Graded resonator arrays for spatial frequency separation and amplification of water waves

TL;DR

This paper introduces a graded array of C-shaped cylinders designed to amplify and spatially separate water waves across a broad frequency spectrum, utilizing linear potential-flow theory and transfer matrix analysis.

Contribution

It presents a novel graded resonator array that effectively amplifies water waves and separates frequencies, advancing wave control techniques.

Findings

Significant wave amplification at targeted locations.

Broad frequency range of effective amplification.

Rayleigh--Bloch wave excitation explains the amplification mechanism.

Abstract

A structure capable of substantially amplifying water waves over a broad range of frequencies at selected locations is proposed. The structure consists of a small number of C-shaped cylinders arranged in a line array, with the cylinder properties graded along the array. Using linear potential-flow theory, it is shown that the energy carried by a plane incident wave is amplified within specified cylinders, for wavelengths comparable to the array length, and for a range of incident directions. Transfer matrix analysis is used to attribute the large amplifications to excitation of Rayleigh--Bloch waves and gradual slowing down of their group velocity along the array.