Enhanced diapycnal mixing by polarity-reversing internal solitary 1 waves in the South China Sea

12 Shoaling internal solitary waves near the Dongsha Atoll in the South China Sea dissipate their 13 energy and thus enhance diapycnal mixing, which have an important impact on the oceanic 14 environment and primary productivity. The enhanced diapycnal mixing is patchy and instantaneous. 15 Evaluating its spatiotemporal distribution requires comprehensive observation data. Fortunately, 16 seismic oceanography meets the requirements, thanks to its high spatial resolution and large spatial 17 range. In this paper, we studied three internal solitary waves in reversing polarity near the Dongsha 18 Atoll, and calculated the spatial distribution of resultant diapycnal diffusivity. Our results show that 19 the average diffusivities along three survey lines are two orders of magnitude larger than the open- 20 ocean value. The average diffusivity in the internal solitary wave with reversing polarity is three 21 times that of the non-polarity-reversal region. The diapycnal diffusivity is higher at the front of one 22 internal solitary wave, and gradually decreases from shallow to deep water in the vertical direction. 23 Our results also indicates that (1) the enhanced diapycnal diffusivity is related to reflection seismic 24 events; (2) convective instability and shear instability may both contribute to the enhanced diapycnal 25 mixing in the polarity-reversing process; and (3) the difference between our and previous diffusivity 26 profiles is about 2-3 orders of magnitude, but their vertical distribution is almost the same. oceanography. line L1. It shows that the water depth becomes shallower from 297 southeast to northwest, and the bottom slope is steeper between 30-60 km. In the deep-water region 298 of 60-100 km, internal waves are developed, and the reflection seismic events fluctuate obviously. 299 Near the seafloor around 80 km, the reflection seismic events are uplifted and discontinuous, 300 forming a fuzzy reflection area. A mode-1 depression internal solitary wave can be identified at 53 301 km, indicating that the transition point has not been reached yet. The internal solitary wave has 302 reversed polarity in the area of 40 km, and a packet of three elevation waves is formed during the 303 polarity reversal process. The reflection seismic events is continuous here, and no obvious wave 304 breaking is found. Five reversal 391 region. Although there are more internal (solitary) waves with larger amplitude in the non-polarity 392 reversal region, the diapycnal diffusivity is lower. The polarity reversal of internal solitary waves significantly increases the diapycnal diffusivity. The turbulence subrange of the polarity reversal region is small, and the lower boundary of the turbulence subrange is greater than 0.01 decreases slowly at the same depth. The value is consistent with that in the open ocean. However, 580 the mixing enhanced obviously on the continental shelf and slope, because of the internal wave 581 shoaling. The mixing scheme underestimates mixing, especially the strong mixing induced by the 582 polarity reversal of internal solitary waves. Our results indicate that near the Dongsha Atoll, where 583 large amplitude internal solitary waves develop, mixing will be enhanced by the shoaling internal 584 solitary waves. The diffusivity gradually decreases from shallow to deep water (not including the 585 bottom boundary layer). This has important implications for improving the mixing scheme for 586 models on the continental shelf and slope.

internal solitary wave, and gradually decreases from shallow to deep water in the vertical direction. 23 Our results also indicates that (1) the enhanced diapycnal diffusivity is related to reflection seismic 24 events; (2) convective instability and shear instability may both contribute to the enhanced diapycnal 25 mixing in the polarity-reversing process; and (3) the difference between our and previous diffusivity 26 profiles is about 2-3 orders of magnitude, but their vertical distribution is almost the same.

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Energy dissipation of internal waves enhances diapycnal mixing, and turbulence in the form of 33 internal wave breaking is the primary mechanism for mixing thermodynamic properties in the ocean 34 global continental shelves and slopes (Holloway et al., 2001). They play an important role in the 38 global oceanic energy balance and provide energy for ocean mixing (Mackinnon and Gregg, 2003). 39 Due to shoaling internal waves and seafloor roughness, turbulent mixing on the continental shelves 40 lines (blue box in (a)) and its 95% confidence interval (blue shadow).

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After a conventional processing of the seismic data, an image of the ocean interior's structure can 124 be obtained. This image can be approximated as a temperature or salinity gradient map of the water 125 column (Ruddick, et al., 2009). The conventional processing of seismic data has 5 main steps, 126 including defining the observation system, noise and direct wave attenuation, velocity analysis, 127 normal moveout (NMO) and horizontal stacking. Then we use a bandpass filter to filter out low-128 frequency noise below 8 Hz and high-frequency noise above 80 Hz. According to the linear 129 characteristics of the direct wave, we use a median filter to extract the direct wave signal, and 130 subtract it from the original signal to achieve the purpose of attenuating the direct wave. 131 Subsequently, we sorted the seismic data from shot gathers into common midpoint gathers (CMPs).  The red dotted line shows the cut off trace, the right part of seismic data is cut off. The unit TWT of (a) 151 (2 ) Where  In practical applications, we use the slope spectrum to distinguish the turbulence subrange from the internal wave subrange. The spectral slope is as 183 follows (Holbrook et al., 2013): This conversion changes the wavenumber power law in the turbulence subrange from -5/3 to 1/3, 186 so that it can be distinguished from the internal wave subrange with -1/2 power law (-5/2 in the 187 displacement spectrum). In calculating the turbulence dissipation in the seismic section, it is 188 necessary to grid the section and calculate the dissipation in each grid separately. The horizontal 189 grid is set as 5 km, and the grid step 2.5 km. As the water depth in the seismic data is shallow, the 190 reflection seismic events are less in the vertical direction. In order to ensure more than two events 191 in each grid, we set the vertical grid to be 75 m and the grid step 37.5 m. In each grid, we calculated 192 the spectral slope of each event and took the average as  streamlines, it is difficult to record reflection seismic data from those areas with closed streamline 219 at the resolution scale of seismic data. The regional density gradient recorded by the reflection 220 events still exists, and the streamline is parallel to the isopycnal at this time. While areas with closed 221 streamlines are strongly mixed, and the density gradient weakens or even disappears, which cannot 222 be recorded in seismic data. Unfortunately, the internal solitary waves we observed do not satisfy 223 the second assumption. The KdV equation can simulate internal solitary waves with small amplitude 224 and weak nonlinearity, but the polarity reversal of the large-amplitude internal solitary waves we 225 observed cannot be simulated well. Here we did not use theoretical models to fit observations. 226 Although there are studies using theory to successfully simulate the polarity reversal of internal 227 solitary waves (Liu et al., 1998;Zhao et al., 2003;), it is difficult to match theories and observations. 228  parameterizations. The expression is as follows: 279 Where z u is the vertical gradient of horizontal wave-induced velocity,  is vertical turbulence    We picked the reflection seismic events in the three sections (Figure 7) and calculated the horizontal 331 slope spectrum using the method described in section 2.2. Figure 6 shows the average horizontal 332 slope spectrum of the three sections. We calculated the horizontal slope spectrum of all tracked 333 events and averaged in logarithmic space to determine the wavenumber of turbulence subrange. The It indicates that the internal waves carry more energy, so the spectral energy in internal wave 358 subrange is larger (Figure 6c). In addition, there are many discontinuous and weak reflections in the  Figure 6 shows that the spectral energy of the L1 section is smaller than that of the other two sections. 371 This may be because the imaging range of the L1 section is different. The observations in the L2 372 and L3 sections are the polarity reversal of internal solitary waves, while the L1 section includes 373 not only the polarity reversal process, but also internal waves in deep water. The spectral energies 374 of these two processes should be different. We calculated the average horizontal slope spectrum of 375 the polarity reversal region and the non-polarity reversal region, respectively (Figure 7). The 376 spectral energy of the polarity reversal region in L1 section is higher than that of the non-polarity 377 reversal region, so does diapycnal diffusivity (Figure 7a). It implies that the wave energy will 378 accelerate to dissipate and transfer to turbulence when its polarity is reversed. Compared with the 379 non-polarity reversal region, the turbulence subrange of the polarity reversal region is smaller. The 380 lower boundary of the turbulence subrange of the polarity reversal region is slightly larger than that 381 of the non-polarity reversal region. It indicates that the turbulence in this region has a smaller scale. 382 The diapycnal diffusivity in the polarity reversal region in L2 section is about 3 times that of the 383 non-polarity reversal region (Figure 7b). The turbulence subrange of the polarity reversal region in 384 L2 section is slightly larger than that of the non-polarity reversal region. From the L2 section, it can 385 be seen that the events are continuous during the polarity reversal process, which indicates that the 386 wave breaking is weak. The internal solitary wave gradually fissions into several tails during the 387 polarity reversal, and energy is dissipated constantly. Therefore, there will be a large turbulence

Diapycnal diffusivity maps 401 402
The diapycnal diffusivity maps of the three survey lines are shown in Figure 8. Figure  high. In addition, there is also an area with increased diffusivity between 100-250 m at 93 km. This 417 may be related to the activity of large amplitude internal waves.

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The diffusivity map of the survey line L2 is shown in Figure 8b. The high value is mainly distributed 420 at the front of head wave during polarity reversal process (4 km), which is consistent with the 421 characteristics on L1. The diffusivity after the head wave is low, but it is still higher than that in

The relationship between diffusivity and reflection seismic events 438 439
When there is a significant impedance difference in the water column, a reflection seismic event analyze the spatial distribution of diapycnal mixing by seismic section. Figure 8 shows that the 447 reflection seismic event in the high diffusivity region is obviously different from that in the low 448 diffusivity region. In the high diffusivity area (red in Figure 8), the reflection seismic events are 449 fuzzy, discontinuous or bifurcate. While in the low diffusivity area (yellow and blue in Figure 8 seismic data processing of the three sections in Figure 8 is the same, so the thicker events in Figure  470 8b do not stem from the low frequency of seismic waves. We think this may be caused by small-471 scale mixing between layers, such as K-H instability. Figure 9 is an enlarged view of the location 472 between 2-3 km in the seismic section of L2 (Figure 5b). The wavelength of the seismic wave (red 473 line) at 80 m is larger than that at the seafloor, which is formed by the overlap of multiple wavelets. wave (Moum et al., 2003). The vertical scale of the K-H instability is small and usually appears on 479 the isopycnal. On the one hand, K-H instability weakens the density gradient so that the reflected 480 seismic wave energy is reduced. On the other hand, the vertical scale of K-H instability is lower 481 than the seismic wave resolution (a quarter of the seismic wave wavelength), so it makes overlapped 482 wavelets and stretched wavelength (Figure 9). Therefore, the reflection event in this area is thicker. 483 Besides, the horizontal scale of the K-H instability train is large, which may explain the larger 484 turbulence subrange on the horizontal slope spectrum (Figure 7b). 485 486 The high diffusivity is mainly in the leading internal solitary wave during the polarity reversal. We 518 suggest that strong mixing may be caused by internal wave breaking due to convective instability. 519 In Figures 8a and 8c, the reflection seismic events are obviously discontinuous in the high 520 turbulence area of the leading wave, indicating that the density gradient is weakened by internal 521 wave breaking. The trough of the internal solitary wave decelerates first when the polarity is 522 reversed (Shroyer et al., 2008), which makes the Froude number (Fr) greater than 1 and causes 523 convective instability. This phenomenon can be found in other observational data. In the high-524 frequency acoustic section, the backscatter at the top of internal solitary wave is increased when it 525 changes from depression to elevation wave (Orr and Mignerey, 2003), which indicates that the 526 turbulence of the front increased. However, in the seismic section of Figure 8b, we did not find the 527 events break at the front the polarity reversal internal solitary wave. The strong mixing of this 528 internal solitary wave may be induced by shear instability (Figure 9). Therefore, both convective 529 instability and shear instability are responsible for the enhanced mixing in this process. In addition, 530 the non-polarity reversal region in Figure 8a has a higher diffusivity in 50-150 m than other regions. 531 This range is in the thermocline (Figure 1c). The internal waves usually greatly increase mixing in 532 the thermocline, which is related to the shear instability of internal waves (Mackinnon and Gregg, 533 2003). Shear instability is an important mechanism of internal wave dissipation (Farmer and Smith, 534 1978), and it more likely occurs in nonlinear internal waves than convective instability (Zhang and 535 Alford, 2014). The results of high-frequency acoustic observations show that the enhanced 536 backscatter at the bottom of the thermocline represents higher shear instability when the internal 537 solitary waves are shoaling (Orr and Mignerey, 2003), which is consistent with the depth range of 538 high diffusivity in our results.

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What is inconsistent with the observed distribution of mixing is that our results are not able to show 541 diffusivity in the bottom boundary layer. Because our seismic data was collected in summer, the 542 strong stratification at this time limits the vertical range of the bottom boundary layer (Mackinnon 543 and Gregg, 2003). So that the bottom boundary layer near the Dongsha Atoll is thin and lower than 544 the thickness that can be recorded by seismic data. So, the diffusivity we calculated does not include 545  Figure 10 shows the vertical distribution of diffusivity from 560 seismic data (solid line) and the diffusivity calculated from mixing scheme (dashed line) at 4 561 positions of the three survey lines (black arrows in Figure 8). The reflection events in the L3 section 562 are broken, and it cannot be guaranteed that the events are parallel to the streamline. Therefore, we 563 did not use the method described in section 2.3 to calculate the wave-induced velocity, and thus did 564 not obtain the diffusivity of the mixing scheme. It can be seen from Figure 10 that the turbulent 565 diffusivity gradually decreases from shallow to deep water. Except for the local low diffusivity value 566 in the deep water at the position D of Figure 10b and 10c, the diffusivity reduction rate at the other 567 location is similar. Figures 10a and 10b show that the parameterized diffusivity is nearly 2--3 orders 568 of magnitude smaller than our result, but they have a similar trend of change. In Figure 10a  found that the former is about 3 times larger than the latter. The diffusivity maps reveal that 602 horizontally high diffusivity is mainly in the leading wavefront of an internal solitary wave in 603 reversing polarity, and vertically high diffusivity is mainly in the thermocline (50-100 m).

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We analyzed the relation between reflection seismic events and diapycnal diffusivity. The result 606 indicates that continuous and clear reflection events correspond to low diffusivity, while 607 discontinuous or fuzzy events correspond to high diffusivity. The strength of the events also affect 608 the magnitude of diffusivity. The stronger the fluctuation, the higher the spectral energy, and the 609 higher the diffusivity. In addition, we observed an area of high diffusivity with a large horizontal 610 scale in L2, and the reflection events did not appear to be discontinuous or fuzzy. We suggest that 611 this is enhanced mixing induced by the K-H instability (Figure 9). The vertical scale of the K-H 612 instability is smaller than the resolution of our seismic data, so we cannot observe clearly in the 613 seismic data. But its high-energy characteristics can be recorded by reflection events.

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Our results show that shoaling internal solitary wave enhance local mixing. The magnitude order of 616 diapycnal diffusivity is consistent with previous studies. We suggest that there are two mechanisms 617 accounting for the enhanced mixing. On one hand, the polarity reversal of internal solitary waves 618 results in convection instability, which induces internal solitary wave breaking. This mechanism 619 appears at the leading edge of one internal solitary wave in the survey lines L1 and L3. The