AI 中文总结
研究关于Falkner-Skan解扰动的特征值和范数渐近展开，将Brown的方法扩展到特定Falkner-Skan解，揭示壁面层变化产生新贡献，通过与数值计算比较证实新壁面修正作用。
AI 中文摘要
我们推导了关于Falkner-Skan边界层剖面的Chen-Libby扰动问题的大模式渐近展开式，用于特征值和特征函数范数。该分析将Brown对Blasius问题的匹配渐近构造扩展到具有正壁面切应力的Falkner-Skan解，包括有利梯度和轻度不利范围的上支。虽然外层和中层结构与Blasius情形相同，但当压力梯度参数β非零时，壁面层性质改变。Falkner-Skan壁面展开以相对阶数Λ^(-1/3)奇异扰动内贝塞尔问题，产生新的壁面诱导贡献s^(-1/3)到特征值展开。新项在Blasius极限中消失，恢复Brown的排序。匹配特征函数也给出了Chen-Libby范数的渐近估计。将特征值和范数公式与β = 1/2的直接数值射击计算进行比较，显示出预期的渐近收敛并证实了新壁面修正的作用。
英文摘要
We derive large-mode asymptotic expansions for the eigenvalues and eigenfunction norms of the Chen-Libby perturbation problem about Falkner-Skan boundary-layer profiles. The analysis extends Brown's matched-asymptotic construction for the Blasius problem to Falkner-Skan solutions with positive wall shear -- both favorable gradients and the upper branch of the mild adverse range. Although the outer and middle layers retain the same structure as in the Blasius case, the wall layer changes qualitatively when the pressure-gradient parameter $β$ is nonzero: the Falkner-Skan wall expansion singularly perturbs the inner Bessel problem at relative order $Λ^{-1/3}$, where $Λ$ is the large eigenvalue parameter. This produces a new wall-induced contribution $s^{-1/3}$ (where $s=n-1$ and $n$ is the large eigenvalue index) to the large-mode eigenvalue expansion, ahead of Brown's $s^{-1/2}$ correction. The new term vanishes in the Blasius limit, where Brown's ordering is recovered. The matched eigenfunction also yields asymptotic estimates for the Chen-Libby norms. The eigenvalue and norm formulae are compared with direct numerical shooting calculations for $β=1/2$, showing the expected asymptotic convergence and confirming the role of the new wall correction.
Comments17 pages
