperature variations within the pycnocline. We estimated the propagation velocity of ISWs to be 0.16 to 0.25 m s⁻¹ by combining mooring observations and SAR images, which is consistent with the theoretical value. According to the statistical analysis, ISWs at the mooring stations do not indicate a clear preference for spring tides, but the RMS vertical velocity of ISWs (ISW intensity) exhibits a spring-neap tidal cycle and is linearly proportional to the barotropic tidal height. Furthermore, while ISWs can be found at the mooring stations at any tidal phase, they are far more prevalent during low tides.

These findings indicate that the ISWs are tidal in origin, with a major generation site. SAR images obtained during the observation period show that most ISWs in this region propagate in the zonal direction, which seems to originate from the Zhangzi and Haiyang islands. This is supported by the horizontal distribution of the depth-integrated internal-tide-generating body force, which shows consistent features of high values around the offshore islands. The ray-tracing method was used to locate the major generation site, which appeared to be located in the straits surrounding Zhangzi Island. The KdV model was used to simulate the propagation of the ISWs from the generation site to the mooring station. The ISWs take ~12 h to propagate from the generation site to the mooring station, which coincides with the observational estimates.

The $\epsilon$ showed two large values (~10⁻⁶ W kg⁻¹) when there were temperatures with high-frequency variations caused by ISW packets. The similar variation trends between $\epsilon$ and vertical velocity confirmed that ISWs cause internal turbulence. Turbulent mixing induced by frequent ISWs can increase the vertical nutrient supply and influence the biogeochemical cycle. Considering that the regions around these offshore islands are now important bottom-aquaculture farms in China, the influence of the prevailing ISWs on aquaculture remains to be examined.