Transition experiments in a boundary layer with embedded streamwise vortices

Abstract

The stability of a flat plate boundary layer modulated by stationary streamwise vortices was studied experimentally in the T-324 low speed wind tunnel in Novosibirsk. Vortices were generated inside the boundary layer by means of roughness elements arranged in a regular array along the spanwise (z-) direction. Transition is not caused directly by these structures, but by the growth of small amplitude traveling waves riding on top of the steady vortices. This situation is analogous to the transition process in Görtler and cross-flows. The waves were found to amplify up to a stage where higher harmonics are generated, leading to turbulent breakdown and disintegration of the spanwise boundary layer structure. For strong modulations, the observed instability is quite powerful, and can be excited ‘‘naturally’’ by small uncontrollable background disturbances. Controlled oscillations were then introduced by means of a vibrating ribbon, allowing a detailed investigation of the wave characteristics. The instability seems to be associated with the spanwise gradients of the mean flow, ∂U/∂z, and at all z-positions, the maximum wave amplitude was found at a wall-normal position where the mean velocity is equal to the phase velocity of the wave, U(y)=c, i.e., at the local critical layer. Unstable waves were observed at frequencies well above those for which Tollmien–Schlichting (TS) waves amplify in the Blasius boundary layer. Excitation at lower frequencies and milder basic flow modulations showed that TS-type waves may also develop. The relation between TS-type waves and the observed high-frequency instability is discussed in the light of previous authors’ findings.

Algebraic growth in a Blasius boundary layer: Nonlinear optimal disturbances

“…It has been reported by Alfredsson (private communication, 1998) that "amplitudes of at least 20%" are needed for an instability of the streaks to emerge. A similar threshold was detected by Bakchinov et al [38] in their experiments in which streaks were generated by roughness elements distributed regularly along the span of the wall, and the instability was triggered by a vibrating ribbon upstream. In the inviscid linear stability analysis of Andersson et al [17] the threshold amplitude for the occurrence of a sinuous (subharmonic) instability of the parallel streaky flow with β = 0.45 was 26% of the free stream speed, whereas a larger value (37%) was found for the amplification of a varicose mode.…”

Concave Surface Boundary Layer Flows in the Presence of Streamwise Vortices

“…4(a)-(d). This phenomenon indicates the presence of the secondary instability mode called sinuous mode that is believed to lead the flow to turbulence [25]. [26].…”

Advanced Fluid Research On Drag reduction In Turbulence Experiments –AFRODITE–

“…Setting up the streamwise streaks in an experiment White (2002) investigated the transient growth of disturbances of small amplitude (stable) steady streaks generated by using a spanwise periodic array of roughness elements of circular section Bakchinov et al (1995); Kendall (1990), after a complex region of growing and decaying modes a high speed region is induced behind the roughness element. An explanation for this behavior can be found by considering the perturbation induced by a roughness element in a wall-bounded shear flow (Hunt et al, 1978;Acarlar & Smith, 1987;Dèlery, 2001).…”