The signature of laminar instabilities in the zone of transition to turbulence

Abstract

We demonstrate that the spacetime statistics of the birth of turbulent spots in boundary layers can be reconstructed qualitatively from the average behaviour of macroscopic measures in the transition zone. The conclusion in [1] that there exists a connection between the patterns in laminar instability and the birth of turbulent spots is strengthened. We examine why the relationship between instability and transition to turbulence is manifest in some cases and appears to be totally absent in others. Novel cellular automaton-type simulations of the transition zone are conducted, and the pattern of spot birth is obtained from secondary instability analysis. The validity of the hypothesis of concentrated breakdown, according to which most turbulent spots originate at a particular streamwise location, is assessed. The predictions made lend themselves to straightforward experimental verification.

Keywords:

• Turbulent spots
• Instability
• Boundary layer

Acknowledgements

We are most grateful to Professor Narasimha for suggesting cellular automaton type simulations for the transition zone, and for several discussions. Financial support from the Aeronautical R&D Board, Government of India, is gratefully acknowledged.