Numerical Simulation-Based Analysis of Seafloor Hydrothermal Plumes: A Case Study of the Wocan-1 Hydrothermal Field, Carlsberg Ridge, Northwest Indian Ocean

<jats:p>Understanding the dynamics of deep-sea hydrothermal plumes and the depositional pattern of hydrothermal particles is essential for tracking the submarine hydrothermal venting site, prospecting polymetallic sulfide resources, as well as deciphering biogeochemistry cycling of marine elements. In this paper, a numerical model of the deep-sea hydrothermal plume is established based on the topography and long-term current monitoring data of the Wocan-1 hydrothermal field (WHF-1), Carlsberg Ridge, Northwest Indian Ocean. The model allows for a reconstruction of the hydrothermal plume in terms of its structure, velocity field, and temperature field. The relationships between the maximum height of the rising plume and the background current velocity, and between the height of the neutral-buoyancy layer and the background current velocity are established, respectively. The transport patterns of the hydrothermal particles and their controlling factors are revealed. Using hydrothermal particles with a density of ~5000 kg/m3 (i.e., pyrite grains) as an example, it is found that pyrite larger than 1 mm can only be found near the venting site. Those in the size 0.3–0.5 mm can only be found within 137–240 m from the venting site, while those smaller than 0.2 mm can be transported over long distances of more than 1 km. Using the vertical temperature profiling data of WHF-1 obtained during the Jiaolong submersible diving cruise in March 2017, we reconstruct the past current velocity of 10 cm/s, similar to the current data retrieved from the observational mooring system. Our model and the findings contribute to a better understanding of the hydrothermal system of WHF-1, and provide useful information for tracing the hydrothermal vents, prospecting the submarine polymetallic sulfide resources, designing the long-term observation networks, and relevant studies on element cycling and energy budget.</jats:p>

section_content: Since the first discovery of submarine hydrothermal vents along the East Pacific Galapagos Rift in 1977 [1], more than 700 hundred active hydrothermal fields have been discovered in the world's oceans [2]. Hydrothermal systems play a significant role in the cycling of energy and mass between the solid earth and the oceans [3] [4] [5]. Hydrothermal plumes form when high-temperature vent fluids are expelled into the cold and stratified oceanic water column, which represents a significant dispersal mechanism for chemicals and heat released from the seafloor to the oceans [6]. Metallic sulfide particles form when this hot metal-and H 2 S-rich, and highly reduced vent fluid mixes with cold, partially oxygenated ocean bottom water [7]. Detection of hydrothermal anomalies in the water column has been widely used to discover hydrothermal fields and associated polymetallic sulfide deposits [8] [9] [10] [11] [12]. 

Compared with on-site investigation and observations, the numerical simulation method, which can realize the quantitative description of the structure of a hydrothermal plume after the model of the hydrothermal plume flow field is established, has the unique advantage of cost-effectiveness and easy use. Morton et al. [13] first proposed the MTT analytical model to describe the transport and mixing process of buoyant plumes and presented an empirical formula for estimating the maximum rising height of plumes through buoyancy flux and buoyancy frequency. Lavelle et al. [14] were the first to use numerical models to study the transverse variation of plumes generated by line-source hydrothermal vents and the distribution of temperature and salinity anomalies, discovering backflow and vortex structures between the plume cap zone and the plume stem zone. Tao et al. [15] established a three-dimensional unsteady numerical model to study the evolution of plumes and found a correlation between the rising height of plumes and the transverse velocity, suggesting that the ratio of the neutral-buoyancy layer height to the maximum rising height of hydrothermal plumes can be used to estimate the heat flux of hydrothermal plumes. Lou et al. [16] took into consideration the interaction between two vent plumes and concluded that the maximum values of turbulent kinetic energy and turbulent dissipation rate decrease with the increase of the distance between the two vents and proposed an empirical formula for the maximum rising height of double-vent plumes. 

The numerical simulation has been applied in the study of submarine hydrothermal plumes. For instance, Jiang et al. [17] conducted a numerical simulation of plumes in the ABE hydrothermal field located in the Eastern Lau Spreading Center of the West Pacific. They found that the maximum values of turbulent kinetic energy and turbulent dissipation rate reach their maximum near the vent, while the maximum value of turbulent viscosity is near the plume top, which indicates the presence of strong turbulent mixing that affects chemical reactions and transport processes. Adams et al. [18] studied the turbulent mixing characteristics of high-temperature hydrothermal vent plumes and estimated the heat flux of the Dante sulfide mound on the Juan de Fuca Ridge in the northwest Pacific. Lou et al. [19, 20] studied the transport and sedimentation characteristics of particles driven by hydrothermal vent plumes in the Daxi hydrothermal field in the northwest Indian Ocean and classified particles of different sizes and densities. However, the existing numerical models were often established under ideal environmental conditions. In reality, a hydrothermal field usually has several to dozens of black smokers with complex terrain [21]. Ocean currents also change temporally in terms of speed and direction. Therefore, it is important to consider the interference of multiple hydrothermal vents and the variability of ocean currents while developing the numerical models for submarine hydrothermal plumes. 

The Wocan-1 hydrothermal field (WHF-1) (6 • 22 N, 60 • 31 E), discovered in 2013 by the Chinese DY28th cruise, is located on an axial volcanic ridge along the Carlsberg Ridge, at a water depth of ~3000 m [22, 23]. It covers an area of about 450 m × 400 m (Figure 1 ) [22], consisting of a high-temperature "Flaming Hill" area and a medium-temperature "Mulberry Forest" area [24]. In the high-temperature Flaming Hill area, approximately 60 black smokers were observed, with the measured temperatures of venting fluid reaching up to 359 • C [22, 25]. The Mulberry Forest area is located ~70 m to the northwest of the Flaming Hill area [25]. Four black smoker clusters were observed there, with the temperature ranging from 250 to 290 • C, according to the spherite geothermometer [22]. The hydrothermal plumes of the Wocan-1 are mainly observed at a water depth of 2750-2880 m. Figure 2 shows the section where "Flaming Hill" area and "Mulberry Forest" area are located. In this paper, we use a numerical simulation method to construct a three-dimensio model of the hydrothermal plume from WHF-1, with the aim of understanding the namics of the hydrothermal plume, the transport law of hydrothermal sulfide particula and its controlling factors. The model is built based on the topography of WHF-1, occurrence and features of black smokers, as well as the measured variability of oce current velocity. Our results provide theoretical guidance and a scientific basis for the terpretation of hydrothermal anomalies detected in the water column and in the se ments, which could provide important clues on the discovery of unknown active hyd thermal vents. 

Figure 2. Variation of water depths along the section AA' crossing WHF-1 as shown in Figure 1 2. Methods In this paper, we use a numerical simulation method to construct a three-dimensional model of the hydrothermal plume from WHF-1, with the aim of understanding the dynamics of the hydrothermal plume, the transport law of hydrothermal sulfide particulates, and its controlling factors. The model is built based on the topography of WHF-1, the occurrence and features of black smokers, as well as the measured variability of ocean current velocity. Our results provide theoretical guidance and a scientific basis for the interpretation of hydrothermal anomalies detected in the water column and in the sediments, which could provide important clues on the discovery of unknown active hydrothermal vents.
section_name: Introduction

section_name: Numerical Simulation Method and Model

section_name: Methods

section_content: We built a three-dimensional numerical model based on the actual topography of the WHF-1. In order to enhance calculation accuracy and simulation precision, the fluid domain volume method (VOF) and the separated flow model are employed. The Realizable K-epsilon two-layer turbulence model is adopted as the turbulence model [26, 27]. In this paper, we use a numerical simulation method to construct a three-dimensional model of the hydrothermal plume from WHF-1, with the aim of understanding the dynamics of the hydrothermal plume, the transport law of hydrothermal sulfide particulates, and its controlling factors. The model is built based on the topography of WHF-1, the occurrence and features of black smokers, as well as the measured variability of ocean current velocity. Our results provide theoretical guidance and a scientific basis for the interpretation of hydrothermal anomalies detected in the water column and in the sediments, which could provide important clues on the discovery of unknown active hydrothermal vents.
section_name: Numerical Simulation Method and Model

section_content: We built a three-dimensional numerical model based on the actual topography of the WHF-1. In order to enhance calculation accuracy and simulation precision, the fluid domain volume method (VOF) and the separated flow model are employed. The Realizable K-epsilon two-layer turbulence model is adopted as the turbulence model [26, 27]. Additionally, the Lagrange multiphase and multiphase interaction are integrated into the model to account for the transport of particles in the plume [28]. 

A section AA' crossing the active venting sites of WHF-1 was selected as the geometric model for simulation (Figure 1b ). According to the topography of section AA', it is simplified into a mound with a height of 50 m and a radius of 220 m at the base. To balance computational efficiency and accuracy, the two black smoker clusters found along the section, i. e., the Flaming Hill area and the Mulberry Forest area, are treated as one composite venting site, respectively. The length of the model is set to 2000 m and its height and width are set to 400 m and 200 m, respectively, according to the actual size of WHF-1 and the height of the hydrothermal plume detected in this area. The model is divided via a mesher with a basic size of 1 m. The grid size in the vent area is refined to 0. 05 m while that in the rising area of the vent to 0. 2 m. Figure 3 illustrates the specific refinement of the whole computational domain grid and the vent area grid. The overall model comprises 7,863,395 squares, including 23,581,668 planes and 8,685,514 points. 

Additionally, the Lagrange multiphase and multiphase interaction are integrated into the model to account for the transport of particles in the plume [28]. 

A section AA' crossing the active venting sites of WHF-1 was selected as the geometric model for simulation (Figure 1b ). According to the topography of section AA', it is simplified into a mound with a height of 50 m and a radius of 220 m at the base. To balance computational efficiency and accuracy, the two black smoker clusters found along the section, i. e., the Flaming Hill area and the Mulberry Forest area, are treated as one composite venting site, respectively. The length of the model is set to 2000 m and its height and width are set to 400 m and 200 m, respectively, according to the actual size of WHF-1 and the height of the hydrothermal plume detected in this area. The model is divided via a mesher with a basic size of 1 m. The grid size in the vent area is refined to 0. 05 m while that in the rising area of the vent to 0. 2 m. Figure 3 illustrates the specific refinement of the whole computational domain grid and the vent area grid. The overall model comprises 7,863,395 squares, including 23,581,668 planes and 8,685,514 points.
section_name: Numerical Simulation Method and Model

section_content: The parameters of the numerical model were set based on the measured data of the WHF-1 collected during our various cruises (Tables 1 and 2 ). Specifically, the data of the background temperature field and density field required by the model were obtained during the Chinese DY57th cruise. According to the CTD profiling, the temperature measured in the water depth of 3000 m was 1. 535 °C and 1. 907 °C in the water depth of 2600 m, with a temperature gradient of 0. 0093 °C/m and a density gradient of 0. 00463 kg/m. The occurrence and features of black smokers were obtained based on geological mapping conducted by the Jiaolong submersible during the Chinese DY38th cruise [22]. The temperature of the vent fluids in the Flaming Hill area was 359 °C according to the measurement, while that in the Mulberry Forest area was 250 °C according to the mineralogy of the sulfide chimney [25]. The vent flow rates were calculated through image simulation based on captured images of video [29], which were determined to be 20 cm/s and 15 cm/s for the Flaming Hill area and Mulberry Forest area, respectively. The background ocean current data were obtained from the long-term observation of a mooring system deployed at 1000 m south to the WHF-1 (station 49V-ST01) (Figure 1a ) [30], the main direction of the background current being northwest-southeast, which is consistent with the trend of the
section_name: Parameter Settings of the Numerical Model

section_content: The parameters of the numerical model were set based on the measured data of the WHF-1 collected during our various cruises (Tables 1 and 2 ). Specifically, the data of the background temperature field and density field required by the model were obtained during the Chinese DY57th cruise. According to the CTD profiling, the temperature measured in the water depth of 3000 m was 1. 535 • C and 1. 907 • C in the water depth of 2600 m, with a temperature gradient of 0. 0093 • C/m and a density gradient of 0. 00463 kg/m. The occurrence and features of black smokers were obtained based on geological mapping conducted by the Jiaolong submersible during the Chinese DY38th cruise [22]. The temperature of the vent fluids in the Flaming Hill area was 359 • C according to the measurement, while that in the Mulberry Forest area was 250 • C according to the mineralogy of the sulfide chimney [25]. The vent flow rates were calculated through image simulation based on captured images of video [29], which were determined to be 20 cm/s and 15 cm/s for the Flaming Hill area and Mulberry Forest area, respectively. The background ocean current data were obtained from the long-term observation of a mooring system deployed at 1000 m south to the WHF-1 (station 49V-ST01) (Figure 1a ) [30], the main direction of the background current being northwest-southeast, which is consistent with the trend of the selected section AA'. The range of current velocity varied from 0. 07 to 23 cm/s, dominated by 2 to 10 cm/s, with an average of 6. 7 cm/s. Accordingly, four sets of background current velocities: 0 (no background current), 2 cm/s (minimum), 6 cm/s (average), and 10 cm/s (maximum) were used for the comparison study. T exit represents the temperature of hydrothermal fluid, T bottom represents the temperature of background seawater at the bottom, T top represents the temperature of background seawater at the top, R represents the equivalent radius of the venting orifice, v represents the velocity of venting fluid flow.
section_name: Parameter Settings of the Numerical Model

section_name: Results

section_content: As illustrated in Figure 4a, in the absence of a background current, the plume rises and expands to form a cone-shaped plume stem, reaching a maximum height of 315. 1 m before forming a plume cap and eventually being transported horizontally. The height of the neutral-buoyancy layer reaches 255 m, which is 80. 9% of the former and close to the theoretical value of 76. 1%, based on the MTT integral model [12]. When a background current velocity of 2 cm/s is introduced (Figure 4b ), the overall structure of the plume is clearly shown and the maximum rise height is 312. 9 m. However, there is a presence of background current that results in a slight bending (3 • ) of the plume axis. If the background current velocity increases to 6 cm/s (Figure 4c ), the plume structure is still discernible, but the enhanced current causes more significant bending, with the central axis of the plume bending by 12 • and the maximum rise height of the plume reduced considerably to 287. 0 m. When the background current velocity is increased to 10 cm/s (Figure 4d ), the plume is characterized by turbulent mixing with no distinct rebound current feature at the top. The buoyancy plume structure is disrupted and the maximum rise height is reduced to 134. 6 m, which is less than half of the height observed under no current conditions. Overall, increasing the background current velocity would cause the plume structure to bend more, which facilitates the diffusion and mixing of the plume with the ambient water and enhances its horizontal transport capacity.
section_name: Plume Structure

section_content: Figure 5 shows the steady-state velocity field of the plume obtained from the numerical model. In the condition of no background current, the rising part of the plume can be divided into three intervals. In the interval of 50-180 m, the plume velocity field is coneshaped, with the velocity ranging from 1 m/s to 1. 62 m/s. The maximum velocity occurs at a height of 70 m. In this interval, the plume and the ambient water undergo continuous entrainment, with similar velocities observed at different heights. In the interval of 180-300 m, the plume velocity field is columnar shaped, with the velocity ranging from 0. 33 m/s to 1 m/s. It shows a decreasing trend from the inner part to the outer part. A vortex structure can also be observed between the rising part of the plume and the buoyancy layer. In the interval from the upper part of the plume to the maximum rise height, the buoyancy plume rises and then falls back, and the velocity decreases to zero at the top, coiling and sucking toward the inside of the plume at the boundary and forming a neutralbuoyancy layer with a thickness of 30 m at 60 m away from the center of the plume and eventually diffusing horizontally near the neutral-buoyancy layer. With the background ocean current increasing from 2 cm/s to 6 cm/s, the plume deformed with lower rising height but the plume structure is still clear. When the ocean current increases to 10 cm/s, the plume is well mixed with the ambient water that the structure of the plume is hardly seen.
section_name: Velocity Field of Hydrothermal Plumes

section_content: Figure 5 shows the steady-state velocity field of the plume obtained from the numerical model. In the condition of no background current, the rising part of the plume can be divided into three intervals. In the interval of 50-180 m, the plume velocity field is cone-shaped, with the velocity ranging from 1 m/s to 1. 62 m/s. The maximum velocity occurs at a height of 70 m. In this interval, the plume and the ambient water undergo continuous entrainment, with similar velocities observed at different heights. In the interval of 180-300 m, the plume velocity field is columnar shaped, with the velocity ranging from 0. 33 m/s to 1 m/s. It shows a decreasing trend from the inner part to the outer part. A vortex structure can also be observed between the rising part of the plume and the buoyancy layer. In the interval from the upper part of the plume to the maximum rise height, the buoyancy plume rises and then falls back, and the velocity decreases to zero at the top, coiling and sucking toward the inside of the plume at the boundary and forming a neutral-buoyancy layer with a thickness of 30 m at 60 m away from the center of the plume and eventually diffusing horizontally near the neutral-buoyancy layer. With the background ocean current increasing from 2 cm/s to 6 cm/s, the plume deformed with lower rising height but the plume structure is still clear. When the ocean current increases to 10 cm/s, the plume is well mixed with the ambient water that the structure of the plume is hardly seen.
section_name: Velocity Field of Hydrothermal Plumes

section_content: Figure 6 shows that in the absence of background current, the temperature at the centerline of the plume drops from 360 • C at the orifice to 219 • C at 0. 5 m above the orifice, 11. 4 • C at 20 m, and 2 • C at 86 m, respectively. When the background current velocities increase to 2 cm/s (Figure 6b ), 6 cm/s (Figure 6c ), and 10 cm/s (Figure 6d ), respectively, the corresponding temperature at the axis of the plume (using the curved centerline as the axis) decreases to 2 • C at 89. 4 m, 18. 1 m, and 10. 3 m above the orifice of black smokers, respectively.
section_name: Temperature Field of Hydrothermal Plumes

section_content: Figure 6 shows that in the absence of background current, the temperature at the centerline of the plume drops from 360 °C at the orifice to 219 °C at 0. 5 m above the orifice, 11. 4 °C at 20 m, and 2 °C at 86 m, respectively. When the background current velocities increase to 2 cm/s (Figure 6b ), 6 cm/s (Figure 6c ), and 10 cm/s (Figure 6d ), respectively, the corresponding temperature at the axis of the plume (using the curved centerline as the axis) decreases to 2 °C at 89. 4 m, 18. 1 m, and 10. 3 m above the orifice of black smokers, respectively.
section_name: Temperature Field of Hydrothermal Plumes

section_name: Discussion

section_content: The structure of hydrothermal plumes is mainly affected by the physical properties and velocities of the background ocean current and the fluid ejected from the hydrother-
section_name: Relationship between Plume Height and Background Current Velocity

section_content: The structure of hydrothermal plumes is mainly affected by the physical properties and velocities of the background ocean current and the fluid ejected from the hydrothermal vents. For a certain hydrothermal field on the seafloor of an open ocean, ocean current velocity is a major variant compared to the other variants such as temperature, salinity and density of the background seawater. Understanding the relationship between the height of a rising plume and the background current velocity is not only important for the design of instrumentation for hydrothermal plume survey in order to detect the hydrothermal anomalies successfully, but also important for the prediction of unknown hydrothermal venting site. Using our numerical model, we extracted the data of the maximum height of the plume and the height of the neutral-buoyancy layer under various background ocean current velocities. Here, the maximum height of the plume is defined as the height at which the vertical velocity of the plume axis is zero, and the height of the neutral-buoyancy layer is the layer where the density of the plume axis first equals that of the environment. Two empirical formulas are obtained via Polynomial Fitting of the results and illustrated in Figure 7 :

Z max = 315. 1 -1. 252v + 0. 4v 2 -0. 162v 3, ( 1 )

where Z max represents the maximum height of a plume, and v is the background current velocity. especially when the background current velocity is <6 cm/s. This suggests that the height of the neutral-buoyancy layer is more insensitive to the variation of background ocean current intensity compared to the maximum height of the plume.
section_name: Relationship between Plume Height and Background Current Velocity

section_content: The temperature anomaly of the hydrothermal plumes is mainly controlled by the extent of mixing of the hydrothermal fluid with the ambient seawater [31]. The temperature gradients between the hydrothermal plume and the ambient seawater decrease dramatically with increasing distance to the venting site. The reported temperature anomalies of hydrothermal plumes detected mostly vary between 0. 005 °C and 0. 05 °C, and those near the vent area can reach 0. 4 °C or higher. Using the temperature anomaly data, it is possible to infer the current velocity of the region by numerical simulation in case no current observation data is available. Here, we use CTD data (38I-CR-CTD-JL125) obtained by the Jiaolong submersible within the Wocan-1 hydrothermal field to conduct an inver- Figure 7 shows clearly that with the increase of background current velocity, both the maximum height and the height of the neutral-buoyancy layer of the plume decrease to some extent. However, the overall influence of background current velocity on the height of the neutral-buoyancy layer is smaller than that of the maximum height of the plume, especially when the background current velocity is <6 cm/s. This suggests that the height of the neutral-buoyancy layer is more insensitive to the variation of background ocean current intensity compared to the maximum height of the plume.
section_name: Reconstruction of Background Current Velocity

section_content: The temperature anomaly of the hydrothermal plumes is mainly controlled by the extent of mixing of the hydrothermal fluid with the ambient seawater [31]. The temperature gradients between the hydrothermal plume and the ambient seawater decrease dramatically with increasing distance to the venting site. The reported temperature anomalies of hydrothermal plumes detected mostly vary between 0. 005 • C and 0. 05 • C, and those near the vent area can reach 0. 4 • C or higher. Using the temperature anomaly data, it is possible to infer the current velocity of the region by numerical simulation in case no current observation data is available. Here, we use CTD data (38I-CR-CTD-JL125) obtained by the Jiaolong submersible within the Wocan-1 hydrothermal field to conduct an inversion study of the background current velocity and test the robustness of our model. A significant temperature anomaly was observed in the water depth between 2930-2960 m about 20 m from the high-temperature black smoker in Flaming Hill, with the maximum temperature anomaly of 1. 65 • C at the water depth of 2945 m. Figure 8 compares the measured temperature profile on site and the temperature profiles extracted from our numerical model at the same location under different ocean current velocities. It is clear that in the absence of a background current, no significant temperature anomaly can be observed. With the increasing background ocean current, the temperature anomaly becomes stronger, the neutral-buoyant layer becomes thinner and lower. Specifically, when the background current is 2 cm/s, a temperature anomaly is observed in the water depth of 2750-2880 m, with the maximum temperature anomaly of 0. 15 • C at 2850 m. When the background current velocity increases to 6 cm/s, a stronger temperature anomaly can be observed in the water depth between 2850-2930 m, with the maximum temperature anomaly of 0. 46 • C at 2907 m. When the ocean current is 10 cm/s, a strong temperature anomaly is seen in the water depth between 2938-2943 m, with a maximum of 1. 36 • C at 2940 m. This case fits the CTD profile very well. The mooring system deployed at 300 m south to the WHF-1 (station 49V-ST02) registered the ocean current velocities vary from 0-24 cm/s, dominated by 3. 5-11 cm/s, with a mean value of about 9 cm/s, indicating that the reconstructed background current velocity agrees well with the on-site observation. This also suggests that our numerical model is robust. Note, there is some offset with depth between our observed data and the computational outcome, this could be originated from the different environment between the location of CTD measurements and the location of the temperature field extracted from the 3D numerical model. is seen in the water depth between 2938-2943 m, with a maximum of 1. 36 °C at 2940 m. This case fits the CTD profile very well. The mooring system deployed at 300 m south to the WHF-1 (station 49V-ST02) registered the ocean current velocities vary from 0-24 cm/s, dominated by 3. 5-11 cm/s, with a mean value of about 9 cm/s, indicating that the reconstructed background current velocity agrees well with the on-site observation. This also suggests that our numerical model is robust. Note, there is some offset with depth between our observed data and the computational outcome, this could be originated from the different environment between the location of CTD measurements and the location of the temperature field extracted from the 3D numerical model.
section_name: Reconstruction of Background Current Velocity

section_content: When the high-temperature metal-and H 2 S-rich hydrothermal fluid is ejected from the black smoker, the rapid changes in temperature and redox conditions result in the formation of sulfide mineral particles in the plume. The settling of hydrothermal particles laden in the hydrothermal plumes would accumulate to form metalliferous sediments in the near field [32], which can be used as a good indicator for the prospecting and exploration of hydrothermal sulfide deposits [33]. Numerical simulation has the advantage to conduct quantitative analysis of the depositional patterns of hydrothermal particles with different physical properties. The background current velocity is set to 10 cm/s according to the dominant frequency of the current velocity in the study area. Considering the morphology, mineralogy, and geochemical characteristics of WHF-1 [34, 35], and the fact that pyrite is the most common hydrothermal sulfide mineral [36], we investigate the transport behavior of pyrite particles of various sizes in the plume. The density of pyrite particles is set to 5000 kg/m 3, and the sizes of pyrite particles are set at 50 µm, 200 µm, 300 µm, 400 µm, 500 µm, and 1000 µm, respectively, based on the results of field surveys. 

Figure 9 shows the transport trajectories of pyrite particles in the plume field. Pyrite particles with a size smaller than 200 µm are strongly influenced by the background current and can be transported at a height of 160 m over a distance of more than 1 km. Particle sizes ranging from 300 to 500 µm can rise to 124-161 m but only can migrate a short distance not farther than 240 m. Specifically, a 300 µm size particle can be transported as far as 240 m, a 400 µm particle can be transported to 198 m, and a 500 µm particle can be transported to 137 m. Particles >1000 µm cannot rise and be transported by the plume. sizes ranging from 300 to 500 µm can rise to 124-161 m but only can migrate a short distance not farther than 240 m. Specifically, a 300 µm size particle can be transported as far as 240 m, a 400 µm particle can be transported to 198 m, and a 500 µm particle can be transported to 137 m. Particles >1000 µm cannot rise and be transported by the plume. Lou et al. [19] did the numerical modeling for the hydrothermal plume of the Daxi hydrothermal field (~62 km northwest to WHF-1) and investigated the depositional pattern of ferrous disulfide particles (density of 5020 kg/m 3 ). The difference between the two studies is that the temperature of the black smoker of Daxi is 300 and WHF-1 is 360. In addition, this study also considers the potential interference of topography on the background current and particle deposition. They found that under a background current of 2 cm/s, particles with a size of 50 µm can participate in long-distance transport. Particles with a size of 100µm will deposit within 760. 41 m from the vent, and particles with a size larger than 200 µm cannot be transported. If the background current increase to 5 cm/s, particles with a size of 100 µm can be transported farther to 826. 45 m, the particles with a size of 200 µm can be transported as far as 584. 40 m from the vent, while the particles with a size larger than 500 µm cannot be transported but suspended above the vent and eventually settled near the venting site. 

The deposition of particles under different environmental conditions exhibits distinct patterns: (1) The transportation distance of hydrothermal particles such as pyrite decreases with the increase of particle size under a certain background current velocity. The increase of background current velocity facilitates the particle to transport a longer distance; (2) Under the conditions of this study, i. e., hotter temperature and stronger background current than the study of Lou et al. [19], a wider range of particle sizes can participate in medium-to long-distance transport. Particles within 200 µm are more likely to be transported over a long distance of 1 km, and particles with a size of 500 µm can also be Lou et al. [19] did the numerical modeling for the hydrothermal plume of the Daxi hydrothermal field (~62 km northwest to WHF-1) and investigated the depositional pattern of ferrous disulfide particles (density of 5020 kg/m 3 ). The difference between the two studies is that the temperature of the black smoker of Daxi is 300 and WHF-1 is 360. In addition, this study also considers the potential interference of topography on the background current and particle deposition. They found that under a background current of 2 cm/s, particles with a size of 50 µm can participate in long-distance transport. Particles with a size of 100 µm will deposit within 760. 41 m from the vent, and particles with a size larger than 200 µm cannot be transported. If the background current increase to 5 cm/s, particles with a size of 100 µm can be transported farther to 826. 45 m, the particles with a size of 200 µm can be transported as far as 584. 40 m from the vent, while the particles with a size larger than 500 µm cannot be transported but suspended above the vent and eventually settled near the venting site. 

The deposition of particles under different environmental conditions exhibits distinct patterns: (1) The transportation distance of hydrothermal particles such as pyrite decreases with the increase of particle size under a certain background current velocity. The increase of background current velocity facilitates the particle to transport a longer distance; (2) Under the conditions of this study, i. e., hotter temperature and stronger background current than the study of Lou et al. [19], a wider range of particle sizes can participate in medium-to long-distance transport. Particles within 200 µm are more likely to be transported over a long distance of 1 km, and particles with a size of 500 µm can also be transported and deposited to a region more than 100 m from the vent; (3) The topography of the mound in our model produces stronger turbulent mixing near the bottom, which affects the transport capacity of particles as well, especially for the particles larger than 300 µm. In this regard, Walker et al. [37] also observed that particles along the slope are more active and continuous in the real environment.
section_name: Transport Pattern of Plume Particles and the Controlling Factors

section_name: Conclusions

section_content: In this study, we build a three-dimensional numerical model of a submarine hydrothermal plume using the field observation data collected in the Wocan-1 Hydrothermal field. The results lead to the following conclusions: The structure of the plume consists of a cone-shaped rising zone, columnar-shaped rising zone, and neutral-buoyancy layer. Background ocean current alters the structure of the plume, causing its bending and increasing of diffusion capacity. The bending angle of the plume axis is positively correlated with the background current velocity. The plume structure would damage when the current velocity would be larger than 10 cm/s. 2. 

An increase in background current velocity significantly reduces the maximum rise height and a neutral-buoyancy layer height of the plume. Two empirical formulas are established to describe the Wocan-1 hydrothermal plume: the maximum rise height Z max = 315. 1 -1. 252v + 0. 4v 2 -0. 162v 3, and the neutral-buoyancy layer height Z neutral = 255 -0. 016v + 0. 245v 2 -0. 112v 3.
section_name: 1.

section_content: Using the temperature anomaly profile obtained by on-site CTD measurement near the flaming hill of WHF-1, by fitting the temperature profile extracted from our numerical model, the background current velocity of 10 cm/s is reconstructed, which is within the dominant range of ocean current velocities registered by the long-term observational mooring system deployed near the WHF-1. This also attests to the robustness of our model.
section_name: 3.

section_content: Under the background current velocity of 10 cm/s, the pyrite grains smaller than 2 mm can be transported over 1 km by the high-temperature black smokers from the flaming hill of WHF-1, those between 3 mm and 5 mm would deposit within 137-240 m from the venting site, while particles larger than 10 mm cannot be transported with the plume and deposit near the venting site. 

Overall, this study complements the existing numerical models of hydrothermal plumes by considering the influence of strong background current and complex topography. The 3D structure of the hydrothermal plumes and the depositional patterns of pyrite obtained in this study provide an important basis for relevant studies on the sediments from the near field and far field of the Wocan-1 hydrothermal field. Besides, our model demonstrates the application potential for data interpretation during hydrothermal plume searching and hydrothermal sulfide resource prospecting elsewhere.
section_name: 4.

section_name: Acknowledgments:

section_content: We would like to thank Zhiguo He and Yingzhong Lou for their assistance in the technical aspects of modeling. We would also like to thank the editor and the anonymous reviewers for their valuable comments and suggestions.
section_name: Acknowledgments:

section_content: Funding: This study was funded by the National Key Research and Development Program of China ( 2021YFF0501304 ), the National Natural Science Foundation of China (No. 91951201, No. 41976076, No. 19151201 ), and the China Ocean Mineral Resources R&D Association Project ( DY135-S2-1 ), and the Talent Program of Zhejiang Province (grant no. 2018R51003 ). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable.

section_content: Data Availability Statement: Not applicable.

section_name: Conflicts of Interest:

section_content: Author Contributions: Conceptualization, X. H. ; methodology, X. H. and K. W. ; modeling, K. W. ; investigation, X. H., Y. W., Z. Q., Y. C. and X. Z. ; writing-K. W. and X. H. ; visualization, K. W. ; supervision, X. H. ; project administration, X. H. All authors have read and agreed to the published version of the manuscript.

section_content: The authors declare no conflict of interest.
section_name: Conflicts of Interest: