Evolution and instability of unsteady nonlinear streaks generated by free-stream vortical disturbances
Evolution and instability of unsteady nonlinear streaks generated by free-stream vortical disturbances
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DOI：
10.1017/jfm.2011.41
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发表时间：
2011-04
影响因子：
3.7
通讯作者：
P. Ricco;Ji-sheng Luo;Xuesong Wu
中科院分区：
文献类型：
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作者：
P. Ricco;Ji-sheng Luo;Xuesong Wu
我们研究了自由流涡扰动对不可压缩层流边界层演化和不稳定性的影响，重点研究了波长足够长的分量，这些分量可以穿透边界层产生流向拉长的条纹。假定自由流扰动足够强(但幅度仍然很小)，使得诱导条纹在边界层厚度与扰动的展向波长相当的区域获得O(1)流向速度。条纹的形成和演化由非线性非定常边界区方程加上适当的上游和远场边界条件来控制。这一初边值问题是在自由流扰动由一对频率相同但展向波数相反的斜涡模来模拟的特殊情况下得到的。非线性被发现抑制了这一反应。非线性相互作用显著地改变了平均流型，其形状与实验测量结果定量一致。在瞬时流向速度分布中检测到壁法向拐点。二次稳定性分析表明，当自由流扰动强度为2.8%时，边界层变得非常不稳定。不稳定正弦模式的特征频率、相速度、群速度和增长率与最近的实验结果基本一致。本文的理论框架原则上允许在自由流湍流特性和二次不稳定性之间建立一个定量的关系，这种关系可以被用来发展一种有效的、基于物理的方法来预测绕流转变。
We investigate the influence of free-stream vortical disturbances on the evolution and instability of an incompressible laminar boundary layer, focusing on components of sufficiently long wavelength, which are known to penetrate into the boundary layer to generate streamwise elongated streaks. The free-stream disturbance is assumed to be sufficiently strong (but still of small amplitude) that the induced streaks acquire an O(1) streamwise velocity in the region where the boundary-layer thickness becomes comparable with the spanwise wavelength of the perturbation. The formation and evolution of the streaks are governed by the nonlinear unsteady boundary-region equations supplemented by appropriate upstream and far-field boundary conditions. This initial-boundary-value problem is solved for the special case where the free-stream disturbance is modelled by a pair of oblique vortical modes with the same frequency but opposite spanwise wavenumbers. Nonlinearity is found to inhibit the response. The nonlinear interaction alters the mean-flow profile appreciably, the shape of which is in quantitative agreement with experimental measurements. Wall-normal inflection points are detected in the instantaneous streamwise velocity profiles. The secondary stability analysis indicates that in the presence of free-stream disturbance with an intensity of 2.8%, the resulting streaky boundary layer becomes inviscidly unstable. The characteristic frequency, phase and group velocities, and growth rate of unstable sinuous modes are found to be in broad agreement with recent experiments. The present theoretical framework allows in principle a quantitative relation to be established between the characteristics of free-stream turbulence and the secondary instability, and this relation may be exploited to develop an efficient and physics-based approach for predicting bypass transition.