Wave scattering by periodic arrays of breakwaters
R. Porter and D. V. Evans. 1996, Wave Motion, 23, 97-120.
Oblique incidence of plane waves upon an infinite array of in-line
periodic screens or breakwaters in finite water depth is considered
using linear water-wave theory. The number of reflected or transmitted
waves is a function of the angle of incidence and the ratio of
wavelength to array periodicity. A simple matrix formulation is
provided for all the reflection and transmission coefficients arising
from a particular set of parameters, using a formulation based either
on the unknown velocity through a gap or on the unknown pressure
difference across a breakwater screen. Integral properties of functions
related to these unknowns form the basis of the matrix structure, the
functions themselves satisfying a set of integral equations which are
solved using a Galerkin approximation that gives highly accurate
approximations with very few terms in the expansion. The problem is
extended to consider two identical parallel arrays and it is shown that
there exists zeros of both reflection and transmission. Finally, a
wide-spacing approximation is derived for two arrays based on the
accurate results found from the single array problem, where the two
arrays do not have to be identical, but must have the same
periodicity.