Transformation of Long Surface and Tsunami-Like Waves in the Ocean with a Variable Bathymetry

Ermakov, Andrei and Stepanyants, Yury ORCID: (2020) Transformation of Long Surface and Tsunami-Like Waves in the Ocean with a Variable Bathymetry. Pure and Applied Geophysics, 177 (3). pp. 1675-1693. ISSN 0033-4553


We consider a transformation of long linear waves in an ocean with a variable depth.We calculate the transformation coefficients (the coefficients of transmission and reflection) as the functions of frequency and the total depth drop for three typical models of bottom profile variation: (i) piecewise-linear, (ii) piecewise-quadratic, and (iii) hyperbolic tangent profiles.For all these cases, exact solutions are obtained, analysed and graphically illustrated. This allows us to derive the transformation coefficients in the analytic form for the subsequent comparison with the results of approximate, numerical, or experimental study. We show that the results obtained are in agreement with both the energy flux conservation and Lamb’s formulae in the limiting case of zero frequency. We also study wave transformation on the underwater barriers and trenches of different shapes and compare the results obtained.

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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Files associated with this item cannot be displayed due to copyright restrictions.
Faculty/School / Institute/Centre: Historic - Faculty of Health, Engineering and Sciences - School of Agricultural, Computational and Environmental Sciences (1 Jul 2013 - 5 Sep 2019)
Faculty/School / Institute/Centre: Current - Faculty of Health, Engineering and Sciences - No Department (1 Jul 2013 -)
Date Deposited: 20 Jan 2020 05:39
Last Modified: 19 Apr 2021 01:01
Uncontrolled Keywords: Shallow water, tsunami wave, variable bathymetry, wave transformation.
Fields of Research (2008): 02 Physical Sciences > 0203 Classical Physics > 020303 Fluid Physics
04 Earth Sciences > 0404 Geophysics > 040403 Geophysical Fluid Dynamics
01 Mathematical Sciences > 0102 Applied Mathematics > 010299 Applied Mathematics not elsewhere classified
Socio-Economic Objectives (2008): E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
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