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Transformation of internal waves passing over a bottom step

Published online by Cambridge University Press:  04 March 2015

Egor N. Churaev ,
Sergey V. Semin  and
Yury A. Stepanyants
Egor N. Churaev
Affiliation:
Department of Applied Mathematics, Nizhny Novgorod State Technical University n.a. R.E. Alekseev, Nizhny Novgorod, 603950, Russia
Sergey V. Semin
Affiliation:
Department of Applied Mathematics, Nizhny Novgorod State Technical University n.a. R.E. Alekseev, Nizhny Novgorod, 603950, Russia
Yury A. Stepanyants*
Affiliation:
School of Agricultural, Computational and Environmental Sciences,University of Southern Queensland, Toowoomba, QLD, 4350, Australia
*
†Email address for correspondence: [email protected]
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Abstract

The transformation of small-amplitude internal waves on the oceanic shelf is studied numerically. The transmission and reflection coefficients are found for the simplified step-wise model of the oceanic shelf in a two-layer fluid. The approximate formulae are proposed for the transformation coefficients as functions of incident wavenumber, density ratio of layers, depth of the pycnocline and height of the bottom step. Results of direct numerical modelling of internal wave transformation are obtained and presented as functions of all aforementioned parameters. It is shown that there is a good agreement between the outcomes of approximate theory and numerical data. Both the theoretical and the numerical results agree well with the law of energy flux conservation.

JFM classification

Geophysical and Geological Flows: Coastal engineering Mathematical Foundations: General fluid mechanics Geophysical and Geological Flows: Internal waves
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 768 , 10 April 2015 , R3
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Copyright
© 2015 Cambridge University Press 

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