Stability analysis of double-diffusive convection in superposed fluid and porous layers using a one-equation model

Interaction of the Longwave and Finite-Wavelength Instability Modes of Convection in a Horizontal Fluid Layer Confined between Two Fluid-Saturated Porous Layers

“…It was found that, there is a range of parameters where the neutral curves are bimodal, i.e., both, a longwave convection, taking place mainly in porous medium, and a finite-wavelength convection, concentrated mainly in a fluid with a characteristic horizontal scale close to the thickness of a layer, may coexist. Later on, the same phenomena were discovered and analyzed for two-layer systems made up of a superposed pure fluid layer and a fluid-saturated porous layer [2][3][4][5][6]. In Reference [7], it is shown that high frequency transversal vibrations cause a stabilizing effect on the disturbances with any wave numbers, but affects finite-wavelength disturbances much more strongly than longwave ones.…”

On the Equivalence of the Discontinuous One- and Two-Domain Approaches for the Modeling of Transport Phenomena at a Fluid/Porous Interface

“…Most of the stability analyses in this configuration have been performed using a two-domain model with Darcy's law (Nield 1977(Nield , 1983Chen and Chen 1988;Carr and Straughan 2003;Carr 2004) or with the Brinkman correction (Hirata et al 2007) in the porous region. Few analyses have been carried out using the one-domain approach (Zhao and Chen 2001) and the comparison with the two-domain approach leads to a qualitative agreement of the marginal stability curves while the critical values of the Rayleigh number may significantly differ (Zhao and Chen 2001;Chen and Chen 1988).…”

Stability of Thermosolutal Natural Convection in Superposed Fluid and Porous Layers

“…In that case, heat and mass transport are governed by a unique set of conservation equations both valid in the fluid and porous regions avoiding the explicit formulation of the boundary conditions at the interface. Very few stability analyses have been performed using the one-domain approach (Zhao and Chen 2001). The comparisons with the two-domain models lead to a qualitative agreement of the marginal stability curves for the thermal case (bimodal behavior) whereas only the "fluid mode" was observed for the thermosolutal case.…”

“…The comparisons with the two-domain models lead to a qualitative agreement of the marginal stability curves for the thermal case (bimodal behavior) whereas only the "fluid mode" was observed for the thermosolutal case. In both cases, the critical values of the thermal or solutal Rayleigh numbers may significantly differ (Zhao and Chen 2001;Chen and Chen 1988). Actually, in this formulation the macroscopic properties of the homogeneous porous layer at the interface (porosity, permeability, effective diffusivity) are Heaviside functions and therefore, their differentiation must be taken in the meaning of distributions (Schwartz 1961;Kataoka 1986).…”