Session A44: Waves: Surface Waves I

Modulation Instability in Standing Water Waves

The modulation instability (MI) is responsible for the formation of strong wave localizations on the water surface and in a variety of nonlinear dispersive wave systems. Recent laboratory studies confirmed the validity of breathers to describe several MI scenarios in hydrodynamics, optics, plasma, and Bose-Einstein condensates. We provide experimental evidence of nonlinear and distinct breather focusing in standing water waves, i.e., in two counterpropagating wave trains. The wave measurements are in excellent agreement with the hydrodynamic coupled nonlinear Schrödinger equation and indicate that MI processes are unimpeded during the interplay of two wave systems.   

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.     

Backscattering reduction in a twisted water wave channel

We study experimentally and numerically the propagation of water waves along a channel with two perpendicular turns. When the wave reaches the first turn, there is naturally a reflected wave. We show that it is possible to reduce almost completely the backscattering in such geometries, in agreement with a recent theoretical prediction. In order to avoid the reflection that naturally arises at that point of the waveguide, a simple metamaterial made of closely-spaced thin vertical plates is used. This metamaterial acts like a negative-refraction index media, producing a waveshift across it. This phenomenon is not restricted only to surface waves but also applies to any type of waves. Furthermore, the efficiency of this arrangement does not depend on the frequency of the incident wave, as long as its wavelength is much larger than the spacing between the plates.   

Nonlinear standing surface waves excited by an oscillating cylinder in a narrow rectangular cavity

Forced standing 2D surface waves in a narrow deep rectangular transparent cavity are studied experimentally and theoretically. Waves are excited by an oscillating fully submerged cylinder with a diameter small relative to the cavity’s length and axis normal to its long walls. The cylinder is forced to oscillate harmonically in the vertical direction with amplitudes smaller than its diameter at frequencies close to the resonant frequencies of the cavity. In experiments, the free surface motion is recorded by a video camera. The motion of the free surface's shape and the wave amplitude's dependence on the forcing amplitude and frequency is extracted from the sequence of video images. The surface motion is also simulated using the volume-of-fluid approach and independently, assuming irrotational flow with small dissipation. The experimental data agree with the results of both theoretical approaches and show that the effective resonance frequencies are downshifted from the cavity’s natural frequencies by a value proportional to the square of the cylinder diameter; the nonlinear effects cause further resonant frequency downshifting.   

Boat wake incidence on a microstructured wall

We conducted experiments investigating the interaction between a boat wake and a subwavelength microstructured wall. In our study, we consider a ship that moves at a constant speed parallel to the wall. We investigated the reflection resulting from the interaction of the ship's wake with the wall. By modifying the geometry of the microstructure to couple its resonant frequency with the wavelength of the ship's wake, we were able to achieve total absorption. Our findings illustrate the successful manipulation of water waves by the use of subwavelength resonances, resulting in the efficient absorption of the incident waves. This study sheds light on the potential for utilizing microstructured surfaces as a means to control and mitigate the impact of ship wakes on surrounding structures.   

Axisymmetric radiation and decay of gravity-capillary waves

Some centimeter-scale water surface bound aquatic insects employ echolocation in search of food, allies, and predators by generating and detecting free surface waves. We present a combined theoretical and experimental study of gravity-capillary waves, which are generated by a disk oscillating vertically about the horizontal free surface. The radiated waves are predicted using matched eigenfunction expansions, as employed in existing models of surface gravity waves. Here we account for surface tension and viscosity to investigate the effects of oscillating a small object on the water surface. Our model was tested against experiments in which the surface topography of waves ranging from 10 to 100 Hz were measured using the free-surface synthetic Schlieren method. Although a small amount of viscosity has minor effects on the dispersion relation and the wavelength of the surface waves, it has long range influence on the amplitude of the surface elevation. Our findings show that surface waves around small floating objects are significantly dampened by viscosity.   

Quantifying Vertical Vorticity Generation from Breaking Waves in Deep Water

It has long been theorized that breaking waves cause an increase in the local vertical vorticity field.  However, few measurements in the field have corroborated this assumption.  A two-dimensional power spectral density technique was applied to video recorded by a stationary quadcopter that hovered over the Gulf of Mexico.  The results show an increase in the local vertical vorticity field around individual breaking waves in deep water.  The magnitude of the generated vorticity is comparable with previous field measurements in shallow water.  It is further observed that the resulting coherent structures persist for some time after the wave breaks.