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Transformation of Narrowband Wavetrains of Surface Gravity Waves 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 waves with narrow spatial-temporal spectra on the bottom shelf is considered in the linear approximation. By means of numerical modeling, the transmission and reflection coefficients are determined as functions of the depth ratio and wave number (frequency) of an incident wave. The approximation formulae are proposed for the coefficients of wave transformation. The characteristic features of these formulae are analyzed. It is shown that the numerical results agree quite satisfactorily with the proposed approximation formulae.

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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