Nonlinear Monotone Energy Stability of Plane Shear Flows: Joseph or Orr Critical Thresholds?

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Applied Mathematics Pub Date : 2024-01-18 DOI:10.1137/22m1535826

Giuseppe Mulone

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引用次数: 0

Abstract

SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 60-74, February 2024.
Abstract. Critical Reynolds numbers for the monotone exponential energy stability of Couette and Poiseuille plane flows were obtained by Orr in 1907 [Proc. Roy. Irish Acad. A, 27 (1907), pp. 9–68, 69–138] in a famous paper, and by Joseph in 1966 [J. Fluid Mech., 33 (1966), pp. 617–621], Joseph and Carmi in 1969 [Quart. Appl. Math., 26 (1969), pp. 575–579], and Busse in 1972 [Arch. Ration. Mech. Anal., 47 (1972), pp. 28–35]. All these authors obtained their results applying variational methods to compute the maximum of a functional ratio derived from the Reynolds–Orr energy identity. Orr and Joseph obtained different results; for instance, in the Couette case Orr computed the critical Reynolds value of 44.3 (on spanwise perturbations) and Joseph 20.65 (on streamwise perturbations). Recently in [P. Falsaperla, G. Mulone, and C. Perrone, Eur. J. Mech. B Fluids, 93 (2022), pp. 93–100], the authors conjectured that the search of the maximum should be restricted to a subspace of the space of kinematically admissible perturbations. With this conjecture, the critical nonlinear energy Reynolds number was found among spanwise perturbations (a Squire theorem for nonlinear systems). With a direct proof and an appropriate and original decomposition of the dissipation terms in the Reynolds–Orr identity we show the validity of this conjecture in the space of three-dimensional perturbations.

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平面剪切流的非线性单调能量稳定性：约瑟夫临界阈值还是奥尔临界阈值？

SIAM 应用数学杂志》第 84 卷第 1 期第 60-74 页，2024 年 2 月。摘要。奥尔在 1907 年的一篇著名论文[Proc. Roy. Irish Acad. A, 27 (1907), pp、33 (1966)，第 617-621 页]，Joseph 和 Carmi 于 1969 年[Quart. Appl. Math.，26 (1969)，第 575-579 页]，Busse 于 1972 年[Arch. Ration. Mech. Anal.，47 (1972)，第 28-35 页]。所有这些作者都是应用变分法计算从雷诺-奥尔能量特性导出的函数比值的最大值而得出的结果。Orr 和 Joseph 获得了不同的结果；例如，在 Couette 情况下，Orr 计算出的临界雷诺值为 44.3（跨向扰动），Joseph 为 20.65（流向扰动）。最近在 [P.Falsaperla, G. Mulone, and C. Perrone, Eur.J. Mech.B Fluids, 93 (2022), pp.根据这一猜想，在跨度扰动中找到了临界非线性能量雷诺数（非线性系统的斯奎尔定理）。通过直接证明和对雷诺-奥尔特性中的耗散项进行适当而新颖的分解，我们证明了这一猜想在三维扰动空间中的有效性。

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来源期刊

SIAM Journal on Applied Mathematics 数学-应用数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.