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New solutions for periodic interfacial gravity waves

Published online by Cambridge University Press:  12 October 2021

X. Guan ,
J.-M. Vanden-Broeck  and
Z. Wang Open the ORCID record for Z. Wang [Opens in a new window]
X. Guan
Affiliation:
Department of Mathematics, University College London, London WC1E 6BT, UK
J.-M. Vanden-Broeck
Affiliation:
Department of Mathematics, University College London, London WC1E 6BT, UK
Z. Wang*
Affiliation:
Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China
*
†Email address for correspondence: zwang@imech.ac.cn
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Abstract

Two-dimensional periodic interfacial gravity waves travelling between two homogeneous fluids of finite depth are considered. A boundary-integral-equation method coupled with Fourier expansions of the unknown functions is used to obtain highly accurate solutions. Our numerical results show excellent agreement with those already obtained by Maklakov & Sharipov using a different scheme (J. Fluid Mech., vol. 856, 2018, pp. 673–708). We explore the global bifurcation mechanism of periodic interfacial waves and find three types of limiting wave profiles. The new families of solutions appear either as isolated branches or as secondary branches bifurcating from the primary branch of solutions.

JFM classification

Waves/Free-surface Flows: Surface gravity waves
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 928 , 10 December 2021 , R5
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Chen, B. & Saffman, P.G. 1980 Numerical evidence for the existence of new types of gravity waves of permanent form on deep water. Stud. Appl. Maths 62, 1–21.CrossRefGoogle Scholar
Grimshaw, R.H.J. & Pullin, D.I. 1986 Extreme interfacial waves. Phys. Fluids 29 (9), 2802–2807.CrossRefGoogle Scholar
Guan, X., Vanden-Broeck, J.-M., Wang, Z. & Dias, F. 2021 A local model for the limiting configuration of interfacial solitary waves. J. Fluid Mech. 921, A9.CrossRefGoogle Scholar
Holyer, J.Y. 1979 Large amplitude progressive interfacial waves. J. Fluid Mech. 93, 433–448.CrossRefGoogle Scholar
Maklakov, D.V. & Sharipov, R.R. 2018 Almost limiting configurations of steady interfacial overhanging gravity waves. J. Fluid Mech. 856, 673–708.CrossRefGoogle Scholar
Meiron, D.I. & Saffman, P.G. 1983 Overhanging interfacial gravity waves of large amplitude. J. Fluid Mech. 129, 213–218.CrossRefGoogle Scholar
Papageorgiou, D.T. & Vanden-Broeck, J.-M. 2004 Antisymmetric capillary waves in electrified fluid sheets. Eur. J. Appl. Maths 15, 609–623.CrossRefGoogle Scholar
Pullin, D.I. & Grimshaw, R. 1983 a Nonlinear interfacial progressive waves near a boundary in a Boussinesq fluid. Phys. Fluids 26 (4), 897–905.CrossRefGoogle Scholar
Pullin, D.I. & Grimshaw, R. 1983 b Interfacial progressive gravity waves in a two-layer shear flow. Phys. Fluids 26 (7), 1731–1739.CrossRefGoogle Scholar
Saffman, P.G. & Yuen, H.C. 1982 Finite-amplitude interfacial waves in the presence of a current. J. Fluid Mech. 123, 459–476.CrossRefGoogle Scholar
Turner, R.E.L. & Vanden-Broeck, J.-M. 1986 The limiting configuration of interfacial gravity waves. Phys. Fluids 29 (2), 372–375.CrossRefGoogle Scholar
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