1 INTRODUCTION

Submarine turbidity currents, often called "submarine rivers", are an important form of sediment transport and are one of the main ways that sediments from continental shelf areas are transported to the deep sea; additionally, valuable oil and gas resources have been found in deposits created by turbid currents (Stetson and Smith, 1938; Mulder et al., 2003; Nilsen et al., 2008; Xu, 2014; Talling, 2015). Large-scale turbidity currents can damage telecommunication cables (which account for over 95% of global data transfers) and oil pipelines (Carter et al., 2014; Azpiroz-Zabala et al., 2017; Gavey et al., 2017). For example, the Pingtung earthquake in southern Taiwan, China, in December 2006 triggered a highspeed turbidity current along the Gaoping GorgeManila Trench axis, destroying several international communication cables, and another submarine cable accident occurred off southern Taiwan, China, in 2009 (Carter et al., 2012). Therefore, it is necessary to understand the motion mechanism and velocity of turbidity currents in submarine canyons.

Recent studies have shown that there is a highly concentrated layer near the bed in turbidity flows (Fang et al., 1998; Winterwerp, 2006; Paull et al., 2018; Heerema et al., 2020; Wang et al., 2020). This scenario differs from the traditional understanding of turbidity currents, and the sediment concentration in this layer is very high, even beyond the range that can be measured by some optical turbidity meters. The existence of a high concentration layer near the bottom also makes the scouring and deposition of the bottom bed complex and intense. However, the complex material exchange between the turbidity current and the sediment bed influences the movement speed of the turbidity current to a certain extent.

During the evolution of turbidity currents, the speed of the turbidity current increases continuously in a self-acceleration stage (Bagnold, 1962; Parker, 1982; Parker et al., 1986; Sequeiros et al., 2009, 2018). One of the many methods for quantitatively studying submarine turbidity current velocity is based on damage to submarine cables. Heezen et al.(1952, 1954) and Kuenen (1952) noted that during the Grand Banks earthquake in 1929, a cable was damaged by a turbidity current caused by the earthquake; by analyzing the sequence of cable damage, the maximum velocity of the turbidity current was inferred to have reached 28 m/s (55 knots); these results represent an early quantitative study of the velocity of turbidity currents. Subsequently, Piper (1988) analyzed a turbidity current and noted that its velocity must have been greater than 18.3 m/s to rupture the observed length of cable. Krause et al. (1970) studied the turbidity currents caused by two earthquakes in western New Britain. The maximum velocities of the two turbidity currents were 14 m/s and 8 m/s. In 2006, the turbidity current caused by an earthquake in southern Taiwan, China, led to the rupture of 11 cables across the Gaoping Gorge and Manila Trench. Through calculations, the maximum velocity of the turbidity current was estimated to have reached 20 m/s (Hsu et al., 2008). In 2009, the turbidity current caused by typhoon Morakot in southern Taiwan, China, reached a speed of 16.6 m/s (Lambert et al., 1976). Subsequently, in 2010, a cable rupture event was caused by a turbidity current in the Manila Canyon, and the estimated turbidity current velocity was 5.9–7.9 m/s (Gavey et al., 2017).

Another method for intuitively obtaining turbidity current velocities is on-site monitoring. The earliest on-site monitoring of turbidity current velocity was completed in freshwater lakes. Due to the low density of freshwater and the small scale of turbidity currents, the detected turbidity current velocity was relatively low at only 30 cm/s (Lambert et al., 1976; Hsu et al., 2008). In the sea off Oahu Island, Hawaii, four turbidity current events were observed during Hurricane Iwa, and the maximum turbidity current velocity reached 2 m/s (Dengle et al., 1984). Cooper et al. (2016) monitored the velocity of turbidity currents in the Congo Strait in 2013 (with a maximum velocity of 1.5 m/s). Paull et al. (2018) monitored turbidity currents in Monterey Canyon, and the results showed that the maximum velocity in front of the turbidity current reached 7.2 m/s.

The above results indicate that the turbidity current velocities inferred from cable ruptures are much higher than the actual measured velocities. The earliest dispute about turbidity current velocity occurred in 1954. Shepard (1954) discussed whether the turbidity current caused by the Grand Banks earthquake in 1929 could have reached 25 m/s. In addition, Zeng et al. (1991) monitored a turbidity current in the Bute Inlet Fjord area, and the current meter measurement results showed that the maximum speed of the turbidity current was 1.1 m/s, whereas the turbidity current velocity according to the time of anchor stress was as high as 3.3 m/s. According to a 3-year monitoring program of turbidity currents south of Taiwan, China, since 2014, the maximum observed velocity was 15 cm/s, while the velocity inferred from cable cutting in August 2015 was 5–8 m/s (Zhang et al., 2018).

It is difficult to explain why the velocity of underwater turbidity currents can exceed 20 m/s, which is much faster than Bolt's average speed over 100 m; even if the dolphins swim as fast as possible (20 m/s), they can barely keep up with the head of a turbidity current. In addition, there is no reasonable explanation for the large difference between the turbidity current velocity inferred from submarine cable ruptures and that observed through direct measurements. Therefore, we make the following assumptions: 1) a single turbidity flow cannot achieve a high velocity, and 2) the velocity of damage propagation along a canyon bed is regarded as the velocity of the turbidity current. Through indoor experiments and the Flow-3D analog method, we discuss the maximum turbidity current velocity that can be achieved and the mechanism by which high turbidity current velocities are generated.

2 EXPERIMENT 2.1 Test 1: sedimentation test of a high-concentration muddy water body in water

In this experiment, the limit condition was used to assess the maximum velocity of a turbidity current.

The average slope of submarine canyons is generally low (Monterey Canyon: 1.6°–2.3° (Paull et al., 2011); Gaoping Canyon: 0.3°–1.0° (Gavey et al., 2017)), and turbidity currents move along these gentle slopes for hundreds or even thousands of kilometers. During this process, various kinds of resistance, such as friction near the bottom interface, are encountered. To study the limit velocity of turbidity currents, we designed a vertical falling test of a high-concentration muddy water body in water. Four different concentrations (with densities of ρ₁=1 720 g/L, ρ₂=1 490 g/L, ρ₃=1 400 g/L, and ρ₄=1 310 g/L) of muddy water were placed in a thinwalled balloon (the balloon had a wall thickness of 0.05 mm, a cross-sectional diameter of approximately 50 mm, and a height of 70 mm, and it was filled with turbid fluid; the balloon was considered able to change its shape according to changes in resistance, and the turbid fluid was not diluted, resulting in an evaluation of the vertical sinking velocity that was as accurate as possible), and the balloon was then vertically dropped in a cylindrical pipe with a length of 4 m and a diameter of 25 cm; the pipe contained seawater with a density of 1 020 g/L.

At the beginning of the experiment, the balloon was placed in the middle of the settling tube and was allowed to settle freely. The whole process was recorded. After the balloon reached a uniform speed, the final velocity was obtained from video playback. To reduce the experimental error, balloons with each concentration were tested three times, and then the average value was calculated.

2.2 Test 2: effect of a turbidity current on a soft sediment bed

The purpose of this experiment was to investigate the relationship between the velocity of turbidity currents and the propagation of bed damage induced by turbidity currents.

A large number of studies have shown that the profiles of submarine canyons are mostly V-shaped or U-shaped (Nie et al., 2017) and that canyon beds are covered with a certain thickness of soft sediments with small particle sizes (silt and clay) (Paull et al., 2013; Symons et al., 2017; Maier et al., 2019). To study the effects of turbidity currents on sediment in submarine canyons, corresponding experiments were designed, as shown in Fig. 1a.

In these experiments, a semicircular channel was used to simulate a submarine canyon and filled with sediment. Pressure sensors were arranged every 40 cm in the channel, and the channel was filled with 5 cm of soft silty sediment to represent the seabed. Then, the left side of the flume was raised to form a slope of 8°, and a channel with a steep slope was created on the left side. Then, high-concentration muddy water (used to simulate a turbidity current) was poured along the channel to simulate the effects of a turbidity current on the sediment in the canyon bed.

Two groups of tests were conducted; in Test 1, the moisture content of the sediment bed in the channel was 45% (1 720 g/L), and in Test 2, the moisture content of the sediment bed in the channel was 55% (1 610 g/L). The sediment in the turbid fluid used in the two groups of tests was the same as that in the sediment bed and had a moisture content of 55% (1 520 g/L).

2.3 Test 3: flat flume test

The purpose of this experiment was to investigate the relationship between the velocity of water waves excited by a turbidity current suddenly entering a submarine canyon and the velocity of the turbidity current.

The device used in the experiment was a straight flume with a height of 15 cm, a width of 20 cm, and a total length of 3.1 m. A 20 cm-long diversion channel was positioned at the front end (to introduce the highconcentration fluid), and a circular wave band with a diameter of 80 cm was positioned at the back end (Fig. 1b).

To measure the force in the process of turbidity current movement, three pressure sensors were installed on the flat flume at distances of 10 cm (A), 75 cm (B), and 140 cm (C) from the baffle plate. The acquisition frequency of the three sensors was 50 Hz, and the accuracy was 0.5%. These sensors monitored the force at each position in the process of turbidity current movement in real time to determine the speed of the turbidity current.

Previous studies have shown that the sediment entrained by turbidity currents is mainly composed of silt and clay particles (Liu et al., 2012), and the flow capacities of turbidity currents with different concentrations and particle size distributions are obviously different (Felix and Peakall, 2006). To obtain good test results, the fluidity of turbidity currents with different silt-clay ratios and sediment concentrations was tested before the tests to obtain turbidity currents with the best flow performance (Fig. 2). The turbidity current with a silt-clay ratio of 8꞉2 and a sediment concentration of 830-g/L yielded the best underwater flow capacity and the highest velocity. Therefore, this turbidity current composition was selected as the experimental turbidity current.

Two groups of tests were conducted. In Experiment 1, the straight section was filled with clear water to accurately describe the motion of the turbid water. In Experiment 2, the clear water was replaced with turbid liquid with 300-g/L kaolin. After standing for a period of time, the water body was stratified: the upper 2-cm layer was clear, and the lower layer was an underwater soft sediment bed. Then, Test 2 was performed. The thickness of fluid in the straight section in both tests was 8 cm.

Before each test, the corresponding fluid (clear water in Test 1 and turbid liquid with 300-g/L kaolin in Test 2) was added to the straight section of the flume to a depth of 8 cm. High-concentration muddy water was then introduced in the diversion section of the straight flume (Fig. 1b). At the start of the test, the dividing wall was vertically and rapidly removed so that the high-density fluid in the diversion section flowed into the straight section, resulting in a turbidity current flowing along the bottom surface. During the test, the pressure sensors monitored the stress conditions imposed by the turbidity current in real time. In addition, the entire test process was visually recorded, and the velocity of the turbidity current was obtained from the response times measured by the pressure sensors and from the video recording.

3 RESULT 3.1 Result of Test 1

At the beginning of the experiment, the balloon was placed in the middle of the settling tube and was allowed to settle freely. The whole process was recorded. After the balloon reached a constant speed, the final velocity was obtained from video playback. To reduce the experimental error, balloons with each concentration were tested three times, and the average value was calculated. The results are shown in Table 1.

The results show that with decreasing sediment concentration, the final vertical settling velocity also decreases, but the maximum velocity does not exceed 1 m/s.

3.2 Result of Test 2

Turbidity currents were poured into the semicircular channel. A video recorder was used to record the whole test process, and the pressure data measured by the pressure sensors were collected with the acquisition instrument at a frequency of 100 Hz. The pressure at each pressure sensor position during the test is shown in Fig. 3 (the effects of fluctuations in the overlying water body are not considered).

During the test, the soft sediment in the semicircular channel did not slide. However, the turbidity current poured into the channel gradually deposited sediment during the flow process. After passing over the No.4 pressure sensor, only a small amount of entrained sediment remained, and it was completely deposited upon reaching the No.5 pressure sensor. With increasing flow distance, the velocity first increased and then decreased, and the thickness of the fluid gradually decreased.

When the turbidity current flows into the channel, the soft sediment originally laid in the semicircular channel is not damaged, and the sediment carried by the turbidity current is gradually deposited. However, when the overlying turbid fluid flows over sensors 3 and 4, the soft sediment bed is damaged, resulting in the secondary acceleration of the whole turbid fluid, and sediment gradually accumulates at the end of the channel. A comparison of the velocities in the two tests is shown in Table 2.

By comparing the experimental phenomena and the sensor response, the original turbidity current velocity can be obtained from Experiment 1, and the velocity following the disruption of the soft bed can be obtained from Experiment 2.

3.3 Result of Test 3

In the two groups of flat flume tests, the underwater motion state of the turbidity current can be seen through the transparent sidewall of the flume. In addition, during the two tests, an excitation wave with the same direction as the turbidity current motion was generated in the straight section of the flume, moving forward in the form of solitary waves, and its motion speed was greater than that of the turbidity current (Fig. 4). Here, we refer to the released turbid fluid that maintains continuity as the original turbidity current and the water wave generated by the movement of the turbidity current as the excitation wave.

In the process of turbidity current movement, the responses of the pressure sensors were monitored in real time. When the turbidity current enters the flat section of the water flume, the excitation wave also creates a response recorded by the pressure sensors. The pressure sensor measurements obtained during the two tests are shown in Fig. 5.

In the two tests, the velocity of the excitation wave generated by the turbidity current flowing into the water was greater than that of the turbidity current. Through video playback and pressure sensor response data, the velocities of the excitation wave and turbidity current head in the two tests were obtained, as shown in Table 3.

4 ANALYSIS AND DISCUSSION 4.1 Settling velocity of a single spherical particle

At present, considerable research has focused on the settling velocity of spherical particles. In the process of settling, the particles are affected by gravity G, buoyancy F, and resistance f. With increasing velocity, the resistance also increases, and the maximum sinking velocity is reached at G=F+f.

The maximum velocity of spherical particles can be expressed as , where υ is the viscosity coefficient of the liquid.

Suppose that the sphere diameter D=10 cm, the density of a spherical particle is ρ_s=2.65 g/cm³, the density of the water body is ρ=1.03 g/cm³, g=9.8 N/kg, and the viscosity coefficient of seawater at 20 ℃ is approximately υ=1.075×10^-3 Pa·s. The maximum settling velocity of spherical particles is 6.42 m/s.

In addition, the maximum settling velocity of the thin-walled balloon in Test 1 is calculated by using this method. The settling velocity of the whole balloon was calculated according to the corresponding density and diameter, and the maximum settling velocity of the balloon with the highest density was only 0.62 m/s. Compared with the test results, the calculated velocity was lower because the thin-walled balloon used in the test could change its shape in response to water resistance to achieve the minimum resistance state, whereas in the calculation, the object was assumed a rigid sphere.

In ideal state, the settling velocity of a single particle in water is far from 20 m/s. Combined with the measured settling velocity (< 1 m/s) of the highconcentration muddy water body, we find that even considering the existence of a high-concentration layer near the bottom of a turbidity current, it is difficult to achieve such a high velocity in a submarine canyon. Moreover, in the process of turbidity current movement, there will be friction with the bed, and if the sediment concentration is too high, the turbulence will be restrained (Bagnold, 1962; Parker, 1982; Heerema et al., 2020).

4.2 Analysis of the failure propagation of weakly stable sediment

Based on a comparison of the test phenomena and the pressure data (Fig. 3) obtained through the analysis of the stress on the soft sediment bed, sensor Nos. 1–4 present results with a clear double peak; the box in Fig. 3a indicates the first peak in the stress on the soft bed. This peak value is associated with the flow of turbid fluid and the deposition of sediment on the soft sediment bed, and the stress decreases with the flow of the turbid fluid. However, the flow of the overlying turbid fluid imposes a shear force on the sediment bed. Due to the high moisture content of the soft sediment bed and the extremely low sediment strength, the fluctuation caused by the shear force can propagate into the bed, and the propagation mode is similar to that of seismic waves. Therefore, this process creates the second stress peak on the bed. For example, for sensor No.3, first, the turbidity current reaches the sensor, which leads to an increase in the stress on the bed (section A); then, the turbidity current flows over the sensor, which causes the pressure value shown in section B to be greater than the initial value. Next, the pressure wave propagates to the sensor, causing another increase in the force measured by the sensor (section C). Finally, as the wave continues to propagate, the pressure gradually decreases and returns to the value observed in section B (section D). After the turbid fluid flows over the No.4 sensor, only approximately 1 mm remains in the sediment layer (inferred from the pressure sensor), so the amount of turbid fluid flowing to the No.5 sensor is very small. Therefore, two peaks are not observed in the data, and only one inflection point appears. Furthermore, no turbid fluid remains to flow over the position of the No.6 sensor; however, a pressure increase is observed at this position and must be caused by wave propagation through the soft sediment.

The pressure values in sections A, B, and C in Fig. 3b represent the sediment thickness before, during and after the test, respectively. The figure shows that the sediment thicknesses at the No.1 and No.2 sensors after the test are significantly higher than those before the test, which indicates that deposition occurred when the turbid fluid flowed over the sensor. Based on the experimental phenomena, when the turbid fluid flows over the No.1 and No.2 sensors, the soft sediment bed is not damaged, and the turbid fluid gradually deposits sediment. In addition, the pressures measured by the No.1 and No.2 sensors exhibit two peaks: the first peak is caused by the flow of the overlying turbid fluid, and the second peak can be considered the propagation of the turbid fluid into the soft sediment after the bed is stressed. When the turbid fluid flows between sensors No.2 and No.3, the bed is disturbed, and the soft sediment bed slides. It should be noted that the pressure values indicated by sensors Nos.3–6 increase progressively after bed failure in Fig. 3, and the obvious time difference between trends reflects the failure mode of the soft sediment bed, which is obviously different from that of a block landslide.

Table 2 shows the velocity along the track recorded by the two test sensors. During the two tests, when the soft bed is damaged (as the overlying turbid fluid flows over the No.1 and No.2 sensors), the velocity remains basically the same. In Test 1, the bed is not damaged in all cases, the overlying turbid fluid gradually deposits sediment, and the velocity gradually decreases. In Test 2, because the bed slides when the turbid fluid flows over sensors No.2 and No.3, the new fluid, which is different from the original turbidity current flow, accelerates twice, and the velocity obviously increases. The results show that when a turbidity current flowing through a submarine canyon acts on a weakly stable soft bed, it pushes the bed, which destabilizes the bed and generates a new turbidity current with a velocity that is much higher than that of the original turbidity current.

By comparing and analyzing the experimental phenomena and data, it can be inferred that the highconcentration layer near the bottom creates a shear force acting on the seabed during the movement of a turbidity current in a submarine canyon, and the shear force propagates in the soft sediment bed in the form of a pressure fluctuation. When the bed is in a metastable state, a small force can make the soft sediment bed flow slip, creating a flow that is different from the original turbidity current flow.

4.3 Effect of turbidity flows on the bed in the flume test

In a relatively new study, Paull et al. (2018) and coworkers found that a high-pressure area can be formed in front of the head of a turbidity current. Here, it is also found that the excitation wave generated by the movement of a turbidity current in the water is characterized by high speeds, and the three sensors arranged in a flat flume during the test detected the excitation wave and force created by the head of the turbidity current (Fig. 5). The pressure sensors were arranged 1.5 cm from the bottom of the straight water tank, the test water depth was 8 cm, and the hydrostatic pressure of the clear water test was 0.65 kPa. In the soft sediment test, the bottom layer featured a high concentration of fine-grained sediment with a density of 1.2 g/L, and the hydrostatic pressure for this group of tests was 1.1 kPa. The hydrodynamic pressure was used to analyze the force caused by the excitation wave and turbidity current during the test.

According to the above analysis, in the two tests, because the first sensor, sensor A, was too close to the pumping plate, the pressure data obtained by sensor A cannot be definitively attributed to the excitation wave or the movement of the head of the turbidity current. However, due to the rapid motion of the excitation wave, the pressure increase is considered to be caused by the excitation wave. The second sensor, sensor B, was located in the middle of the straight flume and could clearly differentiate the response caused by the excitation wave and the response caused by the movement of the turbidity current head. Moreover, after the excitation wave passes the sensor, the subsequent wave surface enters a trough state, and the force generated is equivalent to the resultant force caused by the turbidity current head and the excitation wave trough, so the response caused by the turbidity head is lower in the two tests. The third sensor, sensor C, was located in the far part of the straight flume. When the head of the turbidity current reaches this point, the excitation wave has already moved to the elimination band of the straight flume, so the response here is also extremely clear. Moreover, the value presented by the sensor can best reflect the relationship between the excitation wave force and the force of the head of the turbidity current. By comparing the two responses of sensor C, we found that the resultant force generated by the excitation wave is greater than that created by the head of the turbidity current. In summary, it can be clearly concluded that after the turbidity current flows into the water, an excitation wave will be generated in the process of movement. The excitation wave not only moves faster than the turbidity current but also produces a force greater than the head of the turbidity current by approximately 1.5–2 times. Additionally, the action of the excited waves caused by the turbidity current on the bed cannot be ignored under the experimental conditions.

4.4 Theoretical analog of turbidity flow

In this paper, Flow-3D software is used to establish a numerical flat flume to keep the parameters of the simulated flume consistent with those of the experimental flume. The RNG turbulence model is used in this study. The governing equations of the numerical model calculation include the continuity equation, momentum equation, turbulent kinetic energy equation, and turbulent energy dissipation rate equation.

4.4.1 Mesh generation and boundary condition

According to the prototype of the flat flume test, a 1꞉1 geometric solid model is established. The model range is from the rectangular section (2.3 m) to the circular energy dissipation section, and the diameter of the circular section is 80 cm. The calculation area is divided with the free grid method, and all areas are divided into a structured orthogonal grid. A nested grid is applied locally to the straight section and the interface between the circular section and the straight section. After applying the nested grid, the total number of grid points in the straight section is 800 000, the minimum size of the x-directional grid is 0.005 2 m, the minimum size of the y-directional grid is 0.005 m, and the minimum size of the z-directional grid is 0.004 m. The total number of circular grid points is 500 000, the minimum size of the x-directional grid is 0.007 2 m, the minimum size of the y-directional grid is 0.008 m, and the minimum size of the z-directional grid is 0.004 m.

In terms of boundary conditions, the front and rear sides of the calculation area are symmetrical boundaries, and the remaining boundaries are wall boundaries. A water level with a certain height is set in the flume, and nonslip boundary conditions are adopted for the wall surface.

4.4.2 Analog result

Based on the relevant test parameters used in the two tests, Flow-3D was used for simulation. The simulation results are shown in Fig. 6.

The analog results of the two experiments show that the turbidity current forms an excitation wave after entering the water, and the velocity of the wave is higher than that of the head of the turbidity current. In the two analog processes, the excitation wave velocity and turbidity head velocity are shown in Table 4.

Table 4 shows that the excitation wave velocity and turbidity head velocity calculated from the pressure sensor data are basically consistent with those calculated from the test video data. Therefore, when compared with the analog results, the average of the velocity values obtained from the test is compared with the analog result. A comparison between the measured values and simulated results of the two tests is shown in Table 5.

From the above comparison results, the velocity of the excitation wave and the velocity of the turbidity head in the clean water test are almost the same as the analog values, but the difference between the velocity of the turbidity current head in the soft sediment bed test and the analog result is relatively large. Notably, in the soft sediment bed test, the velocity was determined near the sidewall of the flume. Due to the influence of the soft sediment on line of sight, the observed head of the turbidity current is determined based on the zone with the highest concentration, and its real velocity should be greater than the observed value. In addition, in the analog results, the friction between particles in the two fluids when the turbidity current moves into the soft sediment is not considered. For the above two reasons, the experimental value of turbidity current velocity in soft sediment is smaller than the analog value. However, even if the velocity of the head of the turbidity current given by the analog is relatively high, the velocity of the excited wave is still 2–3 times the velocity of the head of the turbidity current. Therefore, it can be concluded that compared with the velocity of the turbidity current itself, the velocity of the excitation wave generated by the turbidity flow is higher.

4.5 Proposed failure propagation model for weakly stable sediments (WSS-PFP model)

The long-range movement of turbidity currents in canyons is bound to be accompanied by sedimentary replenishment along the way. Most previous studies have linked this replenishment with the erosion generated by turbidity currents. This replenishment occurs through erosion of the soft bed by the highvelocity head or the high-concentration layer near the bottom. However, the above analysis and discussion suggest that a single turbidity current cannot maintain such high-speed movement; therefore, in addition to the conventional understanding of turbidity flows, other movement modes that can explain the causes of high-speed turbidity currents should be considered. The following cases are mainly due to the destruction of the weak sediment bed, which leads to the turbidity current developing continuously at a high speed. This paper summarizes the proposed failure propagation process for weakly stable sediments using the WSSPFP model.

(1) The longitudinal sections of submarine canyons are mostly U-shaped, and the canyon bottoms are covered with thick fine-grained soft sediment. Over years of deposition, under certain slope conditions, the soft sediment in a canyon exhibits a weakly stable state, and a slight external force can cause it to slip. When a turbidity current in a submarine canyon reaches a certain scale, the shear force of the turbidity current on the bed is large, and the shear force propagates in the form of a pressure fluctuation in the soft sediment. When this pressure wave encounters weakly stable sediment, the sediment can slide, destabilizing the bed, and a new turbidity current can form in front of the original turbidity current (Fig. 7a). This model can explain the high-speed and long-range movement of turbidity currents in canyons.

(2) As a turbidity current flows through a canyon, it pushes the water in front of it, resulting in an excitation wave with a velocity that is much higher than that of the turbidity current itself. In the process of turbidity flow movement, damage to the bed occurs in two forms. First, as the excitation wave moves forward, it exerts force on the bed. When it moves to a low-stability portion of the bed, it may lead to the sliding failure of the soft sediment bed, thus forming a new and high-speed turbidity current that begins to move forward (Fig. 7b). Second, the excitation wave induced by the turbidity current causes the resuspension of soft sediment from the bed; this material begins to move downslope and is driven by density differences, resulting in the formation of another turbidity current or contributing to the formation of a larger turbidity current (Fig. 7c).

When subjected to external impacts (earthquakes, landslides, debris flows etc.), the soft sediment deposited in a submarine canyon reach a shear wave propagation velocity of 100–170 m/s; however, after leaving the shock source area, the vibration intensity decreases with increasing propagation distance due to the inelastic impedance of soil and the diffusion of vibration energy. Therefore, the sediment damage in the submarine canyon may not be caused by the vibration wave propagating in the sediment. We performed a vertical falling experiment of mediumand high-concentration sediment-laden water bodies in water bodies, and the velocity considered was less than 1 m/s. However, turbid currents with higher velocities (generally greater than 1.0 m/s, up to 28 m/s) were observed in submarine canyons, with velocities comparable to those of push-type landslides on land (Zhang et al., 2020). The weakly stable sediment in the submarine canyon is destroyed under certain conditions, and the damaged sediment produces an additional compressive force on the sediment below (in front of the movement direction). Then, the soft sediments in its lower part were destroyed and propagated in this way. In the observation of turbidity current, this is considered as the velocity of turbidity current.

4.6 Analysis of sediment movement in submarine canyons based on the WSS-PFP model

For a submarine canyon filled with sediments, the sediments are in a relatively stable state. When there is sediment flow into the head of the canyon (upstream side), aggradation will occur, and the incoming sediment will be deposited on the upstream side of the canyon within its dynamic capacity. At this time, the sediment bed may be stable. When the process of sediment accretion occurs again, the slope of the upper part of the submarine canyon increases because of deposition. At the same time, the aggraded sediment becomes a load on the original sediment. With the increases in slope and load, the sediment bed can experience shear failure, similar to that for the foundation or for a push-type landslide, and continues to develop downstream. Based on the trigger and development model of WSS-PFP, the movement process of sediment in a submarine canyon can be analyzed (Fig. 8).

Sediment transport in this model can be summarized in the following steps: "From top to bottom"—"Turbidite sediment cover"—"Gradually push forward". Specifically, "From top to bottom" suggests that the continuous source of sediment is the nearshore side, and the sediment gradually accumulates and moves to the deep-sea plain from the head of the canyon. "Turbidite sediment cover" indicates that the turbidity current observed after sediment damage (a turbidity current here refers to a fully turbulent sediment cloud with a low sediment concentration in the upper layer) in a submarine canyon bottom can extend far to the downstream side of the submarine canyon in a failure process, and the transported sediment gradually covers the surface of the canyon bottom bed. "Gradually push forward" means that the sediment entering the canyon is not influenced by a turbidity current process and gradually accumulates along the transport path, resulting in the gradual advance of terrigenous sediments into the deep sea until it reaches the deep-sea sedimentary plain. The movement process of sediment in a submarine canyon can provide guidance for the understanding of deep-sea turbidity current deposition and turbidity current observations.

4.7 Explanation of several phenomena observed in the field 4.7.1 Cable rupture caused by a turbidity current

Since the Grand Banks earthquake in 1929, there have been many cable rupture events caused by turbidity currents worldwide (Heezen and Ewing, 1952, 1955; Heezen et al., 1954; Krause et al., 1970; Piper et al., 1988; Gavey et al., 2017). Generally, the cables laid on the seabed, with densities much higher than that of the bottom sediment, will sink and be covered by continuously falling sediment, eventually becoming buried in the sediment at a certain depth. According to the current knowledge of the movement of turbidity currents, if a turbidity current only passes through the upper part of the sediment in a canyon, the force on the buried cable will be very small. If a turbidity current erodes the bottom bed, the erosion depth must be large and exceed the buried depth of the cable. The erosion of the bottom bed will consume the kinetic energy of the turbidity current, which will inevitably reduce its movement speed at the erosion position and weaken the force on the cable. In this way, it is difficult to explain the damage to submarine cables with the existing knowledge of turbidity current movement. Based on the WSS-PFP model, when the push failure of weakly stable seabed sediment occurs through some mechanism in the upstream part of a canyon, the downstream damage will produce a chain reaction. The movement of the damaged sediment downstream can drag the cable buried in it and cause the cable to fracture (Fig. 9a). In 2015, the 800-kg anchor system located on the bed of Monterey Canyon was pushed, and the downward movement of disrupted bottom sediments may have contributed to this process (Paull et al., 2018).

4.7.2 The movement speed of turbidity currents

The velocity of a turbidity current can be inferred from cable fracture information and is usually between 10 m/s and 20 m/s, potentially reaching 25 m/s and 28 m/s (Heezen and Ewing, 1952, 1955; Heezen et al., 1954; Krause et al., 1970; Piper et al., 1988; Gavey et al., 2017). According to the above test results, it is very doubtful that a single turbidity current can move at such a high speed (results of Test 3). According to the WSS-PFP model, the high velocity of a turbidity current is not the velocity of a single turbidity current moving along a submarine canyon but is the velocity of sediment destruction and propagation in the submarine canyon caused by the initial turbidity current, a triggering effect or the movement of weakly stable sediment in front of the current, which is driven by the generated excitation wave. The velocity of propagation is much higher than that of a single turbid fluid. Through field observations in 2016, it was found that the average velocity between two observation points was generally greater than the instantaneous velocity measured at one observation point (Heerema et al., 2020; Fig. 3a). In addition, the maximum instantaneous velocity measured in Monterey Canyon was close to 6 m/s (Paull et al., 2018; Heerema et al., 2020), which was the maximum internal instantaneous velocity measured by acoustic doppler current profilers (ADCPs) fixed on the bed. According to the WSS-PFP model, the instantaneous velocity may be associated with the resuspension of original sediment caused by the extrusion of the front soft sediment by the head of a turbidity current. The velocity of these suspended particles may be high but is not the velocity of the turbidity current itself.

5 CONCLUSION

Through experiments, the high velocity of turbidity currents in submarine canyons is examined and discussed. A single turbidity current cannot achieve a very high velocity in submarine canyons. The high velocities of turbidity currents obtained through inference or monitoring actually represent the speed of the propagation of damage in the weakly stable sediment on the seabed. Additionally, two failure modes for weakly stable sediments are proposed: a progressive failure propagation mode for sediments from top to bottom in a canyon and a failure propagation mode for weakly stable sediments caused by water waves.

(1) A settling test of high-concentration sedimentladen turbid water showed that even in the case of vertical settling, the velocity of a turbid fluid body in water does not reach 1 m/s when the density of the turbid fluid is 1 720 g/L. The velocity of a turbidity current moving along a submarine canyon is higher than that of a pure turbidity current (original turbidity current).

(2) The sediment on the bed of submarine canyons is in a weakly stable state. When the upper part of a canyon (upstream portion of a canyon) is damaged by some event (landslide, turbidity current, etc.), the pushing damage spreads to the lower part of the canyon (downstream portion of the canyon). The propagation speed of the sediment in the canyon may be the turbidity current velocity inferred from submarine cable damage.

(3) When a turbidity current suddenly enters a submarine canyon, an excitation wave appears in front of the turbidity current and exerts force on the sediment bed, and the propagation speed of this wave is faster than that of the turbidity current. When the excitation wave moves downward along the canyon, it can lead to the resuspension and destabilization of weakly stable sediment at the bottom of the canyon.

The high velocity of turbidity currents can be well explained by using the theory of damage propagation in weakly stable sediments in submarine canyons. Sediment resuspension occurs when sediment damage occurs at the bottom of a canyon, and turbidity cells composed of resuspended sediment and water can form the turbidity currents observed in the field. Therefore, turbidity currents can travel long distances at high speeds in submarine canyons, as noted by many researchers, and are caused by the destabilization of weakly stable sediment in submarine canyons. In the future, we should perform further work on the validation and application of the model proposed in this paper. Furthermore, the establishment of this model can provide a new research perspective for marine sediment transport and assessments of the sediment structure of seabed strata.

6 DATA AVAILABILITY STATEMENT

The datasets generated and/or analyzed during the current study are available from the corresponding author upon reasonable request.

7 ACKNOWLEDGMENT

We thank Hanru WU from Ocean University of China for his help in thesis writing, and Hao TIAN and Chenxi WANG from Ocean University of China for their helps in the preparation of the experimental materials. Guohui XU is responsible for the development of the initial concept, processing of test data, and management of coauthor contributions to the paper; Yupeng REN for the experiment setup and drafting of the paper; Yi ZHANG and Xingbei XU for the simulation part of the experiment; Houjie WANG for writing guidance; Zhiyuan CHEN for the experiment setup.