Parametrically excited water surface ripples as ensembles of oscillons

Acoustic, Phononic, Brillouin Light Scattering and Faraday Wave-Based Frequency Combs: Physical Foundations and Applications

Frequency combs (FCs)-spectra containing equidistant coherent peaks-have enabled researchers and engineers to measure the frequencies of complex signals with high precision, thereby revolutionising the areas of sensing, metrology and communications and also benefiting the fundamental science. Although mostly optical FCs have found widespread applications thus far, in general FCs can be generated using waves other than light. Here, we review and summarise recent achievements in the emergent field of acoustic frequency combs (AFCs), including phononic FCs and relevant acousto-optical, Brillouin light scattering and Faraday wave-based techniques that have enabled the development of phonon lasers, quantum computers and advanced vibration sensors. In particular, our discussion is centred around potential applications of AFCs in precision measurements in various physical, chemical and biological systems in conditions where using light, and hence optical FCs, faces technical and fundamental limitations, which is, for example, the case in underwater distance measurements and biomedical imaging applications. This review article will also be of interest to readers seeking a discussion of specific theoretical aspects of different classes of AFCs. To that end, we support the mainstream discussion by the results of our original analysis and numerical simulations that can be used to design the spectra of AFCs generated using oscillations of gas bubbles in liquids, vibrations of liquid drops and plasmonic enhancement of Brillouin light scattering in metal nanostructures. We also discuss the application of non-toxic room-temperature liquid-metal alloys in the field of AFC generation.

Excitation of Faraday-like body waves in vibrated living earthworms

Biological cells and many living organisms are mostly made of liquids and therefore, by analogy with liquid drops, they should exhibit a range of fundamental nonlinear phenomena such as the onset of standing surface waves. Here, we test four common species of earthworm to demonstrate that vertical vibration of living worms lying horizontally on a flat solid surface results in the onset of subharmonic Faraday-like body waves, which is possible because earthworms have a hydrostatic skeleton with a flexible skin and a liquid-filled body cavity. Our findings are supported by theoretical analysis based on a model of parametrically excited vibrations in liquid-filled elastic cylinders using material parameters of the worm's body reported in the literature. The ability to excite nonlinear subharmonic body waves in a living organism could be used to probe, and potentially to control, important biophysical processes such as the propagation of nerve impulses, thereby opening up avenues for addressing biological questions of fundamental impact.

Surface waves control bacterial attachment and formation of biofilms in thin layers

Formation of bacterial biofilms on solid surfaces within a fluid starts when bacteria attach to the substrate. Understanding environmental factors affecting the attachment and the early stages of the biofilm development will help develop methods of controlling the biofilm growth. Here, we show that biofilm formation is strongly affected by the flows in thin layers of bacterial suspensions controlled by surface waves. Deterministic wave patterns promote the growth of patterned biofilms, while wave-driven turbulent motion discourages patterned attachment of bacteria. Strong biofilms form under the wave antinodes, while inactive bacteria and passive particles settle under nodal points. By controlling the wavelength, its amplitude, and horizontal mobility of the wave patterns, one can shape the biofilm and either enhance the growth or discourage the formation of the biofilm. The results suggest that the deterministic wave-driven transport channels, rather than hydrodynamic forces acting on microorganisms, determine the preferred location for the bacterial attachment.

Spatial heterogeneity may form an inverse camel shaped Arnol'd tongue in parametrically forced oscillations

Frequency locking in forced oscillatory systems typically organizes in "V"-shaped domains in the plane spanned by the forcing frequency and amplitude, the so-called Arnol'd tongues. Here, we show that if the medium is spatially extended and monotonically heterogeneous, e.g., through spatially dependent natural frequency, the resonance tongues can also display "U" and "W" shapes; we refer to the latter as an "inverse camel" shape. We study the generic forced complex Ginzburg-Landau equation for damped oscillations under parametric forcing and, using linear stability analysis and numerical simulations, uncover the mechanisms that lead to these distinct resonance shapes. Additionally, we study the effects of discretization by exploring frequency locking of oscillator chains. Since we study a normal-form equation, the results are model-independent near the onset of oscillations and, therefore, applicable to inherently heterogeneous systems in general, such as the cochlea. The results are also applicable to controlling technological performances in various contexts, such as arrays of mechanical resonators, catalytic surface reactions, and nonlinear optics.

Harmonic and subharmonic waves on the surface of a vibrated liquid drop

Liquid drops and vibrations are ubiquitous in both everyday life and technology, and their combination can often result in fascinating physical phenomena opening up intriguing opportunities for practical applications in biology, medicine, chemistry, and photonics. Here we study, theoretically and experimentally, the response of pancake-shaped liquid drops supported by a solid plate that vertically vibrates at a single, low acoustic range frequency. When the vibration amplitudes are small, the primary response of the drop is harmonic at the frequency of the vibration. However, as the amplitude increases, the half-frequency subharmonic Faraday waves are excited parametrically on the drop surface. We develop a simple hydrodynamic model of a one-dimensional liquid drop to analytically determine the amplitudes of the harmonic and the first superharmonic components of the linear response of the drop. In the nonlinear regime, our numerical analysis reveals an intriguing cascade of instabilities leading to the onset of subharmonic Faraday waves, their modulation instability, and chaotic regimes with broadband power spectra. We show that the nonlinear response is highly sensitive to the ratio of the drop size and Faraday wavelength. The primary bifurcation of the harmonic waves is shown to be dominated by a period-doubling bifurcation, when the drop height is comparable with the width of the viscous boundary layer. Experimental results conducted using low-viscosity ethanol and high-viscocity canola oil drops vibrated at 70Hz are in qualitative agreement with the predictions of our modeling.

Experimental analysis of one-dimensional Faraday waves on a liquid layer subjected to horizontal vibrations

In this paper, we experimentally show the synchronous (harmonic) nature of the primary surface waves formed on a layer of water (∼1 mm) pinned to a glass substrate and subjected to horizontal (lateral) vibrations. With well-controlled experiments, we attenuated cross-waves and studied the primary standing waves in a one-dimensional wave configuration, with a high precision mechanical vibrator, capable of generating a range of forcing frequencies (100–500 Hz) and amplitudes (1–5 µm). We demonstrate that the emergence of instability (in the form of standing waves) depends upon the forcing amplitude and frequency and the average thickness of the liquid layer. Experiments reveal that the surface remains stable for sufficiently thin and thick layers of the liquid, while instability appears for thicknesses in between the two mentioned lower and upper limits. We show and analyze that, for the average liquid thickness of h = 1.5 mm, asymmetric modes of oscillations appear on the liquid surface; however, with a change in the film thickness and length of the surface profile, symmetric modes may occur as well (h = 2 mm). The problem studied here, i.e., a liquid film with pinned contact lines subjected to horizontal vibrations, shows some of the characteristics of an infinitely extended lateral liquid film, a liquid layer in a container with walls, and a sessile droplet.

Switching of the harmonic order in free-electron lasers by controlling the density modulation of an electron bunch

It was demonstrated that harmonic order in free-electron laser (FEL) oscillations could be switched by adjusting the dispersive gap of the optical klystron ETLOK-III in the storage ring NIJI-IV. The effective gains for the fundamental and third-harmonic FEL oscillations were evaluated and it was confirmed that the FEL oscillated at the order of the harmonic with the higher effective gain. The ratio between the effective gain for the fundamental and that for the third harmonic was controlled by the dispersive gap. It was also demonstrated that a spectral measurement of the FEL-based Compton scattering X-ray beam was effective for directly observing the switching of the harmonic order. These results contribute to the development of higher-harmonic FEL oscillations suppressing the fundamental FEL oscillation in the extreme ultraviolet and X-ray regions.

Electron-bunch lengthening on higher-harmonic oscillations in storage-ring free-electron lasers

The influence of higher-harmonic free-electron laser (FEL) oscillations on an electron beam have been studied by measuring its bunch length at the NIJI-IV storage ring. The bunch length and the lifetime of the electron beam were measured, and were observed to have become longer owing to harmonic lasing, which is in accord with the increase of the FEL gain. It was demonstrated that the saturated FEL power could be described by the theory of bunch heating, even for the harmonic lasing. Cavity-length detuning curves were measured for the harmonic lasing, and it was found that the width of the detuning curve was proportional to a parameter that depended on the bunch length. These experimental results will be useful for developing compact resonator-type FELs by using higher harmonics in the extreme-ultraviolet and the X-ray regions.

Wave-based liquid-interface metamaterials

The control of matter motion at liquid–gas interfaces opens an opportunity to create two-dimensional materials with remotely tunable properties. In analogy with optical lattices used in ultra-cold atom physics, such materials can be created by a wave field capable of dynamically guiding matter into periodic spatial structures. Here we show experimentally that such structures can be realized at the macroscopic scale on a liquid surface by using rotating waves. The wave angular momentum is transferred to floating micro-particles, guiding them along closed trajectories. These orbits form stable spatially periodic patterns, the unit cells of a two-dimensional wave-based material. Such dynamic patterns, a mirror image of the concept of metamaterials, are scalable and biocompatible. They can be used in assembly applications, conversion of wave energy into mean two-dimensional flows and for organising motion of active swimmers.

Here, Francois et al. propose a method of remotely shaping particle trajectories by using rotating waves on a liquid gas interface. The superposition of orthogonal standing waves creates angular momentum which is transferred from waves to floating microparticles, guiding them along closed trajectories.

Wave-particle interaction in the Faraday waves

Wave motion in disordered Faraday waves is analysed in terms of oscillons or quasi-particles. The motion of these oscillons is measured using particle tracking tools and it is compared with the motion of fluid particles on the water surface. Both the real floating particles and the oscillons, representing the collective fluid motion, show Brownian-type dispersion exhibiting ballistic and diffusive mean squared displacement at short and long times, respectively. While the floating particles motion has been previously explained in the context of two-dimensional turbulence driven by Faraday waves, no theoretical description exists for the random walk type motion of oscillons. It is found that the r.m.s velocity ⟨μ̃(osc)⟩(rms) of oscillons is directly related to the turbulent r.m.s. velocity ⟨μ̃⟩(rms) of the fluid particles in a broad range of vertical accelerations. The measured ⟨μ̃(osc)⟩(rms) accurately explains the broadening of the frequency spectra of the surface elevation observed in disordered Faraday waves. These results suggest that 2D turbulence is the driving force behind both the randomization of the oscillons motion and the resulting broadening of the wave frequency spectra. The coupling between wave motion and hydrodynamic turbulence demonstrated here offers new perspectives for predicting complex fluid transport from the knowledge of wave field spectra and vice versa.

Inhibition of wave-driven two-dimensional turbulence by viscoelastic films of proteins

To model waves, surface flows, and particle dispersion at the air-water interface one needs to know the essential mechanisms affecting the fluid motion at the surface. We show that a thin film (less than 10-nm thick) of adsorbed protein dramatically affects two-dimensional turbulence generated by Faraday waves at the fluid surface. Extremely low concentrations (≈1 ppm) of soluble proteins form a strong viscoelastic layer which suppresses turbulent diffusion at the surface, changes wave patterns, and shows strong resilience to the wave-induced droplet generation. Surface shear properties of the film play a key role in this phenomenon by inhibiting the creation of vorticity at the surface. The addition of surfactants, on the other hand, destroys the nanolayer and restores the fluid mobility.

Observations of highly localized oscillons with multiple crests and troughs

Two types of stable, highly localized Faraday resonant standing waves with multiple crests and troughs are observed in an ethanol-water solution partly filled in a Hele-Shaw cell vertically oscillated with a single frequency. Systematical experiments are performed to investigate the properties of these oscillons. It is found that the wave height of these oscillons is independent of fluid depth from 1 to 5 cm. In particular, some experiments are performed to indicate the high localization of the oscillons, which suggests that these oscillons may be regarded as a combination of the two elementary oscillons discovered by Rajchenbach et al. [Phys. Rev. Lett. 107, 024502 (2011)], for instance, (2,3)=(1,1)+(1,2), where (m,n) denotes an oscillon with m crests and n troughs. So, our experiments also reveal an elegant "arithmetic" of these oscillons. These experimental phenomena are helpful to deepen and enrich our understanding about Faraday waves.

Dissipation-driven behavior of nonpropagating hydrodynamic solitons under confinement

We have identified a physical mechanism that rules the confinement of nonpropagating hydrodynamic solitons. We show that thin boundary layers arising on walls are responsible for a jump in the local damping. The outcome is a weak dissipation-driven repulsion that determines decisively the solitons' long-time behavior. Numerical simulations of our model are consistent with experiments. Our results uncover how confinement can generate a localized distribution of dissipation in out-of-equilibrium systems. Moreover, they show the preponderance of such a subtle effect in the behavior of localized structures. The reported results should explain the dynamic behavior of other confined dissipative systems.

Dark- and bright-rogue-wave solutions for media with long-wave-short-wave resonance

Exact explicit rogue-wave solutions of intricate structures are presented for the long-wave-short-wave resonance equation. These vector parametric solutions feature coupled dark- and bright-field counterparts of the Peregrine soliton. Numerical simulations show the robustness of dark and bright rogue waves in spite of the onset of modulational instability. Dark fields originate from the complex interplay between anomalous dispersion and the nonlinearity driven by the coupled long wave. This unusual mechanism, not available in scalar nonlinear wave equation models, can provide a route to the experimental realization of dark rogue waves in, for instance, negative index media or with capillary-gravity waves.

Inverse energy cascade and emergence of large coherent vortices in turbulence driven by Faraday waves

We report the generation of large coherent vortices via inverse energy cascade in Faraday wave driven turbulence. The motion of floaters in the Faraday waves is three dimensional, but its horizontal velocity fluctuations show unexpected similarity with two-dimensional turbulence. The inverse cascade is detected by measuring frequency spectra of the Lagrangian velocity, and it is confirmed by computing the third moment of the horizontal velocity fluctuations. This is observed in deep water in a broad range of wavelengths and vertical accelerations. The results broaden the scope of recent findings on Faraday waves in thin layers [A. von Kameke et al., Phys. Rev. Lett. 107, 074502 (2011)].

Energy transport in weakly nonlinear wave systems with narrow frequency band excitation

A novel discrete model (D model) is presented describing nonlinear wave interactions in systems with small and moderate nonlinearity under narrow frequency band excitation. It integrates in a single theoretical frame two mechanisms of energy transport between modes, namely, intermittency and energy cascade, and gives the conditions under which each regime will take place. Conditions for the formation of a cascade, cascade direction, conditions for cascade termination, etc., are given and depend strongly on the choice of excitation parameters. The energy spectra of a cascade may be computed, yielding discrete and continuous energy spectra. The model does not require statistical assumptions, as all effects are derived from the interaction of distinct modes. In the example given-surface water waves with dispersion function ω(2)=gk and small nonlinearity-the D model predicts asymmetrical growth of side-bands for Benjamin-Feir instability, while the transition from discrete to continuous energy spectrum, excitation parameters properly chosen, yields the saturated Phillips' power spectrum ~g(2)ω(-5). The D model can be applied to the experimental and theoretical study of numerous wave systems appearing in hydrodynamics, nonlinear optics, electrodynamics, plasma, convection theory, etc.

Oscillon dynamics and rogue wave generation in Faraday surface ripples

We report new experimental results which suggest that the generation of extreme wave events in the Faraday surface ripples is related to the increase in the horizontal mobility of oscillating solitons (oscillons). The analysis of the oscillon trajectories in a horizontal plane shows that at higher vertical acceleration, oscillons move chaotically, merge and form enclosed areas on the water surface. The probability of the formation of such craters, which precede large wave events, increases with the increase in horizontal mobility.

Ejection of uniform micrometer-sized droplets from Faraday waves on a millimeter-sized water drop

This Letter reports the first observation and theoretical analysis of a new phenomenon: one large spherical water drop ejecting simultaneously a very large number of monodisperse microdroplets. An ultrasonic nozzle with multiple-Fourier horns in resonance enables controlled excitation of megahertz Faraday waves on the free water surface. The temporal instability of such waves leads to the ejection of 3.5-4.4  μm monodisperse droplets at a high rate (>4.0×10(7)  droplets/sec). This is in stark contrast to the Rayleigh-Plateau instability, which ejects one droplet at a time.

Propagating solitons generated by localized perturbations on the surface of deep water

We report experimental evidence of the propagating capillary solitary waves generated by a localized water surface perturbation. Solitons are formed at the air-water interface with a solid plunger and then propagate with velocities proportional to their amplitudes. The shape of the forward front of such solitons is independent of the plunger shape and is given by the hyperbolic secant profile. We find that the nonlinearity of capillary waves is responsible for a small dispersion in the capillary wave group velocity and the soliton existence. This dispersion can be further reduced by adding minute concentrations of proteins to water.