Abstract
In this short paper, some analytical results found in “Double-diffusive Soret convection phenomenon in porous media: effect of Vadasz inertia term” by F. Capone, R. De Luca, M. Vitiello, Ricerche Mat. 68, 581–595 (2019), are recalled in order to better explore the dynamic of thermosolutal convection in a horizontal porous layer with the influence of Vadasz and Soret terms.
Highlights
In this note we recall the results on the onset of thermosolutal convection in a horizontal porous layer, uniformly heated and salted from below, with Soret and inertia effects, investigated in [1], with particular regard to analyze the kind of instability arising when the rest state is no longer observable
Since, for the problem under consideration, I1n < 0. These conditions are necessary and sufficient to guarantee that the thermal conduction solution is stable
The instability threshold is given by Rinsta = min{RS, RO }
Summary
In this note we recall the results on the onset of thermosolutal convection in a horizontal porous layer, uniformly heated and salted from below, with Soret and inertia effects, investigated in [1], with particular regard to analyze the kind of instability arising when the rest state is no longer observable. The instability threshold is given by Rinsta = min{RS, RO } On comparing these two numbers, in [1], sufficient conditions guaranteeing the onset of steady and Hopf convection have been found. In this short paper we reconsider the problem in [1] and perform the linear instability analysis of the thermal conduction solution of model (1) of [1] by using a different methodology. In this way, we are able to better state the results found in Theorem 1. We are able to find conditions guaranteeing that oscillatory convection can not occur because RO does not exist or because RO exists and RO > RS
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