Pedal underwater motion triggers highly-peaked resonance on water waves

TL;DR

This paper demonstrates that pedal wavemakers can induce highly-peaked resonance in water waves, with a theoretical and numerical framework for designing deep gravity waves in finite-depth channels, relevant for hydraulics and coastal engineering.

Contribution

It introduces a comprehensive theoretical model for wave resonance triggered by pedal wavemakers in viscous fluids, including design protocols for specific wave properties.

Findings

Pedal wavemakers can cause sharp resonance in water waves.

The system acts as a spatial long-pass and temporal high-pass filter.

Theoretical predictions align with numerical simulations.

Abstract

Pedal wavemakers that generate surface gravity waves through bed orbital motion have been shown to produce particle-excursion patterns that mimic deep-water wave behaviour but in finite-depth channels. In this article, we report that gravity waves in a general viscous fluid can resonate through the action of pedal wavemakers. We analyse the linear response of waves in an infinite channel in terms of the displacement amplitude, frequency, and wavelength of the bottom action. We show that the system behaves as a long-pass filter in space and a high-pass filter in time with a sharp resonance affected by viscosity. Furthermore, we propose a protocol to design deep gravity waves with an on-demand wavelength in a finite-depth water channel. Our theoretical framework agrees with numerical simulations using Smoothed Particle Hydrodynamics. Our results thus quantify the performance of pedal wavemakers and provide essential formulas for industrial and computational applications of the pedal wavemaking technique, useful both in hydraulics and coastal engineering problems.