Thermally driven motion of strongly heated fluids

Boer, P. C. T. de

doi:10.1016/0017-9310(84)90082-6

Cited by 18 publications

(5 citation statements)

References 22 publications

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“…In Figure 9 we have redrawn their results to fit with the critical wavenumber /c c = 1.99. Koschmieder and Switzer [57] [49] while the dotted line corresponds to the experiment by Cerisier et al [43].…”

Section: Eckhaus Instabilitymentioning

confidence: 90%

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Review Article

1997

Journal of Non-Equilibrium Thermodynamics

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A review is provided of salient findings, old and recent, about Benard convection flows in a liquid layer heated from below and open to the ambient air. Instability and subsequent convective patterns past the instability threshold are the consequence of surface tension gradients acting along the open surface and by the temperature gradient maintained across the liquid layer. The onset of hexagons, rolls, squares and their relative stability is described here as well as the appearance of more complex patterns like labyrinthine convection flows. Asymptotic unsteadiness is also expected near the instability threshold as a consequence of the non-variational character of the problem, hence a precursor of space-time chaos, interfacial turbulence already possible at low Marangoni number.

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Section: Eckhaus Instabilitymentioning

confidence: 90%

“…We start with the standard incompressible fluid mechanics equations: Navier-Stokes, continuity and energy equations, that we take in the Boussinesq approximation [40][41][42][43][44]. The assumption of an undeformed open surface corresponds to the limit of strong surface tension.…”

Section: Evolution Toward Patterned Convectionmentioning

confidence: 99%

Review Article

1997

Journal of Non-Equilibrium Thermodynamics

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“…Dimensionless quantities are defined using the following scales: h for length, h 2 /χ for time, χ/h for velocity, µχ/h 2 for pressure and βh for temperature, where µ is the dynamic viscosity and χ is the thermal diffusivity. Assuming the Boussinesq approximation to be valid (Chandrasekhar 1961;Perez-Cordon & Velarde 1975;Velarde & Perez-Cordon 1976;de Boer 1984de Boer , 1986, the linearized equations and boundary conditions for the amplitudes of the normal modes with growth rate Λ and wavenumber k, exp(Λt + ikx), are (see Nield 1964) ikU + W z = 0,…”

Section: Formulation Of the Linear Stability Problemmentioning

confidence: 99%

Rayleigh–Marangoni oscillatory instability in a horizontal liquid layer heated from above: coupling and mode mixing of internal and surface dilational waves

et al. 2000

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An oscillatory instability mechanism is identified for a horizontal liquid layer with undeformable open surface heated from the air side. Although buoyancy and surface tension gradients are expected to play a stabilizing role in this situation, we show that, acting together, they may lead to the instability of the motionless state of the system. The instability is a consequence of the coupling between internal and surface waves, whose resonant interaction and resulting mode mixing are discussed. Predictions amenable to experimental test are given together with a thorough analytical and numerical study of the problem.

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“…In the present note we provide sufficient conditions for instability in the case of an infinitesimaly viscoelastic liquid layer (in the terminology used by Joseph [17,18]) with specific application to a Maxwellian and Boussinesquian fluid [19][20][21]) heated from below and subjected to a uniform and constant rotation. We show that using the viscosity function considered by Sokolov and Tanner [6], for a realistic visco-elastic fluid rotation of the container provides a clear stabilizing effect.…”

Section: Introductionmentioning

confidence: 99%