There are many publications about the flow stability over the Darcy-Brinkman medium with nice and clear results. e.g. Chang M. H., Chen F., Straughan B. "Instability of Poiseuille flow in a fluid overlying a porous layer", J. Fluid Mech. V.564 (2006); Hill A. A. and Straughan B. "Poiseuille flow in a fluid overlying a porous medium", J. Fluid Mech. V.603 (2008); Tilton N., Cortelezzi L. "Linear stability analysis of pressure-driven flows in channels with porous walls" J. Fluid Mech. V.604 (2008); Hill A.A. "Instability of Poiseuille flow in a fluid overlying a glass bead packed porous layer", Acta Mechanica, V.206 (2009); Lyubimova T.P., Baydina D.T. "Stability and nonlinear regimes of flow over a saturated porous medium", Nonlinear Processes in Geophysics V.20 (2013), etc.
All the studies are based on Darcy-Brinkman porous medium model. I'm trying to make a similar research but, due to the project plan, it should be based on pure Darcy and Darcy-Forchheimer model without laplacian in the momentum equation. Are there any publications about the question topic?
After two days, I get some progress here.
First, there is a one mistake in initial thinking bringing an incorrect assumption about the results. Now, I have checked my drafts and have laughed at my memory.
The topic problem just reduces to Orr-Sommerfeld problem for channel with non-typical boundary condition at the interface between pure liquid and porous medium. The Galerkin method or collocation method are applicable by simple way. I'm not sure about their convergence, but the problem is being developed now.
And, the main question about known articles considering an instability of parallel flow over the Darcy porous medium is still open.
Hi all,
I think It is possible to make a small report. Probably, it will be published somewhere during this year.
The main results follow:
1. The two-layer system with Darcy porous layer less stable than system with Brinkman model - typical critical Reynolds number is 2-10 times smaller.
It is a result of Beavers-Joseph condition at the liquid layer-porous layer interface. The condition gives a jump in stationary velocity profile, and that jump is main destabilizing factor. And, of course, It is the main trouble of our approach can't resolve the smooth transition between Darcy and Poiseuille flow.
2. The qualitative system behavior to parameter changes is similar with model includes Brinkman porous medium. There are two minima on neutral curve, the main minimum is long-wave and it always exists, and the short-wave can be found at low Darcy numbers and high Beavers-Joseph constant (the parameter in boundary condition).
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