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- Title
ON THE NON-EXISTENCE OF SURFACE WAVES TRAPPED BY SUBMERGED OBSTRUCTIONS HAVING EXTERIOR CUSP POINTS.
- Authors
MOTYGIN, O. V.
- Abstract
Trapped modes, that is, localized unforced oscillations of fluid in presence of floating structures and bottom topography, have been a topic of considerable interest over many years and substantial effort has been put, for a variety of different geometries, into finding the solutions and conditions of their existence or absence. However, the class of geometries having cusp points has been avoided in the known proofs of non-existence of trapped modes, though waterwave problems for such structures have been considered and examples of trapped modes are known. In this work we consider submerged obstructions having exterior cusp points and establish absence of trapped modes for some classes of such geometries. For this purpose we derive a generalization of the so-called Maz'ya integral identity, which in the case of geometries with cusps also includes algebraic terms containing coefficients of local asymptotics of the trapped mode potential near cusp points of the contour.
- Subjects
SURFACE waves (Fluids); INTEGRAL inequalities; ALGEBRA; FLUID mechanics; CUSP forms (Mathematics)
- Publication
Quarterly Journal of Mechanics & Applied Mathematics, 2002, Vol 55, Issue 1, p127
- ISSN
0033-5614
- Publication type
Article
- DOI
10.1093/qjmam/55.1.127