Large amplitude convection in porous media

Straus, Joe M.

doi:10.1017/s0022112074001996

Cited by 168 publications

(90 citation statements)

References 13 publications

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“…For the pure fluid, similar stability analyses have been carried out by De La Torre Juárez & Busse (1995) and Straus (1974). In agreement with their results, we find that only two instability mechanisms, the zigzag and the crossroll mechanism, limit the region of stable rolls.…”

Section: Stability Boundaries For the Pure Fluidsupporting

confidence: 90%

Roll convection of binary fluid mixtures in porous media

et al. 2010

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We investigate theoretically the nonlinear state of ideal straight rolls in the RayleighBénard system of a fluid layer heated from below with a porous medium using a Galerkin method. Applying the Oberbeck-Boussinesq approximation, binary mixtures with positive separation ratio are studied and compared to one-component fluids. Our results for the structural properties of roll convection resemble qualitatively the situation in the Rayleigh-Bénard system without porous medium except for the fact that the streamlines of binary mixtures are deformed in the so-called Soret regime. The deformation of the streamlines is explained by means of the Darcy equation which is used to describe the transport of momentum. In addition to the properties of the rolls, their stability against arbitrary infinitesimal perturbations is investigated. We compute stability balloons for the pure fluid case as well as for a wide parameter range of Lewis numbers and separation ratios which are typical for binary gas and fluid mixtures. The stability regions of rolls are found to be restricted by a crossroll, a zigzag and a new type of oscillatory instability mechanism, which can be related to the crossroll mechanism.

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Section: Stability Boundaries For the Pure Fluidsupporting

confidence: 90%

Roll convection of binary fluid mixtures in porous media

et al. 2010

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“…1) indicate the material properties that are parallel and perpendicular to the temperature gradient; K k and k k are used in equation (1) in place of the average values (Straus 1974;Straus and Schubert 1978;Kvernvold and Tyvand 1979). A grass canopy may be modeled as a series of upright cylindrical rods (grass blades) of radius a that are spaced a distance 2b apart, as shown in figure 1.…”

Section: Thermal-convection Hypothesismentioning

confidence: 99%

A Porous Convection Model for Grass Patterns

Thompson

Daniels

2010

The American Naturalist

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Spatial ecological patterns are usually ascribed to Turingtype reaction-diffusion or scale-dependent feedback processes, but morphologically indistinguishable patterns can be produced by instabilities in fluid flow. We present a new hypothesis that suggests that fluid convection and chill damage to plants could form vegetation patterns with wavelengths ≈1-2 times the plant height. Previous hypotheses for small-scale vegetation pattern formation relied on a Turing process driven by competition for water, which is thought to occur in large vegetation patterns. Predictions of the new hypothesis were consistent with properties of natural grass patterns in North Carolina, contradicting the Turing hypothesis. These results indicate that similarities in pattern morphology should not be interpreted as implying similarities in the pattern-forming processes, that small-wavelength vegetation patterns may arise from mechanisms that are distinct from those generating long-wavelength vegetation patterns, and that fluid instabilities should be recognized as a cause of ecological patterns.

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“…Wooding (1957Wooding ( , 1960Wooding ( , 1963, Yih (1965) and Elder (1967) examined problems of convection in saturated permeable media~sing analytical and experimental techniques. Straus (1974) investigated large amplitude convection in porous media. Ribandoand Torrance (1976) looked at the effects of confinement, variable.…”

Section: Iii'mentioning

confidence: 99%

Comparative assessment of five potential sites for hydrothermal-magma systems: energy transport

Hardee¹

1980

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Large amplitude convection in porous media

Cited by 168 publications

References 13 publications

Roll convection of binary fluid mixtures in porous media

Roll convection of binary fluid mixtures in porous media

A Porous Convection Model for Grass Patterns

Comparative assessment of five potential sites for hydrothermal-magma systems: energy transport

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