MCIVER and NEWMAN, 2003. Trapping structures in the three-dimensional water-wave problem. Journal of Fluid Mechanics, 484, pp. 283–301.
Trapped modes in the linearized water-wave problem are free oscillations of the fluid
which have finite energy. They are known to exist at isolated frequencies in the presence
of certain special structures. The existence of a trapped mode implies the
non-uniqueness, or non-existence, of the solution to physically relevant radiation and
diffraction problems for such a structure.
Previous work on the three-dimensional problem has established the existence of
vertically axisymmetric structures that support trapped modes with either a single
interior free surface, or two concentric interior free surfaces. In the present work
the existence of several new types of trapping structures is established. These include
non-axisymmetric structures with a single interior free surface and various structures
with multiple interior free surfaces. The method used is an indirect one in which flow
fields without wave radiation are specified, and corresponding structures are found by
constructing suitable stream surfaces. Computations of the added-mass coefficients
for these structures provide independent support for the existence of a trapping mode
and illustrate their hydrodynamic characteristics at other wavenumbers.