Monotone energy stability for Poiseuille flow in a porous medium

2023/04/23 by Giuseppe Mulone, Mulone, Giuseppe
Engineering · #76E05 #76S05 #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Heat and Mass Transfer in Porous Media #Lattice Boltzmann Simulation Studies #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.2304.11545

openalex publication_date 2023/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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. \citeHill.Straughan.2010, \citeNield.2003). 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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