Turbulent parametric surface waves

Snouck, D Daniel; Westra, MT Mark-Tiele; Water, Willem van de

doi:10.1063/1.3075951

Cited by 34 publications

(43 citation statements)

References 27 publications

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“…However, in these previous works, peaks and their harmonics (related to the parametric forcing) are observed on the spectrum with maximal amplitudes decreasing as a frequency powerlaw (Snouck et al, 2009;. The frequency-spectrum exponent estimated in that way is thus not very accurate.…”

Section: Fluctuations Of the Energy Flux In Wave Turbulence 59mentioning

confidence: 91%

“…(2.1) and (2.2) are related through the dispersion relation ω = W (k). This has been checked only recently by comparison of the spatial and temporal spectra determined in experiments of waves on elastic plates (Cobelli et al, 2009) and capillary-gravity surface waves (Snouck et al, 2009;Herbert et al, 2010). A fair agreement has been found in the former case whereas a more complex structure in the spatio-temporal domain exists in the latter ones.…”

Section: Introductionmentioning

confidence: 99%

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Fluctuations of Energy Flux in Wave Turbulence

et al. 2008

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The key governing parameter of wave turbulence is the energy flux that drives the waves and cascades to small scales through nonlinear interactions. In the inertial range, the energy flux is conserved across the scales, and is assumed to be constant in most theoretical approaches. It is only recently that measurements of the injected power into wave turbulence have been performed at the scale of the wave maker (integral scale). In this review, we focus on the statistical properties of the injected power fluctuations in gravity-capillary wave turbulence in a stationary regime. Fluctuations of the injected power have been found much larger than their mean value. In addition, events related to a negative injected power, i.e. an instantaneous reversed energy flux, occur with a fairly large probability. Both features are well described using a Langevin type equation. Finally, we consider the experimental dependence of the scaling law of the wave spectrum with the mean injected power and discuss possible reasons for the discrepancy with weak turbulence theory.

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Section: Fluctuations Of the Energy Flux In Wave Turbulence 59mentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Fluctuations of Energy Flux in Wave Turbulence

et al. 2008

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“…The strange behavior seen by Li et al (2008) in particle collection within sessile droplets, atop fluid free surfaces by Bosch and van de Water (1993), Huepe et al (2006), , and the shift of the frequency of response in atomization from the frequency of excitation by 5 orders of magnitude by Qi et al (2008) are but three examples. By using the analysis techniques from other areas, for example, the work by Barashenkov et al (2002) in applying results from random matrix theory and wave-packet dynamics, the work by Huang et al (1999) to use the Hilbert transform instead of the popular Fourier transform because it is far more appropriate for nonlinear systems, better models of the free surface deformation phenomena such as the Camassa-Holm equations (over the older Korteweg-de Vries equations) discussed by Constantin and Lannes (2009), and improving experimental methods such as those used by Snouck et al (2009), a framework is being built to underpin and thoroughly explain Faraday wave mechanics, and these approaches may be useful in related areas across acoustofluidics.…”

Section: A Improvement Of Analysis Techniquesmentioning

confidence: 99%

Microscale acoustofluidics: Microfluidics driven via acoustics and ultrasonics

2011

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This article reviews acoustic microfluidics: the use of acoustic fields, principally ultrasonics, for application in microfluidics. Although acoustics is a classical field, its promising, and indeed perplexing, capabilities in powerfully manipulating both fluids and particles within those fluids on the microscale to nanoscale has revived interest in it. The bewildering state of the literature and ample jargon from decades of research is reorganized and presented in the context of models derived from first principles. This hopefully will make the area accessible for researchers with experience in materials science, fluid mechanics, or dynamics. The abundance of interesting phenomena arising from nonlinear interactions in ultrasound that easily appear at these small scales is considered, especially in surface acoustic wave devices that are simple to fabricate with planar lithography techniques common in microfluidics, along with the many applications in microfluidics and nanofluidics that appear through the literature.

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“…36,37 Such a broad-band power-law spectrum 12 is a strong indicator of turbulence-like nonlinear behavior in a system. 22 Linear stability theory and similar approaches are therefore inappropriate under these circumstances, unfortunately, because they cannot accommodate the spatiotemporal exchanges in energy exhibited by these nonlinear systems. Kolmogorov 38 first proposed a Rayleigh−Jeans energy spectrum with respect to wavenumber for isotropic hydrodynamic turbulence; the concept has since been applied to wavelike systems, where it has come to be known as wave turbulence.…”

Section: ■ Introductionmentioning

confidence: 99%

Microscale Capillary Wave Turbulence Excited by High Frequency Vibration

Blamey

Yeo²,

Friend

2013

Langmuir

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Low frequency (O(10 Hz−10 kHz)) vibration excitation of capillary waves has been extensively studied for nearly two centuries. Such waves appear at the excitation frequency or at rational multiples of the excitation frequency through nonlinear coupling as a result of the finite displacement of the wave, most often at one-half the excitation frequency in so-called Faraday waves and twice this frequency in superharmonic waves. Less understood, however, are the dynamics of capillary waves driven by high-frequency vibration (>O(100 kHz)) and small interface length scales, an arrangement ideal for a broad variety of applications, from nebulizers for pulmonary drug delivery to complex nanoparticle synthesis. In the few studies conducted to date, a marked departure from the predictions of classical Faraday wave theory has been shown, with the appearance of broadband capillary wave generation from 100 Hz to the excitation frequency and beyond, without a clear explanation. We show that weak wave turbulence is the dominant mechanism in the behavior of the system, as evident from wave height frequency spectra that closely follow the Rayleigh−Jeans spectral response η ≈ ω −17/12 as a consequence of a period-halving, weakly turbulent cascade that appears within a 1 mm water drop whether driven by thickness-mode or surface acoustic Rayleigh wave excitation. However, such a cascade is one-way, from low to high frequencies. The mechanism of exciting the cascade with high-frequency acoustic waves is an acoustic streaming-driven turbulent jet in the fluid bulk, driving the fundamental capillary wave resonance through the well-known coupling between bulk flow and surface waves. Unlike capillary waves, turbulent acoustic streaming can exhibit subharmonic cascades from high to low frequencies; here it appears from the excitation frequency all the way to the fundamental modes of the capillary wave at some four orders of magnitude in frequency less than the excitation frequency, enabling the capillary weakly turbulent wave cascade to form from the fundamental capillary wave upward.

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Turbulent parametric surface waves

Cited by 34 publications

References 27 publications

Fluctuations of Energy Flux in Wave Turbulence

Fluctuations of Energy Flux in Wave Turbulence

Microscale acoustofluidics: Microfluidics driven via acoustics and ultrasonics

Microscale Capillary Wave Turbulence Excited by High Frequency Vibration

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