A mechanism for bypass transition from localized disturbances in wall-bounded shear flows

Abstract

The linear, nonlinear and breakdown stages in the transition of localized disturbances in plane Poiseuille flow is studied by direct numerical simulations and analysis of the linearized Navier–Stokes equations. Three-dimensionality plays a key role and allows for algebraic growth of the normal vorticity through the linear lift-up mechanism. This growth primarily generates elongated structures in the streamwise direction since it is largest at low streamwise wavenumbers. For finite-amplitude disturbances such structures will be generated essentially independent of the details of the initial disturbance, since the preferred nonlinear interactions transfer energy to low streamwise wavenumbers. The nonlinear interactions also give a decrease in the spanwise scales. For the stronger initial disturbances the streamwise vorticity associated with the slightly inclined streaks was found to roll up into distinct streamwise vortices in the vicinity of which breakdown occurred. The breakdown starts with a local rapid growth of the normal velocity bringing low-speed fluid out from the wall. This phenomenon is similar to the low-velocity spikes previously observed in transition experiments. Soon thereafter a small turbulent spot is formed. This scenario represents a bypass of the regular Tollmien–Schlichting, secondary instability process. The simulations have been carried out with a sufficient spatial resolution to ensure an accurate description of all stages of the breakdown and spot formation processes. The generality of the observed processes is substantiated by use of different types of initial disturbances and by Blasius boundary-layer simulations. The present results point in the direction of universality of the observed transition mechanisms for localized disturbances in wall-bounded shear flows.

The initial stage of transition in pipe flow: role of optimal base-flow distortions

“…In particular, it is clear from figure 18 that low-frequency modes (for example modes (3, 1), (4, 0), (5, 1) and (6, 0)) dominate over other nonlinearly generated modes with higher wavenumbers, which do not possess the potential to grow by linear mechanisms. This was already observed by Ma et al (1999) and Henningson, Lundbladh & Johansson (1993), who speak, respectively, of an m-cascade in HagenPoiseuille flow or a β-cascade in plane Poiseuille flow, in which the disturbance energy is mainly transferred through a route with increasing azimuthal or spanwise wavenumber.…”

Modeling of transitional channel flow using balanced proper orthogonal decomposition

“…11. Individual localized disturbances to channel flow were investigated by Henningson et al [10]. Since balanced truncation involves the approximation of the system's Gramians (although in BPOD we do not actually compute the …”

Hairpin-like optimal perturbations in plane Poiseuille flow

“…Wu & Moin (2009) have analysed the generation of hairpin structures from Λ-shaped vortex structures induced in a boundary layer by the receptivity process from large-amplitude free-stream turbulence; Acarlar & Smith (1987) and Henningson, Lundbladh & Johansson (1993) have studied the formation of hairpin vortices from localized disturbances in boundary-layer and channel flows, respectively. Suponitsky, Cohen & Bar-Yoseph (2005) have studied a simple model of interaction between a localized vortical disturbance and a uniform unbounded shear flow, showing that a small-amplitude initial disturbance always evolves into a streaky structure, whereas a large-amplitude one evolves into a hairpin vortex under some conditions.…”