Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On the breaking of water waves on a sloping beach of arbitrary shape

Author: Morton E. Gurtin
Journal: Quart. Appl. Math. 33 (1975), 187-189
DOI: https://doi.org/10.1090/qam/99666
MathSciNet review: QAM99666
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Abstract | References | Additional Information

Abstract: Greenspan [1] considered water waves of finite amplitude on a beach of constant slope. He proved that: ( $ \left( {{G_1}} \right)$) A wave of elevation with nonzero slope at the front propagating shoreward into quiescent water always breaks before the shore.( $ \left( {{G_2}} \right)$) Under the same conditions a wave of depression never breaks.

References [Enhancements On Off] (What's this?)

  • [1] H. P. Greenspan, J. Fluid Mech. 4, 330 (1958) MR 0096463
  • [2] G. F. Carrier and H. P. Greenspan, J. Fluid Mech. 4, 97 (1958) MR 0096462
  • [3] J. J. Stoker, Comm. Pure Appl. Math. 1, 9 (1948)
  • [4] C. Truesdell and R. A. Toupin, The classical field theories, in Handbuch der Physik, Vol. III/1, Berlin: Springer-Verlag (1960) MR 0118005

Additional Information

DOI: https://doi.org/10.1090/qam/99666
Article copyright: © Copyright 1975 American Mathematical Society

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