Wave propagation over a beach within a nonlinear theory

Authors

M. A. Helal, Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, EgyptFollow
S. E. Badawi, Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, EgyptFollow
W. Mahmoud, Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, EgyptFollow

Abstract

Wave propagation over a beach is considered within a nonlinear theory in shallow water. Lagrangian coordinates are used to describe the problem. The solution is expanded in double series involving a small parameter and local oscillations. Two cases are treated: The beach with appreciable inclination on the horizontal (cliff) and the beach of small inclination. We show that finite solutions are obtained, in contrast to the linear theory which involves a logarithmic singularity at the shoreline. For the cliff, it is shown that local oscillations do not appear in the first two orders of approximation, and the incident wave is totally reflected without loss of energy at this order of approximation. The case of an incident wave on the beach is considered. The deformation of this wave is investigated and explicit formulae are obtained for the reflected wave and for the local oscillations, to shed light on the energy transfer due to interaction with the beach.

Recommended Citation

A. Helal, M.; E. Badawi, S.; and Mahmoud, W. (2022) "Wave propagation over a beach within a nonlinear theory," Information Sciences Letters: Vol. 11 : Iss. 5 , PP -.
Available at: https://digitalcommons.aaru.edu.jo/isl/vol11/iss5/31