Eigenmodes in the water-wave problems for infinite pools with cone-shaped bottom. (13th July 2016)

• Record Type: Journal Article
• Authors: Lyalinov, Mikhail A.
• Is Part Of: Journal of fluid mechanics. Volume 800(2016:Aug.)
• Page Start: 645
• Page End: 665
• Publication Date: 2016-07-13
• Subjects: surface gravity waves, -- waves/free-surface flows; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2016.423
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract : In the framework of the assumptions of the linearized theory of small-amplitude water waves, the eigenfunctions of the point spectrum are studied for boundary-value problems in infinite domains. Special types of three-dimensional infinite water pools characterised by cone-shaped bottoms are considered. By means of an incomplete separation of variables and exploiting the Mellin transform, we reduce construction of the eigenmodes to the study and solution of the problems for some functional difference equations with meromorphic coefficients. The behaviour of the eigenmodes at a singular point of the boundary and the rate of their decay at infinity are also examined.