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Internal solitary waves generated by a moving bottom disturbance

Published online by Cambridge University Press:  22 May 2023

Binbin Zhao Open the ORCID record for Binbin Zhao [Opens in a new window] ,
Tianyu Zhang ,
Wenyang Duan ,
Zhan Wang Open the ORCID record for Zhan Wang [Opens in a new window] ,
Xinyu Guo ,
Masoud Hayatdavoodi Open the ORCID record for Masoud Hayatdavoodi [Opens in a new window]  and
R. Cengiz Ertekin Open the ORCID record for R. Cengiz Ertekin [Opens in a new window]
Binbin Zhao
Affiliation:
College of Shipbuilding Engineering, Harbin Engineering University, 150001 Harbin, PR China
Tianyu Zhang
Affiliation:
College of Shipbuilding Engineering, Harbin Engineering University, 150001 Harbin, PR China
Wenyang Duan
Affiliation:
College of Shipbuilding Engineering, Harbin Engineering University, 150001 Harbin, PR China
Zhan Wang*
Affiliation:
College of Shipbuilding Engineering, Harbin Engineering University, 150001 Harbin, PR China Qingdao Innovation and Development Center of Harbin Engineering University, 266000 Qingdao, PR China
Xinyu Guo
Affiliation:
College of Shipbuilding Engineering, Harbin Engineering University, 150001 Harbin, PR China
Masoud Hayatdavoodi
Affiliation:
College of Shipbuilding Engineering, Harbin Engineering University, 150001 Harbin, PR China Civil Engineering Department, School of Science and Engineering, University of Dundee, Dundee DD1 4HN, UK
R. Cengiz Ertekin
Affiliation:
College of Shipbuilding Engineering, Harbin Engineering University, 150001 Harbin, PR China Department of Ocean & Resources Engineering, University of Hawai'i, Honolulu, HI 96822, USA
*
†Email address for correspondence: zhan.wang@hrbeu.edu.cn
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Abstract

The strongly nonlinear Miyata–Choi–Camassa model under the rigid lid approximation (MCC-RL model) can describe accurately the dynamics of large-amplitude internal waves in a two-layer fluid system for shallow configurations. In this paper, we apply the MCC-RL model to study the internal waves generated by a moving body on the bottom. For the case of the moving body speed $U=1.1c_{0}$, where ${c_0}$ is the linear long-wave speed, the accuracy of the MCC-RL results is assessed by comparing with Euler's solutions, and very good agreement is observed. It is found that when the moving body speed increases from $U=0.8c_{0}$ to $U=1.241c_{0}$, the amplitudes of the generated internal solitary waves in front of the moving body become larger. However, a critical moving body speed is found between $U=1.241c_{0}$ and $U=1.242c_{0}$. After exceeding this critical speed, only one internal wave right above the body is generated. When the moving body speed increases from $U=1.242c_{0}$ to $U=1.5c_{0}$, the amplitudes of the internal waves become smaller.

JFM classification

Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Stratified flows Waves/Free-surface Flows: Solitary waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 963 , 25 May 2023 , A32
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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References

Barros, R., Choi, W. & Milewski, P.A. 2020 Strongly nonlinear effects on internal solitary waves in three-layer flows. J. Fluid Mech. 883, A16.CrossRefGoogle Scholar
Barros, R. & Gavrilyuk, S. 2007 Dispersive nonlinear waves in two-layer flows with free surface. Part II. Large amplitude solitary waves embedded into the continuous spectrum. Stud. Appl. Maths 119 (3), 213–251.CrossRefGoogle Scholar
Benjamin, T.B. 1966 Internal waves of finite amplitude and permanent form. J. Fluid Mech. 25 (2), 241–270.CrossRefGoogle Scholar
Brizuela, N., Filonov, A. & Alford, M.H. 2019 Internal tsunami waves transport sediment released by underwater landslides. Sci. Rep. 9, 10775.CrossRefGoogle ScholarPubMed
Camassa, R., Choi, W., Michallet, H., Rusas, P.O. & Sveen, J.K. 2006 On the realm of validity of strongly nonlinear asymptotic approximations for internal waves. J. Fluid Mech. 549, 1–23.CrossRefGoogle Scholar
Choi, W. 2000 Modeling of strongly nonlinear internal gravity waves. In Proceedings of the Fourth International Conference on Hydrodynamics (ed. Y. Goda, M. Ikehata & K. Suzuki), pp. 453–458. ICHD2000.Google Scholar
Choi, W. 2022 High-order strongly nonlinear long wave approximation and solitary wave solution. J. Fluid Mech. 945, A15.CrossRefGoogle Scholar
Choi, W., Barros, R. & Jo, T. 2009 A regularized model for strongly nonlinear internal solitary waves. J. Fluid Mech. 629, 73–85.CrossRefGoogle Scholar
Choi, W. & Camassa, R. 1996 Weakly nonlinear internal waves in a two-fluid system. J. Fluid Mech. 313, 83–103.CrossRefGoogle Scholar
Choi, W. & Camassa, R. 1999 Fully nonlinear internal waves in a two-fluid system. J. Fluid Mech. 396, 1–36.CrossRefGoogle Scholar
Choi, W., Zhi, C. & Barros, R. 2020 High-order unidirectional model with adjusted coefficients for large-amplitude long internal waves. Ocean Model. 151, 101643.CrossRefGoogle Scholar
Duan, W.Y., Wang, Z., Zhao, B.B., Ertekin, R.C. & Kim, J.W. 2018 Steady solution of the velocity field of steep solitary waves. Appl. Ocean Res. 73, 70–79.CrossRefGoogle Scholar
Duchêne, V., Israwi, S. & Talhouk, R. 2016 A new class of two-layer Green–Naghdi systems with improved frequency dispersion. Stud. Appl. Maths 137 (3), 356–415.CrossRefGoogle Scholar
Duchene, V. 2011 Asymptotic models for the generation of internal waves by a moving ship, and the dead-water phenomenon. Nonlinearity 24 (8), 2281–2323.CrossRefGoogle Scholar
Ertekin, R. 1984 Soliton generation by moving disturbances in shallow water: theory, computation and experiment. PhD thesis, University of California, Berkeley.Google Scholar
Ertekin, R.C., Qian, Z.M. & Wehausen, J.V. 1990 Upstream solitons and wave resistance. In Engineering Science, Fluid Dynamics (ed. G.T. Yates), pp. 29–44. World Scientific.Google Scholar
Ertekin, R.C., Webster, W.C. & Wehausen, J.V. 1986 Waves caused by a moving disturbance in a shallow channel of finite width. J. Fluid Mech. 169, 275–292.CrossRefGoogle Scholar
la Forgia, G. & Sciortino, G. 2019 The role of the free surface on interfacial solitary waves. Phys. Fluids 31 (10), 106601.CrossRefGoogle Scholar
la Forgia, G. & Sciortino, G. 2020 Interfacial solitons propagating through a background shear current. Phys. Fluids 32 (10), 106603.CrossRefGoogle Scholar
la Forgia, G. & Sciortino, G. 2021 Free-surface effects induced by internal solitons forced by shearing currents. Phys. Fluids 33 (7), 072102.CrossRefGoogle Scholar
Fuhrman, D.R., Madsen, P.A. & Bingham, H.B. 2006 Numerical simulation of lowest-order short-crested wave instabilities. J. Fluid Mech. 563, 415–441.CrossRefGoogle Scholar
Grimshaw, R. 2010 Transcritical flow past an obstacle. ANZIAM J. 52 (1), 1–25.CrossRefGoogle Scholar
Grimshaw, R.H.J., Chan, K.H. & Chow, K.W. 2002 Transcritical flow of a stratified fluid: the forced extended Korteweg–de Vries model. Phys. Fluids 14 (2), 755–774.CrossRefGoogle Scholar
Grimshaw, R. & Helfrich, K.R. 2018 Internal solitary wave generation by tidal flow over topography. J. Fluid Mech. 839, 387–407.CrossRefGoogle Scholar
Grimshaw, R.H.J. & Maleewong, M. 2016 Transcritical flow over two obstacles: forced Korteweg–de Vries framework. J. Fluid Mech. 809, 918–940.CrossRefGoogle Scholar
Grimshaw, R.H.J. & Smyth, N. 1986 Resonant flow of a stratified fluid over topography. J. Fluid Mech. 169, 429–464.CrossRefGoogle Scholar
Grue, J., Friis, H.A., Palm, E. & Rusas, P.O. 1997 A method for computing unsteady fully nonlinear interfacial waves. J. Fluid Mech. 351, 223–252.CrossRefGoogle Scholar
Grue, J., Jensen, A., Rusas, P.O. & Sveen, J.K. 1999 Properties of large-amplitude internal waves. J. Fluid Mech. 380 (380), 257–278.CrossRefGoogle Scholar
Helfrich, K.R. & Melville, W.K. 2006 Long nonlinear internal waves. Annu. Rev. Fluid Mech. 38, 395–425.CrossRefGoogle Scholar
Huang, X.D., Chen, Z.H., Zhao, W., Zhang, Z.W., Zhou, C., Yang, Q.X. & Tian, J.W. 2016 An extreme internal solitary wave event observed in the northern South China Sea. Sci. Rep. 6, 30041.CrossRefGoogle ScholarPubMed
Jackson, C. 2007 Internal wave detection using the moderate resolution imaging spectroradiometer (MODIS). J. Geophys. Res. 112 (C11), C11012.CrossRefGoogle Scholar
Jo, T. & Choi, W. 2002 Dynamics of strongly nonlinear internal solitary waves in shallow water. Stud. Appl. Maths 109 (3), 205–227.CrossRefGoogle Scholar
Jo, T. & Choi, W. 2008 On stabilizing the strongly nonlinear internal wave model. Stud. Appl. Maths 120 (1), 65–85.CrossRefGoogle Scholar
Kodaira, T., Waseda, T., Miyata, M. & Choi, W. 2016 Internal solitary waves in a two-fluid system with a free surface. J. Fluid Mech. 804, 201–223.CrossRefGoogle Scholar
Lannes, D. & Ming, M. 2015 The Kelvin–Helmholtz instabilities in two-fluids shallow water models. Fields Inst. Commun. 75, 185–234.CrossRefGoogle Scholar
Longuet-Higgins, M.S. & Cokelet, E.D. 1976 The deformation of steep surface waves on water. I. A numerical method of computation. Proc. R. Soc. Lond. A 350 (1660), 1–26.Google Scholar
Melville, W.K. & Helfrich, K.R. 1987 Transcritical two-layer flow over topography. J. Fluid Mech. 178, 31–35.CrossRefGoogle Scholar
Mercier, M.J., Vasseur, R. & Dauxois, T. 2011 Resurrecting dead-water phenomenon. Nonlinear Process. Geophys. 18 (2), 193–208.CrossRefGoogle Scholar
Miles, J.W. 1980 Solitary waves. Annu. Rev. Fluid Mech. 12 (1), 11–43.CrossRefGoogle Scholar
Miyata, M. 1985 An internal solitary wave of large amplitude. La Mer 23 (2), 43–48.Google Scholar
Miyata, M. 1988 Long internal waves of large amplitude. In Nonlinear Water Waves (ed. K. Horikawa & H. Maruo), pp. 399–406. Springer.CrossRefGoogle Scholar
Ostrovsky, L.A. & Stepanyants, Y.A. 2005 Internal solitons in laboratory experiments: comparison with theoretical models. Chaos 15 (3), 037111.CrossRefGoogle ScholarPubMed
Wang, M. 2019 Numerical investigations of fully nonlinear water waves generated by moving bottom topography. Theor. Appl. Mech. Lett. 9 (5), 328–337.CrossRefGoogle Scholar
Zhao, B.B., Duan, W.Y. & Ertekin, R.C. 2014 Application of higher-level GN theory to some wave transformation problems. Coast. Engng 83, 177–189.CrossRefGoogle Scholar
Zhao, B.B., Ertekin, R.C., Duan, W.Y. & Webster, W.C. 2016 New internal-wave model in a two-layer fluid. ASCE J. Waterway Port Coastal Ocean Engng 142 (3), 04015022.CrossRefGoogle Scholar