Linear Water Waves

Kuznetsov, Nikolay; Maz′ya, Vladimir; Vainberg, Boris

doi:10.1017/cbo9780511546778

Cited by 171 publications

(51 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…[10]), in the case of an uneven bottom profile with different depths at infinity. This can be easily seen by using the results obtained from the study of the far-field asymptotics of the bottom-dependent Green's function [25].…”

Section: Article In Pressmentioning

confidence: 99%

“…Mei [1], Kuznetsov et al [10], and Evans and Kuznetsov [11] as concerns the existence of trapped modes in a channel with obstructions. In the case of diffraction of water waves by vertical cylindrical structures (extending throughout the water column) in constant depth, the problem can be reduced to the Helmholtz equation on the horizontal plane and it can be very conveniently treated by applying BEM, as presented by Au and Brebbia [12].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A boundary element method for the hydrodynamic analysis of floating bodies in variable bathymetry regions

Belibassakis

2008

Engineering Analysis with Boundary Elements

View full text Add to dashboard Cite

Section: Article In Pressmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A boundary element method for the hydrodynamic analysis of floating bodies in variable bathymetry regions

Belibassakis

2008

Engineering Analysis with Boundary Elements

View full text Add to dashboard Cite

“…John [6] provided a proof of uniqueness with some restrictions on the body shape, and various extensions have been made, but there is no general proof for this class of boundary-value problems. Recent reviews of this subject can be found in [7] and [8].…”

Section: Introductionmentioning

confidence: 99%

Trapping of water waves by moored bodies

Newman

2007

J Eng Math

View full text Add to dashboard Cite

Certain types of floating bodies are known to support trapped modes, with oscillatory fluid motion near the body and no energy radiation in the far field. Previous work has considered either fixed bodies, where the boundary conditions are homogeneous, or bodies which are freely floating and moving without any exciting force. For a fixed body the existence of a trapped mode implies that there is no unique solution of the boundary-value problem for the velocity potential with a prescribed body motion. For a free body which supports a trapped mode, the solution of the coupled problem for the motions of the fluid and body does not have a unique solution. A more general case is considered here, of a body with a linear restoring force such as an elastic mooring. The limiting cases of a fixed and free body correspond to infinite or zero values of the corresponding spring constant. A variety of body shapes are found including cylinders in two dimensions and axisymmetric bodies in three dimensions, which illustrate this more general case of trapping and provide a connection between the fixed and free cases.

show abstract

“…In the linearised theory of water-waves the wave solutions are described by velocity potentials which satisfy a mixed boundary value problem for the Laplace equation. In particular Steklov spectral boundary condition is posed on the horizontal water surface (see (1.2)-(1.4) below, and [19,5,6] for the physical background), and the spectral parameter is proportional to the frequency of the wave. In unbounded domains the continuous spectrum of this linearised water-wave problem is typically non-empty, a fact which is related to the existence of propagating waves.…”

mentioning

confidence: 99%