Entrainment of Short-wavelength Free-stream Vortical Disturbances into Boundary Layers

Abstract

This paper is concerned with how free-stream vortical disturbances (FSVD) enter the boundary layer, a process which we refer to as entrainment. A self-consistent description of this physical process is presented, which shows that the non-parallel-flow effect plays a leading-order role even for disturbances with short wavelength comparable with the boundary-layer thickness or shorter. The entrained disturbances are thus drastically different from continuous modes of Orr-Sommerfeld/Squire equations, which neglect non-parallelism at outset. Indeed neglecting non-parallelism is found to cause several nonphysical features of continuous modes, including ‘Fourier entanglement’, abnormal anisotropy of FSVD, and for compressible boundary layers, entanglement of vortical and entropy modes. Eigenfunctions of continuous modes and their superpositions have been used to specify the inlet conditions in direct numerical simulations of bypass transition and boundary-layer receptivity. The findings of present study indicate that this popular practice is inappropriate, and a remedy is suggested.