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Journal of Engineering Mathematics

Published in:

01-04-2014

Edge waves propagating in a two-layer fluid along a periodic coastline

Authors: F. S. Cal, G. A. S. Dias, B. M. M. Pereira, J. H. Videman

Published in: Journal of Engineering Mathematics | Issue 1/2014

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Abstract

We investigate the trapping of wave energy along periodic coastlines in a two-layer fluid. We derive conditions on the nearshore slope which, if satisfied, guarantee the existence of edge waves. These conditions are easy to check, and they show that many simple coast profiles such as shelf and cliff coasts and sloping beaches support edge waves.

next article Davies’ surface condition and singularities of deep water waves

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Stokes G (1846) Report on recent researches in hydrodynamics. Rep Br Assoc Adv Sci 1–20

Ursell F (1952) Edge waves over a sloping beach. Proc R Soc Lond A 214:79–97ADSCrossRefMATHMathSciNet

Grimshaw R (1974) Edge waves: a long-wave theory for oceans of finite depth. J Fluid Mech 62:775–791ADSCrossRefMATH

Evans DV, McIver P (1984) Edge waves over a shelf: full linear theory. J Fluid Mech 142:79–95ADSCrossRefMATH

Evans DV, Linton CM (1993) Edge waves along periodic coastlines. Q J Mech Appl Math 46:643–656CrossRefMATHMathSciNet

Jones DS (1953) The eigenvalues of \(\nabla ^2u+\lambda u=0\) when the boundary conditions are given on semi-infinite domains. Proc Camb Phil Soc 49:668–684ADSCrossRefMATH

Bonnet-Ben Dhia AS, Joly P (1993) Mathematical analysis of guided water waves. SIAM J Appl Math 53:1507–1550CrossRefMATHMathSciNet

Mysak LA (1980) Topographically trapped waves. Ann Rev Fluid Mech 12:45–76ADSCrossRefMathSciNet

Kuznetsov N (1993) Trapped modes of internal waves in a channel spanned by a submerged cylinder. J Fluid Mech 254:113–126ADSCrossRefMATHMathSciNet

10.

Zhevandrov PN (1996) Edge waves in a two-layer fluid. Paper presented at the 11th International Workshop on Water Waves and Floating Bodies, Hamburg, p. 17–20

11.

Chakrabarti A, Daripa P, Hamsapriye (2005) Trapped modes in a channel containing three layers of fluids and a submerged cylinder. ZAMP 56:1084–1097ADSCrossRefMATHMathSciNet

12.

Linton CM, Cadby JR (2003) Trapped modes in a two-layer fluid. J Fluid Mech 481:215–234ADSCrossRefMATHMathSciNet

13.

Nazarov SA, Videman JH (2009) A sufficient condition for the existence of trapped modes for oblique waves in a two-layer fluid. Proc R Soc A 465:3799–3816ADSCrossRefMATHMathSciNet

14.

Nazarov SA (2009) Sufficient conditions for the existence of trapped modes in problems of the linear theory of surface waves. Zap Nauchn Sem St.-Petersburg Otdel Mat Inst Steklov 369:202–223 (Transl J Math Sci 167:713–725).

15.

Nazarov SA, Videman JH (2010) Existence of edge waves along three-dimensional periodic structures. J Fluid Mech 659:225–246CrossRefMATHMathSciNet

16.

Wilcox CH (1984) Scattering theory for diffraction gratings. Springer, BerlinCrossRefMATH

17.

Lamb H (1945) Hydrodynamics. Dover, New York

18.

Kuznetsov N, Maz’ya V, Vainberg B (2002) Linear water waves: a mathematical approach. Cambridge University Press, CambridgeCrossRef

19.

Cal FS, Dias GAS, Videman JH (2012) Existence of trapped modes along periodic structures in a two-layer fluid. Q J Mech Appl Math 65(2):273–293CrossRefMATHMathSciNet

20.

Kundu PK, Cohen IM (2004) Fluid mechanics, 3rd edn. Elsevier, Amsterdam

21.

Birman MSh, Solomjak MZ (1987) Spectral theory of self-adjoint operators in Hilbert space. D. Reidel, BostonMATH

22.

Evans DV, Levitin M, Vassiliev D (1994) Existence theorems for trapped modes. J Fluid Mech 261:21–31ADSCrossRefMATHMathSciNet

23.

Weinberger HF (1974) Variational methods for eigenvalue approximation. SIAM, Philadelphia

24.

Kamotskii IV, Nazarov SA (2003) Exponentially decreasing solutions of the problem of diffraction by a rigid periodic boundary. Mat Zametki 73:138–140 (Transl Math Notes 73:129–131)

Title: Edge waves propagating in a two-layer fluid along a periodic coastline
Authors: F. S. Cal
G. A. S. Dias
B. M. M. Pereira
J. H. Videman
Publication date: 01-04-2014
Publisher: Springer Netherlands
Published in: Journal of Engineering Mathematics / Issue 1/2014
Print ISSN: 0022-0833
Electronic ISSN: 1573-2703
DOI: https://doi.org/10.1007/s10665-013-9641-x

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