Nonlinear Pattern Formation of Faraday Waves

Binks, DJ; Water, Willem van de

doi:10.1103/physrevlett.78.4043

Cited by 144 publications

(90 citation statements)

References 9 publications

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“…23,24,26,30,36,46,47 Thickness-mode PZT transducers can be fabricated to effectively generate motion from a few kilohertz to a few megahertz. The thickness-polarized, faceelectroded device used for this work (C-203, Fuji Ceramics, Tokyo, Japan, with Cr−Ag electrodes and dimensions as shown) was driven at its fundamental thickness-mode resonance at 500 kHz ± 2%; the variation is due to ambient temperature changes.…”

Section: ■ Generating and Measuring Microscale Capillary Wavesmentioning

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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Section: ■ Generating and Measuring Microscale Capillary Wavesmentioning

confidence: 99%

Microscale Capillary Wave Turbulence Excited by High Frequency Vibration

Blamey

Yeo²,

Friend

2013

Langmuir

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“…This system has the advantage of fairly short time scales in combination with a very rich bifurcation behavior. During the last two decades the focus in this field was on nonlinear pattern selection [1][2][3][4][5], secondary instabilities [6], the transition towards chaos [7], droplet ejection [8] and stokes drift [9]. However, due to the parametric drive mechanism the mathematical description of the Faraday experiment is more complicated as compared to RBC or TCF and the quantitative understanding is less advanced yet.…”

Section: Introductionmentioning

confidence: 99%

Amplitude measurements of Faraday waves

et al. 2001

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A light reflection technique is used to measure quantitatively the surface elevation of Faraday waves. The performed measurements cover a wide parameter range of driving frequencies and sample viscosities. In the capillary wave regime the bifurcation diagrams exhibit a frequency independent scaling proportional to the wavelength. We also provide numerical simulations of the full Navier-Stokes equations, which are in quantitative agreement up to supercritical drive amplitudes of ε ≃ 20%. The validity of an existing perturbation analysis is found to be limited to ε < 2.5%. PACS: 47.54.+r 47.20.Ma 47.20.Lz

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“…The hydrodynamic equations are closed by the no-slip condition at the bottom of the container, 5) and the kinematic boundary condition at the free surface of the fluid…”

Section: System and Basic Equationsmentioning

confidence: 99%

“…Though typical Faraday waves are subharmonic, the twelvefold quasi-pattern appears to be harmonic in a certain region of parameters. Binks et al have shown experimentally that the depth of the layer [4] and the excitation frequency [5] affect significantly the regions, where either rolls or hexagons or squares are observed. In [6,7,8,9] it is revealed that a two-frequency excitation leads to a great variety of wave patterns.…”

Section: Introductionmentioning

confidence: 99%

Faraday instability on viscous ferrofluids in a horizontal magnetic field: Oblique rolls of arbitrary orientation

Mekhonoshin

Lange

2002

Phys. Rev. E

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A linear stability analysis of the free surface of a horizontally unbounded ferrofluid layer of arbitrary depth subjected to vertical vibrations and a horizontal magnetic field is performed. A nonmonotonic dependence of the stability threshold on the magnetic field is found at high frequencies of the vibrations. The reasons of the decrease of the critical acceleration amplitude caused by a horizontal magnetic field are discussed. It is revealed that the magnetic field can be used to select the first unstable pattern of Faraday waves. In particular, a rhombic pattern as a superposition of two different oblique rolls can occur. A scaling law is presented which maps all data into one graph for the tested range of viscosities, frequencies, magnetic fields and layer thicknesses.

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Nonlinear Pattern Formation of Faraday Waves

Cited by 144 publications

References 9 publications

Microscale Capillary Wave Turbulence Excited by High Frequency Vibration

Microscale Capillary Wave Turbulence Excited by High Frequency Vibration

Amplitude measurements of Faraday waves

Faraday instability on viscous ferrofluids in a horizontal magnetic field: Oblique rolls of arbitrary orientation

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