Scattering of Poincare waves by an irregular coastline. Part 2. Multiple scattering

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Abstract
Kelvin and Poincaré waves are generated when an ocean wave arrives at a nominally rectilinear coastline and interacts with coastal irregularities. The discussion of this problem given by Howe & Mysak (1973) is extended in this paper in order to examine the role of multiple scattering of the Kelvin and Poincaré waves. An integro-differential kinetic equation is derived to describe these processes in the limit in which the irregularities are small compared with the characteristic wavelength. In the absence of dissipative mechanisms it is verified that this description of interactions with the coast conserves total wave energy. The theory is applied to a variety of idealized problems which model tidal and storm surge events, including the generation and decay of Kelvin waves by extensive and localized Poincaré-wave forcing, and the influence of multiple scattering on the radiation of Poincaré-wave noise into the open ocean.

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