The entrainment of free-stream unsteady three-dimensional vortical disturbances in the entry region of a channel is studied via matched asymptotic expansions and by numerical means. The interest is in flows at Reynolds numbers where experimental studies have documented the occurrence of intense transient growth, despite the flow being stable according to classical stability analysis. The analytical description of the vortical perturbations at the channel mouth reveals how the oncoming disturbances penetrate into the wall-attached shear layers and amplify downstream. The effects of the channel confinement, the streamwise pressure gradient and the viscous/inviscid interplay between the oncoming disturbances and the boundary-layer perturbations are discussed. The composite perturbation velocity profiles are employed as initial conditions for the unsteady boundary-region perturbation equations. At a short distance from the channel mouth, the disturbance flow is mostly confined within the shear layers and assumes the form of streamwise-elongated streaks, while farther downstream the viscous disturbances permeate the whole channel although the base flow is still mostly inviscid in the core. Symmetrical disturbances exhibit a more significant growth than anti-symmetrical disturbances, the latter maintaining a nearly constant amplitude for several channel heights downstream before growing transiently, a unique feature not reported in open boundary layers. The disturbances are more intense as the frequency decreases or the bulk Reynolds number increases. We compute the spanwise wavelengths that cause the most intense downstream growth and the threshold wall-normal wavelengths below which the perturbations are damped through viscous dissipation.

中文翻译：

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通道入口区域涡旋扰动的夹带和增长

通过匹配渐近展开和数值方法研究了通道入口区域中自由流非定常涡旋扰动的夹带。感兴趣的是雷诺数的流动，其中实验研究记录了强烈的瞬态增长的发生，尽管根据经典稳定性分析流动是稳定的。对通道口处的涡流扰动的分析描述揭示了迎面而来的扰动如何渗透到附壁剪切层并在下游放大。讨论了通道限制、流向压力梯度以及迎面而来的扰动和边界层扰动之间的粘性/非粘性相互作用的影响。复合扰动速度剖面用作非定常边界区域扰动方程的初始条件。在离河道口很近的地方，扰动流主要局限在剪切层内，呈流向拉长的条带状，而在下游更远的地方，粘性扰动渗透整个河道，尽管基流在岩心中仍然大部分是非粘性的. 对称干扰比反对称干扰表现出更显着的增长，后者在瞬时增长之前在下游的几个通道高度上保持几乎恒定的幅度，这是开放边界层中未报告的独特特征。随着频率降低或体积雷诺数增加，干扰更加强烈。