Capillary–gravity–acoustic triad resonance in laboratory basins

We study weakly nonlinear resonant interactions between two counter-propagating capillary–gravity waves and a horizontally uniform acoustic mode in a slightly compressible fluid of finite depth. Surface tension changes the resonance condition by allowing the large capillary–gravity wavenumbers needed to match the acoustic frequency at laboratory-scale depths. For the Longuet-Higgins configuration, in which the two surface modes have equal and opposite horizontal wavenumbers, the linear eigenfunctions and resonant wavenumber are obtained in closed form in the weakly compressible regime relevant to water-wave experiments. A multiple-scale calculation gives a three-wave interaction system with explicit coupling coefficients. We then use a leading-order spatially modulated approximation to estimate the acoustic pressure signal generated when two localised surface wavepackets collide. The bottom pressure scales quadratically with the characteristic surface-wave amplitude and linearly with the initial surface-wave width; for a representative laboratory configuration, the inviscid estimate is of order tens of Pascals.