张永明^1，2，*

（  1、天津大学力学系，天津 300072；       2、天津市现代工程力学重点实验室，天津 300072；  ）

摘要： 当背景扰动较大时边界层会发生旁路转捩。展向局部自由流湍流下边界层旁路转捩是一种典型的旁路转捩，一般在流体力学中认为其过程可以简单描述为：首先自由流湍流中的低频扰动穿透边界层形成流向的条纹，然后条纹幅值急剧增长至饱和状态，此后带条纹的边界层发生二次失稳进而形成湍流边界层。对条纹的生成和非线性演化至饱和态的研究已经比较充分，本文对条纹边界层二次失稳进行研究。在流向不同位置进行二次失稳分析，并将结果放在空间-时间平面进行整合，发现了对流模态，其特点在于二次失稳的增长可以沿流向累计。通过对增长累计效果的分析和比较，发现二次失稳的以下特性。第一，展向局部自由流湍流下边界层旁路转捩中二次失稳的贡献远大于T-S波。第二，二次失稳中起主导作用的条纹是中间处的强条纹。第三，二次失稳中起主导作用的模态为中间处较强的快条纹的内模态，而中间处较强的慢条纹的正弦型外模态也起一定作用，但相对弱一些。
关键词： 流体力学；二次失稳；旁路转捩；对流模态；内模态；外模态

ZHANG Yongming^*

（  Department of Mechanics, Tianjin University, Tianjin 300072；Tianjin Key Laboratory of Modern Engineering Mechanics, Tianjin 300072；  ）

Abstract： At high level of environmental disturbance, bypass transition takes place in the boundary layer. Bypass transition of boundary layer under spanwise localized free-stream turbulence is a usual type of bypass transition, which is described as the following process in fluid mechanics. Firstly, low-frequency disturbances in free-stream turbulence penetrate into the boundary layer and induce streamwise streaks. Amplitude of the streaks grows significantly until it becomes saturated. Then secondary instability of streaky boundary layer occurs such that the flow becomes turbulent. The generation and nonlinear evolution of streaks until saturation have been studied in literature. In this paper, the secondary instability of streaky boundary layer is investigated. The instability analysis is carried out at different streamwise locations, and the results are taken into consideration in the whole space-time plane, such that convecting modes are found. Along the convecting modes, the growth of secondary instability can accumulate in stramwise direction. Due to comparison of the growth of each convecting mode, the following characters of secondary instability of bypass transition under spanwise localized free-stream turbulence are found. Firstly, the contribution of secondary instability to bypass transition is much more important than T-S waves. Secondly, the center strong streak plays the key role in secondary instability. Thirdly, the inner mode on center high-speed streak is the dominant one in secondary instability, while the sinuous outer mode on center low-speed streak plays a certain role.
Keywords： fluid mechanics; secondary instability; bypass transition; convecting mode; inner mode; outer mode

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