On uniqueness in the problem of gravity–capillary water waves above submerged bodies

Author:

Motygin Oleg V.1,McIver Philip2

Affiliation:

1. Institute of Problems in Mechanical Engineering, Russian Academy of SciencesV. O. Bol'shoy prospect 61, St Petersburg 199178, Russia

2. School of Mathematics, Loughborough UniversityLoughborough, Leicestershire LE11 3TU, UK

Abstract

In this paper, we consider the two-dimensional linear problem of wave–body interaction with surface tension effects being taken into account. We suggest a criterion for unique solvability of the problem based on symmetrization of boundary integral equations. The criterion allows us to develop an algorithm for detecting non-uniqueness (finding trapped modes) for given geometries of bodies; examples of numerical computation of trapped modes are given. We also prove a uniqueness theorem that provides simple bounds for the possible non-uniqueness parameters.

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Reference17 articles.

1. Abramowitz M.& Stegun I.A. Handbook of mathematical functions. 1965 New York NY:Dover.

2. Billingham J.& King A.C. Wave motion. 2000 Cambridge UK:Cambridge University Press.

3. Gilbarg D.& Trudinger N.S. Elliptic partial differential equations of second order. 1983 Berlin Germany:Springer.

4. The effect of surface tension on trapped modes in water-wave problems

5. The effect of surface tension on localized free-surface oscillations about surface-piercing bodies

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