Multicomponent diffusive-convective fluid motions in porous layers: Ultimately boundedness, absence of subcritical instabilities, and global nonlinear stability for any number of salts

摘要

Either for its great geophysical relevance or the frequent occurrence of porous materials in real life, research on convective-diffusive fluid motions in porous horizontal layers has a notable relevance, which is increasing with the number of salts dissolved in the fluid. In the present paper, porous horizontal layers heated from below and salted by m salts partly from above and partly from below are studied ?m∈N. In the Darcy-Boussinesq scheme it is shown that: (i) the L2 solutions are bounded, uniquely determined, and asymptotically converging toward an absorbing set; (ii) for each Fourier component of the perturbations to the thermal conduction solution, there exists an own nonlinear admissible evolution system; (iii) subcritical instabilities do not exist and the conditions of linear stability also guarantee the global nonlinear stability; (iv) global nonlinear stability is guaranteed by the general condition (1.2) holding ?m∈N; (v) condition (1.2) is hidden in the Darcy-Boussinesq equations, it can be found by substituting the salt concentration fields via new suitable unknown fields and looking for symmetries and skew-symmetries in the new system of equations. The present paper - originating from Rionero ["Absence of subcritical instabilities and global nonlinear stability for porous ternary diffusive-convective fluid mixtures," Phys. Fluids24, 104101 (2012)]10.1063/1.4757858 - generalizes the properties (ii)-(iv) (obtained for m = 2) to any m∈N and furnishes the newly obtained properties (i) and (v). We stress the relevant physical meaning of (1.2). In fact (1.2) - in simple algebraic closed form - guarantees that the onset of convection cannot occur and appears to be useful not only for theoreticians but also for experimentalists in the research field of physics of fluids. Analogously, conditions guaranteeing the onset of convection - in simple algebraic closed form (cf. (6.18) and (6.19) reversed) - are furnished.