

Artikel
On the convectively unstable nature of optimal streaks in boundary layers
Författare: 
Brandt, L.B., Cossu, C., Chomaz, J.M., Huerre, P., Henningson, D.S.H. 
Dokumenttyp: 
Artikel 
Tillstånd: 
Publicerad 
Tidskrift: 
J. Fluid Mech. 
Volym: 
485
221242 
År: 
2003 
AbstractThe objective of the study is to determine the absolute/convective nature of the secondary instability experienced by finiteamplitude streaks in the flatplate boundary layer. A family of parallel streaky base flows is defined by extracting velocity profiles from the direct numerical simulations of nonlinearly saturated optimal streaks performed by Andersson, Brandt, bottaro & Henningson (2001). 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 spatiotemporal 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 edgevelocity of a TollmienSchlichting wave packet in the Blasius boundary layer is around 35% of the freestream velocity, while that of the wave packet riding on the streaky base flow is around 70%. This feature is due to the fact that 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 TollmienSchlichting instability. The streak impulse response consists of the sinuous mode of instability triggered by the spanwise wakelike profile, as confirmed by comparing the numerical results with the absolute/convective instability properties of the family of twodimensional 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.

