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The rainbow reflection effect describes the broadband spatial separation ofwave spectral components caused by a spatially graded array of resonators.Although mainly studied in optics and acoustics, this phenomenon has recentlybeen demonstrated both theoretically and experimentally for water wavestravelling through an array of vertical cylinders. Linear water wave scatteringby a array of vertical, surface-piercing barriers is considered here, in whichboth the submergence and spacing between the barriers are spatially graded. Therainbow reflection effect arises naturally as wave energy temporarily becomesamplified at different locations depending on frequency. Band diagramcalculations are used to demonstrate that this is a consequence of the wavegradually slowing down throughout the array. The wave/barriers scatteringproblem is then augmented by positioning heave-restricted, rectangular floatingbodies equipped with a linear damping mechanism between each adjacent pair ofbarrier. A solution to the resulting boundary-value problem is obtained usingan integral equation/Galerkin method. Using constrained optimisation, passiverainbow absorbers are designed that achieve near-perfect absorption over (i) adiscrete set of frequencies, and (ii) over an octave. This suggests potentialapplications of rainbow absorbers in the design of smart coastal technologies.

Graded arrays of vertical barriers: rainbow reflection and broadband energy absorption