Layered double-diffusive convection in porous media

1981 ◽  
Vol 102 ◽  
pp. 221-248 ◽  
Author(s):  
R. W. Griffiths

In this paper it is shown that layered double-diffusive convection of a fluid within a porous medium is possible. A thin ‘diffusive’ interface was observed in a Hele Shaw cell and in a laboratory porous medium, with salt and sugar or heat and salt as the diffusing components. Heat–salt and salt–sugar fluxes through two-layer convection systems were measured and are compared with predictions of a model. For the thermohaline system the salt and heat buoyancy fluxes are approximately in the ratio r ≃ ετm½, where ε is the porosity and Tm is the appropriate ratio of diffusivities. The behaviour of the heat flux is explained in terms of a coupling between purely thermal convection within each convecting layer and diffusion through the density interface. Salinity gradients are important only within the interface. The presence of a ‘diffusive’ interface in the Wairakei geothermal system is postulated. The ratio of heat and salt fluxes (that can be estimated from existing observations) through this convection system is consistent with the laboratory flux ratio.

1986 ◽  
Vol 108 (4) ◽  
pp. 872-876 ◽  
Author(s):  
N. Rudraiah ◽  
M. S. Malashetty

The effect of coupled molecular diffusion on double-diffusive convection in a horizontal porous medium is studied using linear and nonlinear stability analyses. In the case of linear theory, normal mode analysis is employed incorporating two cross diffusion terms. It is found that salt fingers can form by taking cross-diffusion terms of appropriate sign and magnitude even when both concentrations are stably stratified. The conditions for the diffusive instability are compared with those for the formation of fingers. It is shown that these two types of instability will never occur together. The finite amplitude analysis is used to derive the condition for the maintenance of fingers. The stability boundaries are drawn for three different combinations of stratification and the effect of permeability is depicted.


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