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Transformation of Narrowband Wavetrains of Surface GravityWaves Passing over a Bottom Step

Published online by Cambridge University Press:  17 July 2014

A. R. Giniyatullin ,
A. A. Kurkin ,
S. V. Semin  and
Y. A. Stepanyants
A. R. Giniyatullin
Affiliation:
Nizhny Novgorod State Technical University n.a. R.E. Alekseev, Nizhny Novgorod, Russia
A. A. Kurkin
Affiliation:
Nizhny Novgorod State Technical University n.a. R.E. Alekseev, Nizhny Novgorod, Russia
S. V. Semin
Affiliation:
Nizhny Novgorod State Technical University n.a. R.E. Alekseev, Nizhny Novgorod, Russia University of Southern Queensland, Toowoomba, Australia
Y. A. Stepanyants*
Affiliation:
Nizhny Novgorod State Technical University n.a. R.E. Alekseev, Nizhny Novgorod, Russia University of Southern Queensland, Toowoomba, Australia
*
⋆ The authors adhere the principle of alphabetical order of the names.Corresponding author. E-mail: Yury.Stepanyants@usq.edu.au
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Abstract

The problem of transformation of quasimonochromatic wavetrains of surface gravity waveswith narrow spatial-temporal spectra on the bottom shelf is considered in the linearapproximation. By means of numerical modeling, the transmission and reflectioncoefficients are determined as functions of the depth ratio and wave number (frequency) ofan incident wave. The approximation formulae are proposed for the coefficients of wavetransformation. The characteristic features of these formulae are analyzed. It is shownthat the numerical results agree quite satisfactorily with the proposed approximationformulae.

Keywords

wavetrainwave transformationnumerical modelingquasimonochromatic wavereflected and transmitted wavesbottom step
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 9 , Issue 5: Spectral problems , 2014 , pp. 73 - 82
Copyright
© EDP Sciences, 2014

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