Second-order bichromatic waves produced by generic planar wavemaker in a two-dimensional wave flume

Abstract

A complete second-order solution is presented for the wave field produced by the bichromatic harmonic motion of a generic (piston or flap type) planar wavemaker in a semi-infinite two-dimensional channel. The velocity potentials at both first- and second-order are obtained explicitly in terms of eigenfunction expansions. Explicit analytical expressions are presented for the high- and low-frequency second-order potential components which occur at the sum and difference frequencies of the component first-order wavemaker motions. The relative magnitudes of the forced and free second-order waves are investigated for a range of wavemaker geometries, relative water depths and wave frequency combinations.