## 4 Conclusions  
This paper evaluates the numerical results of the rke model and the sst model on the dynamic characteristics of deep-sea hydrothermal plume in the Longqi hydrothermal field. The calculated results are compared with the CTD 05-2 observation data, [PERSON]'s results and [PERSON]'s results. Therefore, the following conclusions can be drawn.  
The turbulent viscosity obtained by the rke model is larger than that obtained by the sst model, and its trend is closer to the reference. These results show that the rke model can predict the turbulent viscosity of hydrothermal plume more reasonably. Except for the difference in the turbulent kinetic energy at the horizontal diffusion, the maximum turbulent kinetic energy calculated by the two models is not much different, and the corresponding curves have a similar change trend. These results show that the rke model and the sst model have equivalent effect on the prediction of turbulent kinetic energy of hydrothermal plume. The high deviation of the sst model in predicting turbulent dissipation rate of neutral buoyant layer and its prediction results are not as accurate as those of the rke model.  
In the vertical velocity of the center line of the hydrothermal plume, the velocity of the RMS of the rke model is smaller than that of the sst model. This shows that the rke model can better predict the velocity of hydrothermal plume. Compared with the data of the CTD 05-2 observation station, the temperature of the RMS of the rke model is slightly larger than that of the sst model. But overall, both models calculate temperatures that are close to the observed data. Therefore, the rke model and the sst model can predict the hydro-thermal plume temperature in a similar way.  
The results of characteristic heights show that both the rke model and the sst model can predict macroscopical processes of hydrothermal plumes well. Overall, the two commonly used RANS models accurately capture the macroscopic physical characteristics of buoyancy plumes in stratified environments. But the rke model is more suitable for numerical study of hydrothermal plume than the sst model. At present, due to the lack of experimental data, it is impossible to compare the entrainment coefficient quantitatively. Observation and experiment should be required in the Longqi hydrothermal field in the future.  
Conceptualization, W.Z. ([PERSON]) and S.C.; methodology, [PERSON] ([PERSON]) and S.C.; software, [PERSON] ([PERSON]) and [PERSON] ([PERSON]); validation, W.Z. ([PERSON]), S.C. and J.Y.; formal analysis, S.C. and J.Y.; investigation, S.C.; resources, S.C. and J.Y.; data curation, W.Z. ([PERSON]) and S.C.; writing--original draft preparation, W.Z. ([PERSON]); writing--review and editing, W.Z. ([PERSON]), S.C. and J.Y.; project administration, S.C.; funding acquisition, S.C. and J.Y. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (42006167), Open Fund for Key Laboratory of Submarine Geoscience, Ministry of Natural Resources (KLSG2205), National Key Research and Development Program (2022 YFC2803903, 2022 YFC2803905) and Graduate Research and Innovation Fund of Hangzhou Dianzi University (CXJJ)2021064).  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** All data included in this study are available upon request by contact with the corresponding author.  
**Acknowledgments:** The authors would like to thank all the scientists and crew on the R/V \"DaYangYi Hao\" during Cruise DY30. Special thanks are extended to [PERSON] for his help in plume modelling technical assistance. The authors would like to thank the reviewers for valuable comments that helped to improve this manuscript.  
**Conflicts of Interest:** The authors declare no conflict of interest.