Transformation of surface waves over a bottom step
We analyze in detail the problem of the transformation of surface gravity waves over a bottom step in a basin of arbitrary depth in the linear approximation. We found that strict analytical results can be obtained only when a denumerable set of modes condensed near the step is taken into account. At the same time, one can use the formulas suggested in this work for the practical calculations. They provide an accuracy of 5% for the wave transmission coefficient. The specific peculiarities of transformation coefficients are discussed, including their nonmonotonic dependence on the parameters, asymptotic behavior at strong depth variations, etc. The data of a direct numerical simulation of wave transformation over a step are presented, which are compared with the exact and approximate formulas. The coefficients of excitation of modes condensed near the step by an incident quasi-monochromatic wave are found. A relationship between the transformation coefficients that follows from the conservation law of wave energy flux is found.
Keywordssurface waves wave transformation transmission coefficient reflection coefficient oceanic shelf bottom step evanescent modes
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- 1.H. Lamb, Hydrodynamics (Cambridge Univ. Press., Cambridge, 1933).Google Scholar
- 2.E. N. Pelinovskii, Hydrodynamics of Tsunami Waves (IPF RAN, Nizhnii Novgorod, 1996) [in Russian].Google Scholar
- 6.K. Takano, “Effet d’un changement brusque de profondeur sur une houle irrotationelle (The effect of a sudden change in depth on an irrotational wave),” La mer 5 (2), 100–116 (1967).Google Scholar
- 8.S. R. Massel, Hydrodynamics of the Coastal Zone (Elsevier, Amsterdam, 1989).Google Scholar
- 10.L. N. Sretenskii, Theory of Wave Motions of Fluid (Nauka, Moscow, 1977) [in Russian].Google Scholar
- 12.A. R. Giniyatullin, A. A. Kurkin, S. V. Semin, and Y. A. Stepanyants, “Transformation of narrowband wavetrains of surface gravity waves passing over a bottom step,” Math. Modell. Nat. Processes 9 (5), 32–41 (2014).Google Scholar
- 13.L. M. Brekhovskikh and V. V. Goncharov, Introduction to Continuum Mechanics (Nauka, Moscow, 1982) [in Russian].Google Scholar
- 14.Yu. A. Stepanyants and A. L. Fabrikant, Propagation of Waves in Shear Flows (Nauka-Fizmatlit, Moscow, 1996) [in Russian].Google Scholar