Order and Disorder in Turbulent Flows

  • John L. Lumley
Conference paper


Examination of pictures of turbulent flows reveals a wide range of order and apparent disorder, seeming to depend on the geometry, Reynolds number and initial conditions. The ordered component may arise as the remnant of an instability of the laminar flow that first gave rise to the turbulence, or as an instability of the turbulent profile and transport. Sometimes it is necessary to take the ordered component explicitly into account in a description of the flow (if the ordered component has arisen from a source different from that of the smaller scale, apparently disordered, component), and sometimes it is not necessary, if everything has arisen from the same source, both components are in equilibrium with each other, and there is only one scaling law for both. The disordered component, on the evidence of exact numerical simulations, is deterministic. By analogy with temporal chaos in mechanical systems with small numbers of degrees of freedom, it is tempting to identify it as resulting from a strange attractor, although there is no real evidence for this. The question seems to be of primarily philosophical interest. What evidence there is suggests that at reasonable Reynolds numbers the dynamical structure would in any event be too complex to be computable, nor are we interested in the details. It seems that a statistical approach to the structure in the phase space would make most sense, since we are interested presumably in global statements, bounds, and the like.


Reynolds Stress Turbulent Boundary Layer Proper Orthogonal Decomposition Wall Region Drag Reduction 
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© Springer-Verlag New York Inc. 1991

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  • John L. Lumley

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