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

Published online by Cambridge University Press:  26 April 2006

Dan S. Henningson ,
Anders Lundbladh  and
Arne V. Johansson
Dan S. Henningson
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA Also at The Aeronautical Research Institute of Sweden (FFA), Bromma.
Anders Lundbladh
Affiliation:
Department of Mechanics, Royal Institute of Technology, S-10044 Stockholm, Sweden Also at The Aeronautical Research Institute of Sweden (FFA), Bromma.
Arne V. Johansson
Affiliation:
Department of Mechanics, Royal Institute of Technology, S-10044 Stockholm, Sweden
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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.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 250 , May 1993 , pp. 169 - 207
Copyright
© 1993 Cambridge University Press

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