Highly peaked resonance in a synchrotron water waveguide*

Pedal wavemakers mimic the particle-excursion patterns in deep-water waves through bed orbital motion to generate surface gravity waves. We report that gravity waves in a viscous fluid can resonate through the action of pedal wavemakers. We analyze the linear response of waves in an infinite channel in terms of the displacement amplitude, frequency, and wavelength of the bottom action to show that the system displays a sharp resonance affected by viscosity. Numerical simulations using Smoothed Particle Hydrodynamics agree with our theoretical results. 

We used this framework to devise and assemble a synchrowave, i. e. a synchrotron waveguide built to accelerate and sustain water waves traveling on the surface of a fluid in a closed circular channel similar to the synchrotrons that accelerate ions. Wave dampening, analogous to energy losses due to electromagnetic radiation and inelastic collisions in conventional particle accelerators, are counteracted through the synchronous action of pedal wavemakers at the soft bottom of the synchrowave. A lab-scale prototype proves the technique is unique for generating anomalously large traveling waves.

Our results quantify the performance of pedal wavemakers and provide essential formulas for industrial and computational applications of the pedal wavemaking technique, which are helpful in hydraulics and coastal engineering problems.