Abstract
The problem of gravity waves in a fluid over a sloping beach has long received much attention. Waves propagating on the horizontal free surface in both directions, parallel to as well as perpendicular to the shore line were discussed in the frame of a linearized theory leading to solutions expressed in a closed form, for any frequency and any value of the slope of the beach [1], [2]. The method devised in [1] was subsequently improved and successfully applied to many other physical problems which require solving Helmholtz equation in a sector with appropriate conditions on the boundaries (edge waves [3], waves in an open channel of variable depth [4], sustained oscillations in porous media [5], diffraction of internal waves by a wedge [6]).
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References
M. Roseau, Sur les mouvements ondulatoires de la mer sur une plage, C. R. Acad. Sci. Paris, t. 232,.479–481 (1951).
J. J. Stoker, Water Waves, Interscience, New York 1957.
M. Roseau, Short waves parallel to the shore over a sloping beach, Commun. Pure Appl. Math., 11, 433–493 (1958).
M. Roseau, Asymptotic Wave Theory, North-Holland, Amsterdam 1976.
M. Roseau, Diffusion dans un sol perméable d’ondes liquides entretenues par la marée, Ann. Sc. Ec. Norm. Sup., 77, 1–40 (1960).
M. Roseau, Ondes internes évanescentes à l’infini dans un fluide pesant limité par un dièdre convexe, C. R. Acad. Sci. Paris, t. 284, 517–520 (1977)
M. Roseau, Sur certaines solutions du problème des ondes internes de seconde classe et la représentation des ondes de bord, C. R. Acad. Sci. Paris, t. 284, 567–570 (1977)
M. Roseau, Ondes internes de première classe et condition de radiation de Sommerfeld; résultat de non unicité, C. R. Acad. Sci. Paris, t. 284, 629–632 (1977)
M. Roseau, Diffraction d’ondes internes par une barrière semi-infinie, C. R. Acad. Sci. Paris, t. 284, 711–714 (1977).
P. H. Leblond and L. A. Mysak, Waves in the Ocean, Elsevier, Amsterdam 1978.
D. V. Evans, Edge waves over a sloping beach, Quart. J. Mech. Appl. Math., 42 ptl, 131–142 (1989).
G. B. Whitham, Lectures on Wave Propagation, Springer, New York 1979.
M. Roseau, Sur une équation fonctionnelle de la théorie des ondes liquides de gravité, Proceedings of the Int. Symp. on Applications of the Theory of Functions in Continuum Mechanics, Tbilisi, USSR, 2, 358–361 (1963).
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Dedicated to Paul M. Naghdi on the occasion of his 70th birthday
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© 1995 Birkhäuser Verlag Basel/Switzerland
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Roseau, M. (1995). Water waves over a sloping beach in a rotating frame. In: Casey, J., Crochet, M.J. (eds) Theoretical, Experimental, and Numerical Contributions to the Mechanics of Fluids and Solids. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9229-2_31
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DOI: https://doi.org/10.1007/978-3-0348-9229-2_31
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