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.

Selection and Impact of an Aerofoil Leading Edge on Boundary Layer Transition

“…The turbulent spot propagation rate can thus be thought of as an indicator of the magnitude of disturbance that enters the boundary layer due to the presence of the leading-edge AR. This can further be corroborated using the conclusions proposed by [9] [10], which indicate that the receptivity of the boundary layer to freestream disturbances greatly depends on the leading-edge curvature, discontinuities in the surface curvature and surface inhomogeneities.…”

Parametric study of a frequency-modulated pulse jet by measurements of flow characteristics

“…The previous studies on the pulsed jet in crossflow showed that, as the duty cycle increases up to 80%, successive vortex rings get closer together and finally interact, resulting in the destruction of vortex rings structure and production of the elongated turbulent puffs [62][63][64]. The vortex ring/turbulent puff can be correlated with spatio-temporal wave front (STWF) for wall bounded transitional and turbulent flows [65][66][67][68].…”

Optimizing control of stationary cross-flow vortices excited by surface roughness

“…1. Coupled together surface roughness (12) and the control mechanism (15) establish a stationary cross-flow instability qn = qe + qc,n , for a given Reynolds number Re and spanwise wavenumber β , but with an unknown amplitude. Here qe represents the stationary cross-flow instability excited by the surface roughness, while the equivalent disturbance generated by the control mechanism qc,n is assumed to be of the form (8) with an amplitude given by (24) qc,n (x, y) = a n e iϕ n I q(x, y).…”

“…Nonmodal stability theory suggests that the superposition of linearly stable non-orthogonal perturbations can lead to a shorttime transient amplification of the energy contained within the initial flow conditions and establish transition to turbulence 8,9 . Numerous studies on the nonmodal mechanism for transition have been undertaken, including the flow within a duct of square cross section 10 and the flow over a flat plate 11,12 . In addition, a recent review by Kerswell 13 presents an optimisation technique based on nonlinear nonmodal analysis.…”