Cross-waves induced by the vertical oscillation of a fully immersed vertical plate

TL;DR

This study investigates capillary cross-waves generated by vertical oscillations of a submerged plate, revealing a resonant mechanism and a specific wave angle distinct from classical Faraday waves.

Contribution

It provides a detailed analysis of the formation and characteristics of cross-waves induced by a vertical oscillating plate, highlighting a resonant wave selection mechanism.

Findings

Cross-waves appear above a specific acceleration threshold.

The cross-wave pattern involves two nearly anti-parallel waves at a small angle.

The wave angle results from a resonance between parametric waves.

Abstract

Capillary waves excited by the vertical oscillations of a thin elongated plate below an air-water interface are analyzed using time-resolved measurements of the surface topography. A parametric instability is observed above a well defined acceleration threshold, resulting in a so-called cross-wave, a staggered wave pattern localized near the wavemaker and oscillating at half the forcing frequency. This cross-wave, which is stationary along the wavemaker but propagative away from it, is described as the superposition of two almost anti-parallel propagating parametric waves making a small angle of the order of $20^\mathrm{o}$ with the wavemaker edge. This contrasts with the classical Faraday parametric waves, which are exactly stationnary because of the homogeneity of the forcing. Our observations suggest that the selection of the cross-wave angle results from a resonant mechanism between the two parametric waves and a characteristic length of the surface deformation above the wavemaker.