Hydrodynamics of a body floating in a two-layer fluid of finite depth. Part 1. Radiation problem

The problems of radiation (sway, heave and roll) of surface and flexural-gravity waves by a submerged cylinder are investigated for two configurations, concerning; (i) a freely floating finite elastic plate modelling an ice floe, and (ii) two semi-infinite elastic plates separated by a region of open water (polynya). The fluid of finite depth is assumed to be inviscid, incompressible and homogeneous. The linear two-dimensional problems are formulated within the framework of potential-flow theory. The method of mass sources distributed along the body contour is applied. The corresponding Green’s function is obtained by using matched eigenfunction expansions. The radiation load (added mass and damping coefficients) and the amplitudes of vertical displacements of the free surface and elastic plates are calculated. Reciprocity relations which demonstrate both symmetry of the radiation load coefficients and the relation of damping coefficients with the far-field form of the radiation potentials are found. It is shown that wave motion essentially depends on the position of the submerged body relative to the elastic plate edges. The results of solving the radiation problem are compared with the solution of the diffraction problem. It is noted that resonant frequencies in the radiation problem correlate with those frequencies at which the reflection coefficient in the diffraction problem has a local minimum.

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On the radiation and scattering of short surface waves. Part 2

Journal of Fluid Mechanics ◽

10.1017/s0022112073001461 ◽

1973 ◽

Vol 59 (1) ◽

pp. 129-146 ◽

Cited By ~ 14

Author(s):

F. G. Leppington

Keyword(s):

Surface Waves ◽

Simple Wave ◽

Finite Depth ◽

Short Wave ◽

Asymptotic Estimates ◽

Radiation Problem ◽

Expansion Technique ◽

Wave Trains ◽

Intersection Points ◽

Scattering And Radiation

A short-wave asymptotic analysis is undertaken for problems concerned with the radiation and scattering of surface waves by a cylinder whose cross-section S intersects the free surface normally. It is assumed that S is locally smooth and convex at the two intersection points with the fluid, which may be of infinite or finite depth. For both the scattering and radiation problem, a matched expansion technique is used to provide asymptotic estimates, in terms of relatively simple wave-free limit potentials, for the amplitudes of the surface wave trains that propagate from S. Explicit details are given for some particular geometries, confirming and extending earlier results. The method can, in principle, be extended to deal with other geometries.

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