Application of Arnoldi method to boundary layer instability

作者：Zhang Yong Ming^*; Luo Ji Sheng

来源：Chinese Physics B, 2015, 24(12): 124701.

DOI：10.1088/1674-1056/24/12/124701

• Arnildi method
• linear stability theory
• Floquet theory
• secondary instability

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.

• 出版日期2015-12
• 单位天津大学