Document Type

Article

Publication Date

1999

DOI

10.1063/1.870124

Publication Title

Physics of Fluids

Volume

11

Issue

9

Pages

2626-2631

Abstract

The decay of laminar disturbances and turbulence in mean shear-free flows is studied. In laminar flows, such disturbances are linear superpositions of modes governed by the Orr-Sommerfeld equation. In turbulent flows, disturbances are described through transport equations for representative mean quantities. The link between a description based on a deterministic evolution equation and a probability-based mean transport equation is established. Because an uncertainty in initial conditions exists in the laminar as well as the turbulent regime, a probability distribution must be defined even in the laminar case. Using this probability distribution, it is shown that the exponential decay of the linear modes in the laminar regime can be related to a power law decay of both the (ensemble) mean disturbance kinetic energy and the dissipation rate. The evolution of these mean disturbance quantities is then described by transport equations similar to those for the corresponding turbulent decaying flow.

Original Publication Citation

Thacker, W.D., Gatski, T.B., & Grosch, C.E. (1999). Analyzing mean transport equations of turbulence and linear disturbances in decaying flows. Physics of Fluids, 11(9), 2626-2631. doi: 10.1063/1.870124

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