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Onset and development of turbulence in two-dimensional periodic shear flows

Published online by Cambridge University Press:  21 April 2006

Roland Grappin ,
Jacques Leorat  and
Pasquale Londrillo
Roland Grappin
Affiliation:
Observatoire de Meudon, CNRS UA173, F-92190 Meudon, France
Jacques Leorat
Affiliation:
Observatoire de Meudon, CNRS UA173, F-92190 Meudon, France
Pasquale Londrillo
Affiliation:
Osservatorio di Astronomico, Universita di Bologna, Italy
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Abstract

We investigate numerically the time evolution of a two-dimensional flow submitted to a spatially periodic shear force. Initially, the flow is at equilibrium, the forcing balancing viscous stresses. At Reynolds numbers slightly above critical, a large-scale, linear instability drives the fluid towards a stable laminar state. At larger Reynolds number turbulence finally develops after several transient states. These transient states are described by measuring the divergence rate of linearized trajectories from the turbulent flow. This rate gives asymptotically a measure of the first Lyapunov exponent of the flow. We find that the first Lyapunov exponent scales as the characteristic frequency of the flow at large scale. We show here data on incompressible, isothermal and perfect gas (subsonic) two-dimensional flows with unit Prandtl number, and Reynolds number around 30.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 195 , October 1988 , pp. 239 - 256
Copyright
© 1988 Cambridge University Press

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