On transition due to three-dimensional disturbances in plane Poiseuille flow

Abstract

The purpose of the present study is to characterize the process of laminar–turbulent transition at Reynolds numbers which are subcritical from the two-dimensional linear point of view. The development of a point-like disturbance was studied in an air flow channel with hot-wire anemometry at a Reynolds number of 1600. Localized disturbances were triggered at one of the walls and their development followed downstream by traversing the hot-wire probe in the streamwise direction over a distance of 90 half channel heights, as well as in the normal and spanwise directions. The disturbance evolved into elongated streaky structures with strong spanwise shear (i.e. normal vorticity) which grew in amplitude and streamwise extension and thereafter either decayed or gave rise to a turbulent spot. The results indicate that the mechanism underlying the initial growth is a linear one resulting from the coupling between the normal velocity and the normal vorticity, as described by the three-dimensional linear equations. The nonlinear development of the structure leads to the formation of intense normal shear layers and the appearance of oscillations and ‘spikes’, which multiply and form the rear or a turbulent spot.

Colour of turbulence

“…It has been demonstrated that velocity fluctuations around a laminar base flow exhibit high sensitivity to different sources of perturbations. This has provided reconciliation with experimental observations (Klebanoff et al 1962;Klebanoff 1971;Klingmann 1992;Westin et al 1994;Matsubara & Alfredsson 2001) that, even in the absence of modal instability, bypass transition can be triggered by large transient growth (Gustavsson 1991; Butler & Farrell 1992;Henningson & Reddy 1994;Schmid & Henningson 1994) or large amplification of deterministic and stochastic disturbances (Trefethen et al 1993;Farrell & Ioannou 1993b;Bamieh & Dahleh 2001;Jovanović 2004;Jovanović & Bamieh 2005). The non-normality of the linearized dynamical generator introduces interactions of exponentially decaying normal modes (Trefethen et al 1993;Schmid 2007), which in turn result in high flow sensitivity.…”

Turbulent spots in a channel: large-scale flow and self-sustainability

“…In the case of plane Poiseuille flow, the maximum streamwise fluctuations are expected near planes y = ±0.5h. The plane y = +0.5h is preferred to y = −0.5h due to the non-symmetric character of the injection (Klingmann 1992). The fluid is lit with a 1 mm thick light sheet and seeded with neutrally buoyant particles (d p ≈ 20 µm).…”

Experimental investigation of relaminarizing and transitional channel flows

“…The temperature variation during the taking of a set of the measurements was monitored to ensure that the temperature drift of the flow from the calibration did not exceed more than 0.7 • C. The voltages of the hot-wire anemometer were acquired via an analog/digital converter with a sampling frequency of 20 kHz, and a sampling time of 30 s for a streamwise positioning measurement and 300 s for a detailed measurement at the most downstream position. A wedge mechanism modeled on that used by Klingmann 26 was employed for probe positioning in the wall-normal direction. It was attached at the ends of two 2300 mm long bars and was moved by a linear actuator in the streamwise direction.…”