Instability and Turbulence in Shear Flows

Abstract

Increasing attention is being paid to the large scale structure of turbulence and to the so-called "coherent" vortical structures which have been disclosed and studied for a number of turbulent shear flows in laboratory experiments and in numerical simulations. The coherent structures develop from the instability waves which create the flow; they portray the genesis of the turbulence in the primary instability of the global vorticity distribution. This is not in the sense of classical laminar instability, whichinitiates transition to turbulence, but as thedriving instability in the fully developed turbulence. That instability provides the link to the amplitude of the turbulent motion, which in classical turbulent modelling must be calibrated empirically as a fundamental step or steps in the closure of the Reynolds averaged equations of motion. It also rationalizes the dependence on various parameters, such as compressibility, clarifies response to external disturbances, and suggests the possibility of "turbulence control". The global instability is being incorporated into new models of turbulent shear flow development and the coherent structures form the basis for new, Lagrangian models of chemical mixing and reaction in these flows.

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