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Characterizing free-stream disturbances and their entrainment into a shear layer is of a crucial first step towards understanding and predicting receptivity and bypass transition. In some recent studies of bypass transition, continuous modes of the O-S equation have been used to represent free-stream vortical disturbances and the signature induced by them in the boundary layer. For the Blasius boundary layer, a recent study by the present authors shows that continuous modes and entrained disturbances are fundamentally different. The former exhibit some nonphysical features such as ‘entanglement of Fourier components’ and ‘abnormal anisotropy’, which are found to be caused by neglecting the non-parallelism. In the present paper, we consider the asymptotic suction boundary layer, which is an exactly parallel flow. Both temporal and spatial continuous spectra may be defined mathematically. However, at a finite R neither of them represents the physical process of free-stream vortical disturbances penetrating into the boundary layer. The latter must instead be characterized by a peculiar type of continuous modes whose eigenfunctions increase exponentially with the distance from the wall. In the limit R>>1, all three types of continuous spectra are identical at leading order, and hence can be used to represent free-stream vortical disturbances and their entrainment. Low-frequency disturbances are found to generate a large-amplitude streamwise velocity in the boundary layer, which is reminiscent of longitudinal streaks.
Author(s):
Xuesong Wu
Imperial College London
United Kingdom
Ming Dong
Tianjin University
China