Session A27: Waves: Surface Waves

Diffraction of particles in a hydrodynamic pilot-wave theory

The seminal experiments of Yves Couder and Emmanuel Fort demonstrated that a droplet walking on the surface of a fluid bath may exhibit behavior thought to be peculiar to the quantum realm. One of their experiments suggested that single-particle diffraction and interference may be obtained when a walker crosses a single- or a double-aperture between submerged barriers (Couder & Fort Phys. Rev. Lett. 2006). Later experiments with finer control of experimental parameters yielded different results, thus reopening the question of the extent of the analogy between walkers and quantum particles (Andersen et al. Phys. Rev. E 2015; Pucci et al. J. Fluid Mech. 2018; Rode et al. Phys. Rev. Fluids 2019; Ellegaard & Levinsen, Phys. Rev. E 2020). Here we use the pilot-wave model developed by Oza et al. (J. Fluid Mech. 2013) to explore numerically the diffraction of a wave-driven particle by barriers, which are represented as an array of reflecting point sources of waves. The statistical distribution of the particle's deflected position generally exhibits multiple peaks, the number of which depends on the obstacle geometry and the bath's forcing acceleration. We will discuss the similarities and differences between these statistical distributions and the Fresnel and Fraunhofer diffraction patterns in optics.   

Surface Wave and Transport Dynamics of a Self-propelling Vibrating Robot Fan Boat

Active agents on fluid surfaces can perturb their surroundings by creating waves that can reciprocally affect the agent. Inspired by the rich wave-mediated dynamics of surface-bouncing droplets, we study the motion and wave field dynamics of an 11.7 cm diameter, 8.8 cm tall vibrating robot fan boat moving on the surface of a 4-10 cm deep pool of water. The boat's vibration motor creates outwardly propagating surface waves with frequency range 10-63 Hz; a Schlieren method enables surface wave visualization with submillimeter resolution. Far from boundaries, the boat generates circular waves for frequencies below 42.8 Hz with maximum amplitude 0.6 mm; above 42.8 Hz, the waves gain subharmonic components. In obstacle-laden environments (lattices of posts 16.7 cm apart), the wave field becomes complex, and the presence or lack of vibration strongly affects boat trajectories. Without vibration, the boat pins itself permanently to any obstacle encountered with incident angle less than 34°, often occurring within three collisions; with vibration, the boat displays spontaneous reorientations about obstacles, enabling escapes and producing ballistic motion at all tested timescales. We posit these dynamics are due to both hydrodynamic wave-obstacle and vibratory boat-obstacle interactions.   

Effect of wind on a soliton's shape shoaling up a planar slope

Wave shape influences sediment transport, beach morphology, and ship safety. Previously, shoaling and wind forcing have been shown to cause wave growth and change wave shape separately. However, the combined influence of these two phenomena has not been studied theoretically despite their joint prevalence in the nearshore environment. Here, we force small-amplitude, shallow-water solitary waves with a Jeffreys-type wind-induced surface pressure and allow them to propagate up a gentle, planar bathymetry. The resulting variable-coefficient KdV--Burgers equation is solved numerically. The resulting wave consists of a solitary wave and bound shelf as described by Miles in combination with a wind-induced, bound, dispersive tail. The wind-induced tail is consistent with prior studies of wind-forced shallow-water waves on flat bottoms. Additionally, onshore winds cause a narrowing of the wave peak and depress the wave's rear shelf. Finally, the wind influences the width of the pre-breaking zone in qualitative agreement with prior laboratory measurements and numerical experiments.   

Not Participating

We consier the wave motion generated by a moving submerged object in a rectilnear 18 meter wave tank experimentally.  Depending on the Froude number, several different regimes are studied.  Precursor solitary waves periodically generated and moving ahead of the obstacle are seen to co-exist with hydraulic jumps with capillary wave breaking.  Mode sorting is observed after the obstacle is stopped.  The data are collected with wave gauges, PIV, and co-moving video tracking of the interface.  The effects of pre-existing wave currents on the propagation of the wave train is also examined and demonstrate novel deconstructive interference.  Long wave models as well as direct numerical simulations will be presented time permitting.   

Amplitude equation model for prediction of super-harmonic double-crest wave dynamics in orbital shaken cylindrical containers

The container motion along a planar circular trajectory at a constant angular velocity, i.e. orbital shaking, is of interest in several industrial applications, e.g. for fermentation processes or in cultivation of stem cells, where good mixing and efficient gas exchange are the main targets. Under these external forcing conditions, the free surface typically exhibits a  single-crest dynamics, whose wave amplitude, as a function of the external forcing parameters, displays a Duffing-like behavior. However, previous experiments in lab-scale cylindrical containers have shown that, owing to the excitation of super-harmonics, diverse dynamics are observable in certain driving-frequency range. Among these super-harmonics, the double-crest wave dynamics is particularly relevant. We formalize here a weakly nonlinear (WNL) analysis via multiple timescale method, leading to amplitude equation suitable to describe such a super-harmonic dynamics. The WNL prediction is shown to be in fairly good agreement with previous experimental measurements. Lastly, we show how an analogous amplitude equation can be formally derived by solving asymptotically for the first super-harmonic of the forced Helmholtz-Duffing equation with small nonlinearities.   

Not Participating

Objects moving at the surface of water thanks to a cyclic propulsion often travel at a constantly changing velocity. This talk focuses on the consequence of such unsteadiness on the wave resistance.

The average wave drag in unsteady motion is studied experimentally with force measurements, and described by an extended version of Havelock's theory. Towing hulls of size L at sinusoidal speed, the mean drag is measured for different amplitudes, frequencies of the fluctuating velocity, as well as different Froude numbers associated with the mean velocity (Fr=U/√(gL) ).

Depending on the Froude number, the wave drag is either increased or decreased by velocity fluctuations and depends linearly on the square of their amplitude. The effect is maximum for a resonance frequency identified as the Wehausen frequency, scaling like the inverse of the Froude number Ω ∝ 1/Fr. These results are rationalized on the basis of a theoretical framework for the unsteady wave drag.   

Transient total absoprtion for water waves : a two port setup

We show, experimentally, the possibility to observe a transient total absorption of a wave exciting scattering zeros at a complex frequencies in a two ports setup. Those scattering zeros are accessible sending an incident wave with a temporal shape envelop (divergent exponential) toward a resonant cavity. The transient total absorption leads to the capacity to store wave energy in a cavity and to release it when the incident wave signal is stopped. This idea, first introduced in optics and named coherent virtual absorption CVA, is applied here in water waves physics. To obtain CVA, a one port system is used inducing that the scattered wave (reflected wave) is always superimposed to the incident wave. In the present study, we would like to extend this idea and to obtain situation where there is a part without incident wave. To do so, we use a two ports system and we implement a virtual barrier : a system where the transmission can be tuned to zero due to temporal shaping of the incident wave. Choosing the right cavity geometry, the scattering zeros corresponding to the transmission and the reflection can occured at the same complex frequency leading to transient total absorption. Considering a lossless system, all the incident energy is stored and then released through the two ports when the excitation of the cavity by the incident wave is stopped. Experimentally, only a part of the stored energy is released (the other part is dissipated in the cavity), but we show that the concept of transient total absportion is still robust in lossy system.    

Hydrodynamic modelling and optimisation of flexible oscillating wave surge converters, comparison with rigid-motion devices.

Oscillating wave surge converters (OWSCs) are wave energy devices which predominantly exploit the horizontal wave-induced fluid motion. This work explores the hydrodynamic modelling and optimisation of flexible OWSCs, similar to seaweed or kelp, arranged in periodic rows. The hydroelastic problem is solved numerically, based on an eigenfunction expansion method, hence generalising previous works on rigid devices. The relative merits of OWSCs with flexible vs rigid modes of deformation are assessed. Optimisation of the deformation mode shape to reduce drag-induced losses is discussed.   

Helmholtz resonator analogue for water waves

We present a theoretical and experimental study of a resonator of the Helmholtz type for the wave control. An experimental demonstration of the shielding effect by a belt made of evenly distributed resonators is given. We then provide in-depth analysis of the Fano resonance resulting from the interference between the dock scattering (the background) and the resonant cavity scattering. This is done thanks to space–time resolved experiments which provides the complex valued scattering coefficients and amplitude within the resonator. We provide a one-dimensional model derived in the shallow water regime owing to asymptotic analysis. The model contains the two ingredients of the Fano resonance and allows us to exhibit the damping due to leakage. When adding heuristically the damping due to losses, it reproduces the main features of the resonance observed experimentally.