Receptivity Of Secondary Instability Mode In Streaky Boundary Layers

In the event of relatively high free-stream turbulence(FST),the boundary-layer transition follows the bypass route.This process,in general,can be described as follows:(1)the low-frequency component of the free-stream vortical disturbances with large amplitude enter the boundary layer and excite streaky structures;(2)after the transient growth of the streaks,high-frequency disturbances grow rapidly under the regime of secondary instability;(3)when the high-frequency disturbances have accumulated to finite amplitudes,the nonlinear effect would lead to the breakdown of the streaks,followed by the emergence of the intermittent turbulence spots.However,there still exists one process unclear,namely,how the secondary instability modes are excited in the early stage of bypass transition.In this paper,we firstly study the evolution of both the low-and high-frequency vortical disturbances in the boundary layer via direct numerical simulation(DNS),which provides the justification of the boundary-region equation and the edge-layer asymptotic solution on describing the boundary-layer responds to the free-stream lowand high-frequency disturbances,respectively.By introducing a pair of low-frequency vortical disturbances with large amplitudes and a high-frequency disturbance with a small amplitude in the free stream,we perform DNS on the generation of the high-frequency instability modes in the streaky boundary layers.Through comparison with the linear results obtained from the bi-global analysis,the generated instability mode is confirmed to be the secondary instability mode.The Wigner-Ville Distribution(WVD)transformation is employed on analyzing the numerical data,and the formation of the secondary instability modes in the vicinity of inlet of the computational domain is exhibited.We established a simplified model by selecting the streaky base flow according to the group velocity of secondary instability mode,which is confirmed to be an efficient way to determine the receptivity coefficient.Moreover,the nonlinear evolution of the secondary instability modes as they have accumulated to finite amplitudes are simulated,exhibiting the emergence of intermittent turbulent spots.