Abstract
The onset of oscillatory bifurcations in a porous horizontal layer L, uniformly rotating about a vertical axis, with vertically stratified porosity, heated from below and salted from above and below, is investigated. Denoting by Pi,(i=1,2), the Prandtl numbers of the salt Si salting L from below (i=1) and above (i=2) respectively, it is shown that: (i) in L the oscillatory bifurcations can occur only if one of the structural conditions P1>1,P2<1 or P1=1,P2<1 or P1>1,P2=1 is verified; (ii) exists a bound R¯2 for the Rayleigh number R2 of S2 such that R2<R¯2 guarantees the absence of cold convection; (iii) via a new approach based on the instability power of each coefficient of the spectrum equation, criteria of existence, location and frequency of oscillatory (Hopf) bifurcations are furnished for any porosity stratification law. These criteria, as far as we know are, for the case at stake, the first criteria of Hopf bifurcations appearing in literature. We are confident that, via experimental results, will be validated.
Highlights
The onset of thermal convection in porous layers with vertically stratified permeability and/or viscosity, for its importance in geophysical phenomena and in the construction of artificial porous materials, has attracted—in the past as nowadays—the attention of scientists [1,2,3,4,5,6,7,8,9,10,11,12,13,14]
The scope is to analyze the effects of such stratifications on the onset of Hopf bifurcations
He has shown that, via (45), the following property guaranteeing the existence of Hopf bifurcations holds
Summary
The onset of thermal convection in porous layers with vertically stratified permeability and/or viscosity, for its importance in geophysical phenomena and in the construction of artificial porous materials, has attracted—in the past as nowadays—the attention of scientists [1,2,3,4,5,6,7,8,9,10,11,12,13,14]. The increase in viscosity with depth in the earth’s mantle has been studied in [1,2]; the changes in permeability due to mineral diagenesis in fractured crust has been analyzed in [3]; in references [4,5] the porosity changes due to the subterranean movement and the increase in permeability and porosity near solid wall, are considered; the influence of porosity stratification on the onset of thermal convection in the construction of artificial porous materials is studied in [2].
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