Details

Giuseppe Mulone^[a]

Monotone energy stability for Poiseuille flow in a porous medium

Pages: 175-183
Received: 21 March 2023
Accepted: 18 September 2023
Mathematics Subject Classification: 76E05, 76S05.
Keywords: Porous media, Poiseuille flow, Brinkman equation, monotone energy stability
Author address:
[a]: University of Catania (retired), Department of Mathematics and Computer Science, Viale andrea Doria 6, Catania, 95125, Italy

Abstract: We study the monotone energy stability of ''Poiseuille flow" in a plane-parallel channel with a saturated porous medium modeled by the Brinkman equation, on the basis of an analogy with a magneto-hydrodynamic problem (Hartmann flow) (cf. [2], [8]). We prove that the least stabilizing perturbations, in the energy norm, are the two-dimensional spanwise perturbations. This result implies a Squire theorem for monotone nonlinear energy stability. Moreover, for Reynolds numbers less than the critical Reynolds number \(R_E\) there can be no transient energy growth.

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