The lift-up effect: The linear mechanism behind transition and turbulence in shear flows

Abstract

The formation and amplification of streamwise velocity perturbations induced by cross-stream disturbances is ubiquitous in shear flows. This disturbance growth mechanism, so neatly identified by Ellingsen and Palm in 1975, is a key process in transition to turbulence and self-sustained turbulence. In this review, we first present the original derivation and early studies and then discuss the non-modal growth of streaks, the result of the lift-up process, in transitional and turbulent shear flows. In the second part, the effects on the lift-up process of additives in the fluid and of a second phase are discussed and new results presented with emphasis on particle-laden shear flows. For all cases considered, we see the lift-up process to be a very robust process, always present as a first step in subcritical transition.

The planar X-junction flow: stability analysis and control

“…To determine the instability mechanism in our flow, we note that the present instability is stationary, the mode shape streamwise elongated, and the streamwise velocity component order of magnitude larger than the vertical component ( figure 4 a and b). This strongly indicates a lift-up mechanism, where a small initial v-perturbation induces a strong u-perturbation (for a review on lift-up see Brandt (2014)). …”

Transient energy growth of optimal streaks in parallel round jets

“…This transient growth is related to inviscid instabilities whereby shear flows can be unstable to disturbances in the cross-stream velocity components, whose kinetic energy grows linearly in time, even though the base flow does not contain any inflection point. 11,12 For the particular case of round jets, recent works on non-modal instability 13,14 have shown that transient growth of helical perturbations (azimuthal wavenumber m = 1) is favored by this algebraic instability, due mainly to the lift-up effect, 11,12,15 although the Orr mechanism, 16 i.e., the progressive vortex sheet alignment with shear, has been also proven to occur in jets subjected to optimal harmonic forcing. 17 In an attempt to unravel the role of different transient mechanisms in round jets, Jiménez-González et al 18 have recently identified two mechanisms, within the framework of a parametric study aiming at analyzing the influence of the jet velocity profile on the instability of axisymmetric (m = 0) and helical (m = 1) perturbations.…”

“…If the transient amplification of kinetic energy for axially invariant perturbations is sufficiently large, in view of previous results on shear flows, 15 it could be conjectured that a nonlinear transition may be eventually triggered in the jet, when the perturbation is initially injected, which might be used to control unstable asymptotic disturbances. For instance, the generation of Kelvin-Helmholtz vortex rings and its subsequent subharmonic instability leading to the merging of vortices in pairs, i.e., vortex pairing, 19 is a source of aeroacoustic noise which is important to control or even suppress in many industrial applications because of noise nuisance or acoustic stealth.…”

Acoustic receptivity and transition modeling of Tollmien-Schlichting disturbances induced by distributed surface roughness

“…For larger disturbance environments other mechanisms which bypass linear growth may come into play. This process generally involves transient growth which is described by nonmodal stability theory 2,3 . The term receptivity was coined in 1969 by Morkovin 4 .…”