Faraday instability: Linear analysis for viscous fluids

Beyer, Julian; Friedrich, R.

doi:10.1103/physreve.51.1162

Cited by 50 publications

(42 citation statements)

References 5 publications

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“…This is in contrast with other mean flows that appear in, for example, strictly inviscid water waves , Poiseuille flow (Davey, Hocking & Stewartson 1974), and Rayleigh-Benard convection (Zippelius & Siggia 1982). Most theoretical studies in the viscous limit (Beyer & Friedrich 1995;Müller et al 1997;Cerda & Tirapegui 1998;Mancebo & Vega 2002) are linear. Nonlinear terms have been considered in the viscous limit only by Chen & Viñals (1999), who in fact considered three-dimensional deep containers, but ignored both spatial modulation and the mean flow.…”

Section: Introductionmentioning

confidence: 91%

Viscous Faraday waves in two-dimensional large-aspect-ratio containers

Mancebo

Vega

2006

J. Fluid Mech.

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A weakly nonlinear analysis of one-dimensional viscous Faraday waves in twodimensional large-aspect-ratio containers is presented. The surface wave is coupled to a viscous long-wave mean flow that is slaved to the free-surface deformation. The relevant Ginzburg-Landau-like amplitude equations are derived from first principies, and can be of three different types, depending on the ratio between wavelength, depth and the viscous length. These three equations are new in the context of Faraday waves. The coefficients of these equations are calculated for arbitrary viscosity and compared with their counterparts in the literature for small viscosity; a discrepancy in the cubic coefficient is due to a dramatic sensitivity of this coefficient on a small wavenumber shift due to interplay between viscous effects and parametric forcing.

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Section: Introductionmentioning

confidence: 91%

Viscous Faraday waves in two-dimensional large-aspect-ratio containers

Mancebo

Vega

2006

J. Fluid Mech.

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“…We will adopt their methods below. Beyer 18 also solved the full viscous problem numerically, and with an arbitrary forcing function. Bechhoefer et al 19 compared experiments to viscous theory using the methods of Kumar and Tuckerman accounted heuristically for the effects of a finite-sized container.…”

Section: A Faraday Excitationmentioning

confidence: 99%

An experimental study of micron-scale droplet aerosols produced via ultrasonic atomization

et al. 2004

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In the last 10 years, laser-driven fusion experiments performed on atomic clusters of deuterium have shown a surprisingly high neutron yield per joule of input laser energy. Results indicate that the optimal cluster size for maximizing fusion events should be in the 0.01-1 m diameter range, but an appropriate source of droplets of this size does not exist. In an attempt to meet this need, we use ultrasonic atomization to generate micron-scale droplet aerosols of high average density, and we have developed and refined a reliable droplet sizing technique based on Mie scattering. Harmonic excitation of the fluid in the MHz range yields an aerosol of droplets with diameters of a few microns. The droplet diameter distribution is well-peaked and the relationship between average droplet size and forcing frequency follows an inviscid scaling law, predictable by dimensional analysis and consistent with the linear theory for Faraday excitation of an infinitely deep fluid.

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“…If we tried to obtain the whole marginal instability curve in this regime then we would obtain a non-local Mathieu equation similar to those considered by Beyer & Friedrich (1995) and Müller et al (1997). But for most valúes of the parameters in this regime, namely whenever (cf.…”

Section: Nearly Inviscid Limitsmentioning

confidence: 99%

“…There has been two types of such approximations reported. Beyer & Friedrich (1995) and Müller et al (1997) derived a non-local Mathieu equation in the nearly inviscid limit C g -• 0, the non-local term resulting from the solution in the Stokes boundary layer attached to the bottom of the container. That equation reduces to (3.4) if the forcing frequency is not too large and only monochromatic solutions are sought, but it also provides the non-monochromatic solutions considered in § 3.2.…”

Section: Some Approximations In the Literaturementioning

confidence: 99%

Faraday instability threshold in large-aspect-ratio containers

Mancebo

Vega

2002

J. Fluid Mech.

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We consider the Floquet linear problem giving the threshold acceleration for the appearance of Faraday waves in large-aspect-ratio containers, without further restrictions on the valúes of the parameters. We classify all distinguished limits for varying valúes of the various parameters and simplify the exact problem in each limit. The resulting simplified problems either admit closed-form solutions or are solved numerically by the well-known method introduced by Kumar & Tuckerman (1994). Some comparisons are made with (a) the numerical solution of the original exact problem, (b) some ad hoc approximations in the literature, and (c) some experimental results.

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Faraday instability: Linear analysis for viscous fluids

Cited by 50 publications

References 5 publications

Viscous Faraday waves in two-dimensional large-aspect-ratio containers

Viscous Faraday waves in two-dimensional large-aspect-ratio containers

An experimental study of micron-scale droplet aerosols produced via ultrasonic atomization

Faraday instability threshold in large-aspect-ratio containers

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