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Influence of centrifugal forces on the development of wave packets in boundary layers with a uniformly valid model

机译：统一有效模型对离心力对边界层波包发展的影响

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The behavior of three-dimensional wave packets in the boundary layer on curved surfaces is analyzed in this study based on a modification of the triple-deck theory referred to as the "criss-cross" interaction model. The equations of the criss-cross interaction describe a particular type of boundary layer instability mode that possesses underlying properties of both the Tollmien-Schlichting waves and Taylor-Gortler vortices. Previous analysis of the criss-cross interaction regime suggests a possibility for upstream propagation of perturbations in the boundary layer and possible absolute instability of the flow. However, these results cannot be considered as conclusive because the initial-value problem for the criss-cross interaction equations is ill-posed. In a recent work [Turkyilmazoglu M, Ruban AI. A uniformly valid well-posed asymptotic approach to the inviscid-viscous interaction theory. Stud Appl Math 2002;108:161-85] a regularized non-asymptotic model to describe criss-cross interaction has been proposed. Whereas in the original version of the theory, perturbations have an unbounded growth rate as the longitudinal wave number |k| → ∞, in the new model of [Turkyilmazoglu and Ruban, 2002], as physically expected the amplification rate remains bounded for both spatially growing and temporally growing waves, A Fourier transform method is used in the present study to solve the linearized equations for the flow over concave roughness and humps and it is found that disturbances develop and are convected downstream as wave packets. The behavior of the wave packets is consistent with convective instability, and the upstream influence is no longer present at large times.
机译：在这项研究的基础上，对三层甲板理论（称为“十字交叉”相互作用模型）的改进，分析了曲面边界层中三维波包的行为。纵横交错的相​​互作用方程描述了一种特殊类型的边界层不稳定性模式，该模式具有托尔米-施利希特波和泰勒-戈特勒涡旋的基本特性。纵横交错相互作用机制的先前分析表明，扰动在边界层向上游传播的可能性以及流动的绝对不稳定性。但是，这些结果不能被认为是结论性的，因为纵横交错相互作用方程式的初值问题是不恰当的。在最近的工作中[Turkyilmazoglu M，Ruban AI。一种无粘性-粘稠相互作用理论的统一有效的适定渐近方法。 Stud Appl Math 2002; 108：161-85]提出了一种描述纵横交错相互作用的正则化非渐近模型。而在该理论的原始版本中，随着纵向波数| k |的变化，扰动具有无限的增长速度。 →∞，在[Turkyilmazoglu and Ruban，2002]的新模型中，由于物理上预期放大率对于空间增长和时间增长的波仍然是有界的，因此在本研究中使用傅里叶变换方法来求解线性化方程。在凹面粗糙和隆起上流过，发现扰动在波包中发展并在下游对流。波包的行为与对流不稳定性相一致，并且上游影响不再大量出现。

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