Stability criteria for the vertical boundary layer formed by throughflow near the surface of a porous medium

Duijn, van Cj Hans; Pieters, Gjm Gert-Jan; Wooding, R. A.; Ploeg, van der Auke

doi:10.1029/129gm15

Cited by 36 publications

(70 citation statements)

References 15 publications

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“…We note that this is almost identical to the Rayleigh number defined by van Duijn et al (2002), with the exception that the effective upflow velocity now becomes V + v 0 . It is then convenient to eliminate some components of the velocity u = (u, v, w) from the problem.…”

Section: Non-dimensional Formulationsupporting

confidence: 49%

“…As in many other convection problems (Straughan 1992), subcritical nonlinear instabilities may be possible below the threshold of linear instability, and this is indeed observed in the analysis of van Duijn et al (2002). This phenomenon lies beyond the scope of the current study, but is an important direction for future treatments of the problem.…”

Section: Boundary and Initial Conditionsmentioning

confidence: 92%

“…This assumption is motivated by the fact that the front will be stabilised both by gravity and by evaporation, as vapour overlies liquid water; consequently, we may expect the fastest-growing perturbations to be those which involve little or no perturbation to the front. Our analysis resembles that by van Duijn et al (2002), but is generalised to allow for a moving front.…”

Section: Boundary and Initial Conditionsmentioning

confidence: 99%

“…This builds on a substantial body of research on salt transport in groundwater, though few previous studies have investigated travelling evaporation fronts. In particular, Wooding (1960), Wooding, Tyler & White (1997), van Duijn et al (2002) and Pieters & van Duijn (2006) have used Darcian models to investigate instabilities driven by conditions fixed at the soil surface; Yakirevich, Berliner & Sorek (1997) have modelled evaporation from the soil surface and the vertical profiles of soil saturation and ion content beneath it; Gowing, Konukcu & Rose (2006) have used a quasi-steady model based on Richards' equation to predict vertical profiles including a descending evaporation front, and tested it against laboratory experiments. Most relevantly to the current study, Tsypkin & Brevdo (1999) and Tsypkin (2003b) (see also Tsypkin 2003a) have developed one-dimensional models of Darcian flow with salt and heat transport and a moving evaporation front, but the stability of their solutions has not previously been considered.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Instability of the salinity profile during the evaporation of saline groundwater

Ильичев¹,

Tsypkin²,

Pritchard³

et al. 2008

J. Fluid Mech.

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We investigate salt transport during the evaporation and upflow of saline groundwater. We describe a model in which a sharp evaporation-precipitation front separates regions of soil saturated with an air-vapour mixture and with saline water. We then consider two idealised problems. We first investigate equilibrium configurations of the fresh-water system when the depth of the soil layer is finite, obtaining results for the location of the front and for the upflow of water induced by the evaporation. Motivated by these results, we develop a solution for a propagating front in a soil layer of infinite depth, and we investigate the gravitational stability of the salinity profile which develops below the front, obtaining marginal linear stability conditions in terms of a Rayleigh number and a dimensionless salt saturation parameter. Applying our findings to realistic parameter regimes, we predict that salt fingering is unlikely to occur in low-permeability soils, but is likely in high-permeability (sandy) soils under conditions of relatively low evaporative upflow.

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Section: Non-dimensional Formulationsupporting

confidence: 49%

Section: Boundary and Initial Conditionsmentioning

confidence: 92%

Section: Boundary and Initial Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Instability of the salinity profile during the evaporation of saline groundwater

Ильичев¹,

Tsypkin²,

Pritchard³

et al. 2008

J. Fluid Mech.

View full text Add to dashboard Cite

show abstract

“…The onset of convection with internal heat generation and net through ow (strong and weak) for di erent hydrodynamic boundary conditions is examined in the article by Khalili and Shivakumara [23]. The stability of a saline boundary layer formed by through ow near surface of the porous medium was studied in Van Duijn et al [24] and Pieters and Schuttelaars [25]. The linear instability of boundary layer formed by vertical through ow in horizontal porous medium with local thermal nonequilibrium was examined in Patil and Rees [26].…”

Section: Introductionmentioning

confidence: 99%

Onset of Darcy-Brinkman convection with a uniform internal heat source and vertical throughflow

Deepika

Narayana

Hill

2017

International Journal of Thermal Sciences

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The problem of thermal convection in a horizontal uid-saturated porous layer is examined, where the ow is governed by the Brinkman extension of Darcy's law. A uniform internal heat source and vertical through ow are also considered. The linear and nonlinear stability analyses are performed in order to determine the stability characteristics of the system. The linear and nonlinear thresholds give good agreement in the absence of vertical through ow. However, it is shown that there are potential regions of sub-critical instabilities for increasing values of internal heat source parameter Q, Péclet number P e and Darcy number Da.

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A differential constraint approach to obtain global stability for radiation‐induced double‐diffusive convection in a porous medium

Hill

2008

Math Methods in App Sciences

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SUMMARYThe stability of double-diffusive porous convection with a concentration-based internal heat source is studied. Owing to the significant sensitivity of standard energy method, a highly desirable reduction in the number of required coupling parameters is achieved through the novel energy method of van Duijn et al. Owing to the widespread use of coupling parameters in analysing porous media stability, this result strongly advocates the differential constraint approach for obtaining optimal nonlinear stability thresholds.

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Stability criteria for the vertical boundary layer formed by throughflow near the surface of a porous medium

Cited by 36 publications

References 15 publications

Instability of the salinity profile during the evaporation of saline groundwater

Instability of the salinity profile during the evaporation of saline groundwater

Onset of Darcy-Brinkman convection with a uniform internal heat source and vertical throughflow

A differential constraint approach to obtain global stability for radiation‐induced double‐diffusive convection in a porous medium

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