  The rainbow reflection effect describes the broadband spatial separation of
wave spectral components caused by a spatially graded array of resonators.
Although mainly studied in optics and acoustics, this phenomenon has recently
been demonstrated both theoretically and experimentally for water waves
travelling through an array of vertical cylinders. Linear water wave scattering
by a array of vertical, surface-piercing barriers is considered here, in which
both the submergence and spacing between the barriers are spatially graded. The
rainbow reflection effect arises naturally as wave energy temporarily becomes
amplified at different locations depending on frequency. Band diagram
calculations are used to demonstrate that this is a consequence of the wave
gradually slowing down throughout the array. The wave/barriers scattering
problem is then augmented by positioning heave-restricted, rectangular floating
bodies equipped with a linear damping mechanism between each adjacent pair of
barrier. A solution to the resulting boundary-value problem is obtained using
an integral equation/Galerkin method. Using constrained optimisation, passive
rainbow absorbers are designed that achieve near-perfect absorption over (i) a
discrete set of frequencies, and (ii) over an octave. This suggests potential
applications of rainbow absorbers in the design of smart coastal technologies.
