On a bound for the frequency of surface waves trapped near a cylinder spanning a channel
This paper derives a lower bound on the frequency of trapped waves in a channel of finite width in which a cylinder spans the width of the channel. First, the non-existence of trapped waves for an infinitely deep channel spanned by a body which intersects the free surface and is entirely contained between vertical planes through the free-surface intersections is proved using a method based on integrals of the velocity potential on vertical lines drawn down from the free surface. This method is then used to derive a lower bound on the frequency of trapped modes for the case of finite depth (which may vary along the channel). Next a method for deriving frequency bounds is developed which involves integrals of the potential along nonvertical lines drawn down from the free surface. As such, the method is more flexible in that it can be applied to a wider variety of domain geometries. Application of the method yields lower bounds for trapped wave frequencies for the cases of infinite and finite depth.
scientific article; zbMATH DE number 108911