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Abstract <p>The instability of Poiseuille flow in a flat channel with compliant walls without damping with respect to inviscid perturbations in the limit of high Reynolds numbers is studied using the asymptotic theory of free interaction. It is shown that unstable inviscid perturbations can exist only if the inertia of the walls is taken into account. It is found that, for any values of elasticity, longitudinal tension, and bending stiffness, there always exists a range of wave numbers at which the flow is unstable, and the maximum growth rates of perturbations increase with these parameters.</p>

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Inviscid Instability of Poiseuille Flow in a Flat Channel with Compliant Walls

  • 期刊论文

  • 发表日期：

    2026年4月1日

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  • I. V. Savenkov

摘要

Abstract

The instability of Poiseuille flow in a flat channel with compliant walls without damping with respect to inviscid perturbations in the limit of high Reynolds numbers is studied using the asymptotic theory of free interaction. It is shown that unstable inviscid perturbations can exist only if the inertia of the walls is taken into account. It is found that, for any values of elasticity, longitudinal tension, and bending stiffness, there always exists a range of wave numbers at which the flow is unstable, and the maximum growth rates of perturbations increase with these parameters.