Asymptotic study and weakly nonlinear analysis at the onset of Rayleigh–Bénard convection in Hele–Shaw cell

Aniss, Saı̈d; Souhar, M.; Brancher, Jean-Pierre

doi:10.1063/1.868568

Cited by 35 publications

(11 citation statements)

References 12 publications

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“…They found that for low Prandtl number fluids, modulations in gravity and temperature produce the same flow field both in structure and in magnitude. Clever et al [8], Aniss et al [9,10], Rogers et al [11], Bhadauria et al [12] showed that the gravitational modulation, which can be realized by vertically oscillating a horizontal liquid layer, acts on the entire volume of liquid and may have a stabilizing or destabilizing effect depending on the amplitude and frequency of the forcing. Boulal et al [13] focused attention on the influence of a quasi-periodic gravitational modulation on the convective instability threshold.…”

Section: Introductionmentioning

confidence: 99%

Effect of internal-heating on weakly non-linear stability analysis of Rayleigh–Bénard convection under g-jitter

Bhadauria¹,

Hashim²,

Siddheshwar³

2013

International Journal of Non-Linear Mechanics

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a b s t r a c tIn this paper, we study the combined effect of internal-heating and time-periodic gravity modulation on thermal instability in a viscous fluid layer, heated from below. The time-periodic gravity modulation, considered in this problem can be realized by vertically oscillating the fluid layer. A weak non-linear stability analysis has been performed by using power series expansion in terms of the amplitude of gravity modulation, which is assumed to be small. The Nusselt number has been obtained in terms of the amplitude of convection which is governed by the non-autonomous Ginzburg-Landau equation derived for the stationary mode of convection. Effects of various parameters such as internal Rayleigh number, Prandtl number, and amplitude and frequency of gravity modulation have been analysed on heat transport. It is found that the response of the convective system to the internal Rayleigh number is destabilizing. Further, it is found that the heat transport can be controlled by suitably adjusting the external parameters of the system.

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Section: Introductionmentioning

confidence: 99%

Effect of internal-heating on weakly non-linear stability analysis of Rayleigh–Bénard convection under g-jitter

Bhadauria¹,

Hashim²,

Siddheshwar³

2013

International Journal of Non-Linear Mechanics

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“…In the Hele-Shaw approximation, the order of magnitude of the Prandtl number Pr in the system of equations (4)- (8) has been discussed in [29]. In what follows, we distinguish two different formulations depending on the order of magnitude of the Prandtl number.…”

Section: Asymptotic Study and Stabilitymentioning

confidence: 99%

“…To introduce a perturbation parameter involving only the aspect ratio of the cell, ǫ, we perform a dimensional analysis by means of an appropriate choice of scales used in convection problems in Hele-Shaw cell [29]. Thus, the time is scaled by d 2 /κ, the coordinates (x, y, z) are scaled…”

Section: Formulationmentioning

confidence: 99%

Effect of quasi-periodic gravitational modulation on the convective instability in Hele-Shaw cell

Boulal

Aniss

Belhaq

et al. 2008

International Journal of Non-Linear Mechanics

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The aim of the present paper is to examine the effect of a quasi-periodic gravitational modulation on the onset of convective instability in Hele-Shaw cell. The quasi-periodic modulation considered here consists in a modulation having two incommensurate frequencies. This study is an extension of a previous work by Aniss et al. [10] in which only a periodic gravitational modulation was considered. We have shown that for P r = O(1) or P r >> 1, the gravitational modulation has no effect on the convective threshold as expected. However, for P r = O(ǫ 2 ), it turns out that a modulation with two incommensurate frequencies has a stabilizing or a destabilizing effect strongly depending on the frequencies ratio.

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“…Under these assumptions and as in the traditional HeleShaw flow, where the aspect ratio of the cell is considered smaller than unity, a first approximation of the base flow, [17,18], is obtained from the system of equations (1)- (2) as follows…”

Section: Base Flow Solutionmentioning

confidence: 99%

Interfacial instability in a time-periodic rotating Hele-Shaw Cell

Bouchgl

Aniss

Souhar

et al. 2014

MATEC Web of Conferences

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Abstract. The effect of time-periodic angular velocity on the interfacial instability of two immiscible, viscous fluids of different densities and confined in an annular Hele-Shaw cell is investigated. An inviscid linear stability analysis of the viscous and time dependent basic flow leads to a periodic Mathieu oscillator describing the evolution of the interfacial amplitude. We show that the relevant parameters that control the interface are the Bond number, viscosity ratio, Atwood number and the frequency number.

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Asymptotic study and weakly nonlinear analysis at the onset of Rayleigh–Bénard convection in Hele–Shaw cell

Cited by 35 publications

References 12 publications

Effect of internal-heating on weakly non-linear stability analysis of Rayleigh–Bénard convection under g-jitter

Effect of internal-heating on weakly non-linear stability analysis of Rayleigh–Bénard convection under g-jitter

Effect of quasi-periodic gravitational modulation on the convective instability in Hele-Shaw cell

Interfacial instability in a time-periodic rotating Hele-Shaw Cell

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