Effects of free stream excitation on the boundary layer over a semi-infinite flat plate

Abstract

Transition to turbulence for flow over a semi-infinite flat plate can occur due to disturbances convecting in the free stream, and various routes have been studied in the literature. Specifically, this has been discussed in great detail as a global receptivity problem [Sengupta et al., “Nonmodal nonlinear route of transition to two-dimensional turbulence,” Phys. Rev. Res. 2, 012033(R) (2020)]. Here, the same is studied for the deterministic excitation of a vortex translating with a fixed speed at a fixed height outside the boundary layer. The study aims to capture the fundamental differences in the mechanisms followed by linear and nonlinear global formulations, the existence of the nonmodal spatio-temporal wave front (STWF), onset of nonlinearity, and nonlinear saturation of the STWF by dispersion and phase effects. Other issues related to the initial location of the vortex and its strength are addressed in the present work. The main finding of the investigation is that the onset of the STWF is captured by both formulations, but it occurs at different locations and times. The nonlinear global receptivity study shows earlier onset and saturation of the STWF, while the corresponding linear study shows a delayed onset and no saturation. Overall, it is essential to operate within a nonlinear framework to capture the later stages of transition, phase shift due to nonlinear dispersion and saturation, which depend strictly on nonlinearity.