Application of Arnoldi method to boundary layer instability
Application of Arnoldi method to boundary layer instability
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DOI：
10.1088/1674-1056/24/12/124701
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发表时间：
2015-10
影响因子：
1.7
通讯作者：
Yongmin Zhang;Ji-sheng Luo
中科院分区：
文献类型：
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作者：
Yongmin Zhang;Ji-sheng Luo
边界层失稳采用Arnoldi方法，为避免有限元方法的局限性，采用有限差分方法。这一做法得到了三个比较案例的验证，即，对一维基流的二维扰动与线性稳定性理论（LST）进行了比较，对一维基流的三维扰动与线性稳定性理论（LST）进行了比较，对二维基流的三维扰动与Floquet理论进行了比较。然后将其应用于展向局部化自由流湍流（FST）下条纹边界层的二次失稳分析。发现了三种不稳定模式，即，高速中心条纹处的内模式、低速中心条纹处的弯曲型外模式以及低速侧条纹处的弯曲型外模式。所有这些模式都比Tollmien-Schlichting（TS）波不稳定得多，这意味着在旁路过渡的二次不稳定性的主要贡献。强中心条纹处的模比弱侧条纹处的模更不稳定，因此中心条纹在二次不稳定中是“危险的”。
The Arnoldi method is applied to boundary layer instability, and a finite difference method is employed to avoid the limit of the finite element method. This modus operandi is verified by three comparison cases, i.e., comparison with linear stability theory (LST) for two-dimensional (2D) disturbance on one-dimensional (1D) basic flow, comparison with LST for three-dimensional (3D) disturbance on 1D basic flow, and comparison with Floquet theory for 3D disturbance on 2D basic flow. Then it is applied to secondary instability analysis on the streaky boundary layer under spanwise-localized free-stream turbulence (FST). Three unstable modes are found, i.e., an inner mode at a high-speed center streak, a sinuous type outer mode at a low-speed center streak, and a sinuous type outer mode at low-speed side streaks. All these modes are much more unstable than Tollmien–Schlichting (TS) waves, implying the dominant contribution of secondary instability in bypass transition. The modes at strong center streak are more unstable than those at weak side streaks, so the center streak is 'dangerous' in secondary instability.