Surface Waves Induced by a Moving Submarine Model

Abstract

A moving submarine can generate internal waves, as well as extremely small free surface waves, in a fluid with density stratification. In this study, the internal and free surface wave wakes caused by a moving submarine in two layers of constant density fluid were studied numerically using the commercial software STAR-CCM+. The realizable k−ε turbulence model was used to solve the Reynolds-averaged Navier—Stokes equation, and the volume of the fluid method was used to monitor the fluctuations of the internal interface and free surface. Different cases of a moving submarine with different cruising speeds and relative diving depths were studied. Results showed that the maximum fluctuation amplitude of the free surface increased as the speed of the submarine increased; however, the maximum fluctuation amplitude of the internal interface first decreased and then increased. When the submarine moved at the maximum cruising speed, the maximum fluctuation amplitude of the free surface decreased as the diving depth increased, while the wavelength of the free surface wave was basically the same. If the submarine moved at the minimum cruising speed, then the wave elevation in the free surface was extremely small, but the internal surface had obviously large-amplitude internal waves, and the relative diving depth had a great influence on internal waves.

Keywords

Free surface wave / Internal wave / Submarine / Density stratification / Cruising speed / Relative diving depth

References

[1] Denner F, Wachem B. Compressive vof method with skewness correction to capture sharp interfaces on arbitrary meshes. Journal of Computational Physics, 2014, 279: 127-144

[2] Ding Y, Duan F, Han PP, Niu MC. Research on the relationship between moving patterns of submerged body and the features of induced internal waves in two layer fluid. Journal of Ship Mechanics, 2016, 20(5): 523-529 (in Chinese)

[3] Dong GH, Yao CB, Feng DK, Wang W, Tan Y. Study on drag performance of submarine in density stratified flow. Shipbuilding of China, 2022, 63(3): 11 (in Chinese)

[4] Faltinsen OM. Hydrodynamics of high-speed marine vehicles, 2006, Cambridge, New York: Cambridge University Press, 138-140

[5] Grue J, Friis HA, Palm E, Rusås PO. A method for computing unsteady fully nonlinear interfacial waves. Journal of Fluid Mechanics, 1997, 351: 223-252

[6] He GH, Liu S, Wang W, Pan YJ. The analysis of the influence of density stratification on the wave resistance of the submersible surface of the near water. Journal of Harbin Engineering University, 2021, 42(8): 1125-1132 (in Chinese)

[7] He GH, Liu S, Zhang ZG, Zhang W, Wang W, Gao Y, Pan YJ. Analysis on the wake of submarine navigating in deeper density layer. Journal of Harbin Institute of Technology, 2022, 54(1): 40-48 (in Chinese)

[8] Hu KY, Pan LM, Yu X, Yang ZC, Shi LF (2020) Numerical simulation of moving ellipsoidal wake field in stratified flow with hyocline. Proceedings of the 31st National Symposium on Hydrodynamics, Xiamen, 402–411. (in Chinese) DOI: https://doi.org/10.26914/c.cnkihy.2020.036988

[9] Huang FL, Cao LS, Wan DC (2020) Numerical simulation of complex flow field in submarine near surface navigation in continuous density stratified flow. Proceedings of the 31st National Symposium on Hydrodynamics, Xiamen, 857–870. (in Chinese) DOI: https://doi.org/10.26914/c.cnkihy.2020.037045

[10] Huang FL, Meng QJ, Cao LS, Wan DC. Wakes and free surface signatures of a generic submarine in the homogeneous and linearly stratified fluid. Ocean Engineering, 2022, 250: 111062

[11] Landau LD, Lifshitz EM. Fluid mechanics, 1959, Oxford, England: Pergamon Press, 35-37

[12] Li SQ, Xiao CR, Cao ZJ. Numerical analysis of wake flow and hydrodynamics for a submarine based on STAR-CCM+. Chinese Journal of Ship Research, 2018, 13(S1): 29-35 (in Chinese)

[13] Liu JF, Mao KX, Zhang XJ, Liang XY, Li Y. The general distribution characteristics of pycnocline of China Sea. Marine Forecasts, 2013, 30(6): 21-27 (in Chinese)

[14] Liu S, He GH, Wang W, Wang ZK, Luan ZX, Zhang ZG. Resistance and flow field of a submarine in a density stratified fluid. Ocean Engineering, 2020, 217(1): 107934

[15] Liu S, He GH, Wang W, Gao Y. Analysis on the wake of a shallow navigation submarine in the density-stratified fluid. Journal of Harbin Institute of Technology, 2021, 53(7): 52-59 (in Chinese)

[16] Liu S, He GH, Wang W, Gao Y. Effect of appendages on hydrodynamic characteristics of submarine in stratified fluid. Acta Armamentarii, 2021, 42(1): 108-117 (in Chinese)

[17] Liu S, He GH, Wang W, Pan YJ. Effect of density stratification on wave-making resistance of submarine navigating in deep-water. Journal of Harbin Engineering University, 2021, 42(9): 1373-1379 (in Chinese)

[18] Luo H, Chen K, You YX, Wei G (2007) The numerical simulation of interaction between free surface wake generated by a moving submerged body and stochastic ocean waves. Journal of Shanghai Jiao Tong University (9): 1435–1440. (in Chinese) DOI: https://doi.org/10.16183/j.cnki.jsjtu.2007.09.010

[19] Ma WZ, Li YB, Ding Y, Duan F, Hu KY. Numerical investigation of internal wave and free surface wave induced by the DARPA Suboff moving in a strongly stratified fluid. Ships and Offshore Structures, 2020, 15(6): 587-604

[20] Wang C, Du W, Li GH, Du P, Zhao S, Li ZY, Chen XP, Hu HB. Numerical simulation of underwater vehicle hydrodynamic characteristics influenced by ocean internal waves. Chinese Journal of Ship Research, 2022, 17(3): 102-111 (in Chinese)

[21] Wei G, Le JC, Dai SQ. Surface effects of internal wave generated by a moving source in a two-layer fluid of finite depth. Applied Mathematics and Mechanics, 2003, 24(9): 13

[22] Yeung RW, Nguyen TC. Waves generated by a moving source in a two-layer ocean of finite depth. Journal of Engineering Mathematics, 1999, 35: 85-107

[23] Yu X, Hu KY. Influence of submarine’s acceleration and deceleration on wake spectrum characteristics in stratified flow. Chinese Journal of Ship Research, 2022, 17(3): 67-77 101. (in Chinese)

[24] Zhang MN, Liu JF, Mao KX, Li Y, Zhang XH. The general distribution characteristics of thermocline of China Sea. Marine Forecasts, 2006, 23(4): 51-58 (in Chinese)

[25] Zhao BB, Zhang TY, Li LJ, Wang Z, Duan WY, Hayatdavoodi M (2022) Extension of MCC-FS model to bottom time-varying problems. The 37th International Workshop on Water Waves and Floating Bodies, Giardini Naxos, Italy, 190–193