Analyzing mean transport equations of turbulence and linear disturbances in decaying flows

The decay of laminar disturbances and turbulence in mean shear-free flows i s studied. In laminar flows, such disturbances are linear superpositions of modes governed by the Orr-Sommerfeld equation. In turbulent flows, disturb ances are described through transport equations for representative mean qua ntities. The link between a description based on a deterministic evolution equation and a probability-based mean transport equation is established. Be cause an uncertainty in initial conditions exists in the laminar as well as the turbulent regime, a probability distribution must be defined even in t he 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 quantiti es is then described by transport equations similar to those for the corres ponding turbulent decaying flow. (C) 1999 American Institute of Physics. [S 1070-6631(99)00609-1].