On the convectively unstable nature of optimal streaks in boundary layers

Abstract

International audienceThe objective of the study is to determine the absolute/convective nature of the secondary instability experienced by finite-amplitude streaks in the flat-plate boundary layer. A family of parallel streaky base flows is defined by extracting velocity profiles from direct numerical simulations of nonlinearly saturated optimal streaks. The computed impulse response of the streaky base flows is then determined as a function of streak amplitude and streamwise station. Both the temporal and spatio-temporal instability properties are directly retrieved from the impulse response wave packet, without solving the dispersion relation or applying the pinching point criterion in the complex wavenumber plane. The instability of optimal streaks is found to be unambiguously convective for all streak amplitudes and streamwise stations. It is more convective than the Blasius boundary layer in the absence of streaks; the trailing edge-velocity of a Tollmien-Schlichting wave packet in the Blasius boundary layer is around 35% of the free-stream velocity, while that of the wave packet riding on the streaky base flow is around 70%. This is because the streak instability is primarily induced by the spanwise shear and the associated Reynolds stress production term is located further away from the wall, in a larger velocity region, than for the Tollmien-Schlichting instability. The streak impulse response consists of the sinuous mode of instability triggered by the spanwise wake-like profile, as confirmed by comparing the numerical results with the absolute/convective instability properties of the family of two-dimensional wakes introduced by Monkewitz (1988). The convective nature of the secondary streak instability implies that the type of bypass transition studied here involves streaks that behave as amplifiers of external noise

Evolution and instability of unsteady nonlinear streaks generated by free-stream vortical disturbances

“…The propagation speed does not appear to be sensitive to the profile and amplitude of streaks. Similar values were obtained from numerical studies of impulse propagation in a boundary boundary perturbed by an optimal disturbance (Brandt et al 2003;Schlatter et al 2008). The spatial growth rates of unstable modes, calculated by solving the spatial eigenvalue problem as described above, are displayed in figure 13c.…”

“…The sinuous mode instability was found to be more dangerous, and occurs when the streak amplitude, measured by its streamwise velocity, exceeds a threshold 0.26U ∞ . The instability has been shown to be of convective nature (Brandt et al 2003).…”

Self-Sustained Localized Structures in a Boundary-Layer Flow

“…It features at all times a pair of elongated low-speed streaks. These streaks support convective instabilities in the form of timedependent wavy modulations [18]. Visualization of the vortices using the 2 vortex identification criterion [19] reveals longitudinal vortices staggered on the flanks of the streaks, as well as hairpin-shaped vortices forming precisely above the region where streaks pinch.…”

“…4. The lowest velocity is the signature of the streaks near the wall, the others corresponding to convective streak instabilities [18]. Both depart clearly from the Blasius profile, the departure being maximal closest to the wall, as in the turbulent regime [25].…”

Transition induced by linear and nonlinear perturbation growth in flow past a compressor blade

“…Brandt et al (2003) found that the instability of optimal streaks is convective and that the streaks behave as amplifiers of external noise. The secondary instabilities and the associated modes can be calculated through linear Floquet analyses of the streak base flow extracted from DNS or experiential results (Elofsson, Kawakami & Alfredsson 1999;Ricco, Luo & Wu 2011).…”