Onset of oscillatory binary fluid convection in finite containers

Batiste, Oriol; Mercader, Isabel; Net, Marta; Knobloch, Edgar

doi:10.1103/physreve.59.6730

Cited by 20 publications

(34 citation statements)

References 20 publications

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“…In some models, the features of binary convection near the onset (critical temperature difference, wavenumber and frequency) have been obtained neglecting the effect of transverse walls, both in infinite extended horizontal layers often referred to as 'bulk binary mixtures' (Knobloch and Moore, 1988;Cross and Kim, 1988), and in laterally bounded domains (Batiste et al, 1999). The results obtained with these two-dimensional models are correct for wide enough containers.…”

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confidence: 57%

Onset of oscillatory binary fluid convection in three-dimensional cells

Alonso

Batiste

2004

Theor. Comput. Fluid Dyn.

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Abstract. The purpose of this work is to investigate the influence of the transverse walls on the onset of convection in a horizontal rectangular cavity of infinite length filled with a binary mixture when heated from below. For the first time we take into account the effect of the third dimension without making any approximation and considering realistic boundary conditions. In previous numerical works the width of the cell was either taken to be infinity (bulk mixtures) or different approximations usually valid in the narrow cell limit were assumed (i.e. Hele-Shaw and non-ideal Hele-Shaw approximations). The results we find show that the presence of the walls has a considerable effect on the onset of convection even for intermediate transverse aspect ratio cells. They also show that the approximations generally assumed fail to reproduce the correct behaviour of the critical parameters in an important range of aspect ratio values when the primary bifurcation is oscillatory. We have compared the critical values of the Rayleigh number and the frequency that we obtain with those reported in the literature (Ohlsen et al., 1990) and we find a quantitative agreement within the experimental error.

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confidence: 57%

Onset of oscillatory binary fluid convection in three-dimensional cells

Alonso

Batiste

2004

Theor. Comput. Fluid Dyn.

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“…This phenomenology was also described for stress-free boundary conditions in the pioneering numerical work of Zhang & Busse (1987). The interchange of like-parity modes is analysed in detail for the onset of oscillatory binary fluid convection in Batiste et al (1999). According to these authors, the interchange takes place at a resonant double-Hopf bifurcation (surely hidden by the critical non-resonant double-Hopf bifurcations), where the crossing neutral curves become tangent.…”

Section: Dependence Of Low-prandtl-number Flows On the Ekman Numbermentioning

confidence: 99%

On the onset of low-Prandtl-number convection in rotating spherical shells: non-slip boundary conditions

Net¹,

García²,

Sánchez³

2008

J. Fluid Mech.

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Accurate numerical computations of the onset of thermal convection in wide rotating spherical shells are presented. Low-Prandtl-number (σ ) fluids, and non-slip boundary conditions are considered. It is shown that at small Ekman numbers (E), and very low σ values, the well-known equatorially trapped patterns of convection are superseded by multicellular outer-equatorially-attached modes. As a result, the convection spreads to higher latitudes affecting the body of the fluid, and increasing the internal viscous dissipation. Then, from E < 10 −5 , the critical Rayleigh number (R c ) fulfils a power-law dependence R c ∼ E −4/3 , as happens for moderate and high Prandtl numbers. However, the critical precession frequency (|ω c |) and the critical azimuthal wavenumber (m c ) increase discontinuously, jumping when there is a change of the radial and latitudinal structure of the preferred eigenfunction. In addition, the transition between spiralling columnar (SC), and outer-equatorially-attached (OEA) modes in the (σ , E)-space is studied. The evolution of the instability mechanisms with the parameters prevents multicellular modes being selected from σ & 0.023. As a result, and in agreement with other authors, the spiralling columnar patterns of convection are already preferred at the Prandtl number of the liquid metals. It is also found that, out of the rapidly rotating limit, the prograde antisymmetric (with respect to the equator) modes of small m c can be preferred at the onset of the primary instability.

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“…A compilation of most of the pertinent information given by recent research in double-diffusive convection in porous media can be found in the Porous Media handbook edited by Vafai 4 . For the studies concerning the Soretdriven convection in fluid we can refer to Platten and Legros 5 and to Batiste et al 6 . For binary mixtures in a porous medium we can refer to Brand and Steinberg 7,8 , to Bahloul et al 9 and to Bourich et al 10,11 .…”

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Analytical and numerical stability analysis of Soret-driven convection in a horizontal porous layer

2007

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We present an analytical and numerical stability analysis of Soret-driven convection in a porous cavity saturated by a binary fluid. Both the mechanical equilibrium solution and the mono-cellular flow obtained for particular ranges of the physical parameters of the problem are considered. The porous cavity, bounded by horizontal infinite or finite boundaries, is heated from below or from above. The two horizontal plates are maintained at different constant temperatures while no mass flux is imposed. The influence of the governing parameters and more particularly the role of the separation ratio, ψ , characterizing the Soret effect and the normalized porosity, ε , are investigated theoretically and numerically.From the linear stability analysis, we find that the equilibrium solution loses its stability via a stationary bifurcation or a Hopf bifurcation depending on the separation ratio and the 2 normalized porosity of the medium. The role of the porosity is important, when it decreases, the stability of the equilibrium solution is reinforced.

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Onset of oscillatory binary fluid convection in finite containers

Cited by 20 publications

References 20 publications

Onset of oscillatory binary fluid convection in three-dimensional cells

Onset of oscillatory binary fluid convection in three-dimensional cells

On the onset of low-Prandtl-number convection in rotating spherical shells: non-slip boundary conditions

Analytical and numerical stability analysis of Soret-driven convection in a horizontal porous layer

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