Space–time dynamics of optimal wavepackets for streaks in a channel entrance flow

Abstract

The laminar–turbulent transition of a plane channel entrance flow is revisited using global linear optimization analyses and direct numerical simulations. The investigated case corresponds to uniform upstream velocity conditions and a moderate value of Reynolds number so that the two-dimensional developing flow is linearly stable under the parallel flow assumption. However, the boundary layers in the entry zone are capable of supporting the development of streaks, which may experience secondary instability and evolve to turbulence. In this study, global optimal linear perturbations are computed and studied in the nonlinear regime for different values of streak amplitude and optimization time. These optimal perturbations take the form of wavepackets having either varicose or sinuous symmetry. It is shown that, for short optimization times, varicose wavepackets grow through a combination of Orr and lift-up effects, whereas for longer target times, both sinuous and varicose wavepackets exhibit an instability mechanism driven by the presence of inflection points in the streaky flow. In addition, while the optimal varicose modes obtained for short optimization times are localized near the inlet, where the base flow is strongly three-dimensional, when the target time is increased, the sinuous and varicose optimal modes are displaced farther downstream, in the nearly parallel streaky flow. Finally, the optimal wavepackets are found to lead to turbulence for sufficiently high initial amplitudes. It is noticed that the resulting turbulent flows have the same wall-shear stress, whether the wavepackets have been obtained for short or for long time optimization.

Growth of vortical disturbances entrained in the entrance region of a circular pipe

“…The inviscid streamwise velocity is larger than unity near the wall because it accelerates along x to conserve the mass flow rate as the radial velocity decreases from its boundary-layer blowing value as the pipe axis is approached. This acceleration gives rise to the local near-wall peak in the Ū profile, also reported in Durst et al (2005) for entry-pipe flow and in Sparrow, Lin & Lundgren (1964), Panton (2013) and Alizard et al (2018) for entry-channel flows. The peak occurs because the inviscid streamwise velocity is larger than the viscous streamwise velocity deficit of the boundary layer.…”

Entrainment and growth of vortical disturbances in the channel-entrance region

“…They reported the generation of streaks, their subsequent transient growth, and the eventual flow breakdown caused by the interaction between the upper and lower boundary layers. More recently, Alizard et al (2018) studied the problem of laminar-to-turbulent transition of a channel-entrance flow subject to optimal wavepackets as initial conditions. Transition was found to be triggered by the secondary instability of the streaky structures forming within the boundary layers.…”