Onset of convection in an anisotropic porous medium with oblique principal axes

Tyvand, Peder A.; Storesletten, L.

doi:10.1017/s0022112091002422

Cited by 83 publications

(54 citation statements)

References 9 publications

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“…Qin and Kaloni [52] develop a non-linear energy stability analysis for thermal convection in an anisotropic porous solid when the permeability axes are orthogonal to the layer. Tyvand and Storesletten [53], however, considered an anisotropic permeability with axes inclined at an arbitrary angle to the convection layer and showed this could have a strong e ect on thermal convection behaviour. Storesletten [54] develops a similar analysis for an anisotropic thermal di usivity with axes non-orthogonal to the layer; the ÿndings here are also signiÿcantly di erent from the orthogonal case.…”

Section: Anisotropic Porous Mediamentioning

confidence: 99%

“…Storesletten [54] develops a similar analysis for an anisotropic thermal di usivity with axes non-orthogonal to the layer; the ÿndings here are also signiÿcantly di erent from the orthogonal case. Straughan and Walker [23] adopted the Tyvand and Storesletten [53] situation but allowed the density to be quadratic in temperature, i.e.…”

Section: Anisotropic Porous Mediamentioning

confidence: 99%

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Effect of anisotropic permeability on Darcy's law

Payne

Rodrigues

Straughan

2001

Math Methods in App Sciences

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SUMMARYThe concept of structural stability is discussed and brie y reviewed within the context of uid ow in porous media. Then the equations for non-Boussinesq (penetrative) convection in a porous medium with anisotropic permeability are analysed. It is shown, by deriving truly a priori estimates, that the solution exists in the natural functional framework and depends continuously on changes in the permeability. Since under appropriate circumstances the onset of thermal convection may be via Hopf bifurcation rather than stationary convection, such a priori continuous dependence estimates are of much value.

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Section: Anisotropic Porous Mediamentioning

confidence: 99%

Section: Anisotropic Porous Mediamentioning

confidence: 99%

Effect of anisotropic permeability on Darcy's law

Payne

Rodrigues

Straughan

2001

Math Methods in App Sciences

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“…The orientation of the principal axes of K are assumed to be parallel to the sides of the domain. For the situation of an arbitrary orientation of coordinate axes, the reader is referred to Tyvand and Storesletten [25]. The dynamic £uid viscosity W is taken as a constant.…”

Section: Formulationmentioning

confidence: 99%

Chaotic thermohaline convection in low-porosity hydrothermal systems

Schoofs

Spera

Hansen

1999

Earth and Planetary Science Letters

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Fluids circulate through the Earth's crust perhaps down to depths as great as 5^15 km, based on oxygen isotope systematics of exhumed metamorphic terrains, geothermal fields, mesozonal batholithic rocks and analysis of obducted ophiolites. Hydrothermal flows are driven by both thermal and chemical buoyancy; the former in response to the geothermal gradient and the latter due to differences in salinity that appear to be ubiquitous. Topographically driven flows generally become less important with increasing depth. Unlike heat, solute cannot diffuse through solid matrix. As a result, temperature perturbations advect more slowly than salinity fluctuations by the factor P, but diffuse more rapidly by the factor U/D and are so smoothed out more efficiently. Here, P is porosity, while U and D denote the thermal and chemical molecular diffusivity, respectively. Double-advective instabilities may play a significant role in solute and heat transport in the deep crust where porosities are low. We have studied the stability and dynamics of the flow as a function of P and thermal and chemical buoyancy, for situations where mechanical dispersion of solute dominates over molecular diffusion in the fluid. In the numerical experiments, a porous medium is heated from below while solute provides a stabilizing influence. For typical geological parameters, the thermohaline flow appears intrinsically chaotic. We attribute the chaotic dynamical behavior of the flow to a dominance of advective and dispersive chemical transfer over the more moderate convective heat transfer, the latter actually driving the flow. Fast upward advective transport and lateral mixing of solute leads to formation of horizontal chemical barriers at depth. These gravitationally stable interfaces divide the domain in several layers of distinct composition and lead to significantly reduced heat flow for thousands of years. The unsteady behavior of thermochemical flow in low-porosity regions has implications for heat transport at mid-ocean ridges, for ore genesis, for metasomatism and metamorphic petrology, and the diagenetic history of sediments in subsiding basins. ß 1999 Elsevier Science B.V. All rights reserved.

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“…A few studies have also been concerned with the case when the principal axes of anisotropy of the porous structure are inclined with respect to the gravity force. For this situation, the onset of motion in a porous layer heated from below was predicted by Tyvand and Storesletten (1991) [12] and Zhang et al (1993) [13]. It was demonstrated that the influence of the anisotropy orientation considerably modifies the stability limit.…”

Section: Introductionmentioning

confidence: 92%

Hydrodynamic Anisotropy Effects on Radiation-Mixed Convection Interaction in a Vertical Porous Channel

Degan¹,

Akowanou²,

Fagbemi³

et al. 2016

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The effects of hydrodynamic anisotropy on the mixed-convection in a vertical porous channel heated on its plates with a thermal radiation are investigated analytically for fully developed flow regime. The porous medium is anisotropic in permeability whose principal axes are oriented in a direction that is oblique to the gravity. The generalized Brinkman-extended Darcy model which allows the no-slip boundary-condition on solid wall is used in the formulation of the problem. The flow reversal, the thermal radiation influence for natural, and forced convection are considered in the limiting cases for low and high porosity media. It was found that the anisotropic permeability ratio, the orientation angle of the principal axes of permeability and the radiation parameter affected significantly the flow regime and the heat transfer.

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Onset of convection in an anisotropic porous medium with oblique principal axes

Cited by 83 publications

References 9 publications

Effect of anisotropic permeability on Darcy's law

Effect of anisotropic permeability on Darcy's law

Chaotic thermohaline convection in low-porosity hydrothermal systems

Hydrodynamic Anisotropy Effects on Radiation-Mixed Convection Interaction in a Vertical Porous Channel

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