发表机构
Birla Institute of Technology and Science Pilani（比拉理工学院皮拉尼校区）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究带泊肃叶流动的双柔性板通道中结构声壁模的临界层不稳定性，推导闭式低马赫数修正，发现对称模式为对流不稳定、反对称模式受宇称保护不被吸收，该不稳定性与托尔明-施利希廷等机制不同。
AI 中文摘要
承载平面泊肃叶流动的两块薄弹性板之间的可压缩流体柱支持离散的结构-声壁模。本文分析了它们的耦合色散关系，并报告了一种由流动诱导的不稳定性。由于无滑移剖面在壁面处速度为零，柔性壁边界条件中的对流（Ingard-Myers）项完全消失，因此板导纳条件与马赫数无关，且弗雷德霍姆可解性论证给出了每个耦合波数的闭式O(M)修正，该修正对任何光滑无滑移剪切剖面均有效。在内部临界层首次出现的临界马赫数M_c=Ω/ξ之上，两个结构分支表现出相反的行为：反对称模式不会被临界层吸收，其零值由精确的中平面压力节点而非弱耦合保护；对称模式没有此类节点，因此是对流不稳定的，其增长率由锚定在耗散壁-斯托克斯项上的空间计算以及与约定无关的时间计算共同确定，且向无粘极限增强，这表明该不稳定性是无粘临界层不稳定性而非粘性伪影。布里格斯-伯斯（Briggs-Bers）分析将其归类为对流不稳定性，其中性曲线遵循M_c(Ω)，且增长率与壁顺应性成正比，在刚性壁处消失，因此它与托尔明-施利希廷（Tollmien-Schlichting）机制及开尔文-亥姆霍兹（Kelvin-Helmholtz）机制不同。三种独立数值方案的结果在10^9分之一的精度上一致，且闭式修正与三种剪切剖面的数值微分结果匹配。
英文摘要
A compressible fluid column between two thin elastic plates carrying plane Poiseuille flow supports discrete structural-acoustic wall modes. This paper analyses their coupled dispersion and reports a flow-induced instability. Because a no-slip profile has zero velocity at the wall, the convective (Ingard-Myers) term in the compliant-wall boundary condition vanishes identically, so the plate-admittance conditions stay Mach-independent and a Fredholm solvability argument yields a closed-form $O(M)$ correction to every coupled wavenumber, valid for any smooth no-slip shear profile. Above the critical Mach number $M_c=Ω/ξ$ at which an interior critical layer first appears, the two structural branches behave oppositely. The antisymmetric mode is not absorbed by the critical layer, a null protected by an exact mid-plane pressure node rather than by weak coupling. The symmetric mode, which carries no such node, is convectively unstable. Its growth rate, fixed both by a spatial calculation anchored to the dissipative wall-Stokes term and by a convention-independent temporal one, strengthens towards the inviscid limit, identifying an inviscid critical-layer instability rather than a viscous artefact. A Briggs-Bers analysis classifies it as convective. Its neutral curve follows $M_c(Ω)$, and its growth rate is proportional to the wall compliance, vanishing for rigid walls, so it is distinct from the Tollmien-Schlichting and Kelvin-Helmholtz mechanisms. Three independent numerical schemes agree to one part in $10^9$, and the closed-form correction matches numerical differentiation across three shear profiles.
Comments54 pages, 13 figures. Code and data: https://github.com/i4mGr0ot/Acoustics . DOI: https://doi.org/10.5281/zenodo.22288009
