Non-Linear Waves and Quasi-Ordered Structures in Turbulence.

摘要

The research seeks a deterministic analytical model, derived from first principles without empiricism, for the development and evolution of quasi-ordered, large scale, events/structures in turbulent flows. Upon a careful analysis of recent experiments with homogeneous incompressible transitional and turbulent mixing layers, the events/structures are associated with non-linear instability waves whose behavior is dominated by self-induced effects rather than by interactions among instabilities which are resonant according to the linear dispersion relation. The non-linear transport of vorticity in the neighborhood of the critical layer is identified as the flow process responsible for the self-induced effects beginning at modest wave amplitudes A > or = .01. A mathematical model of the attendant generation of bound-wave harmonics, subharmonics and sideband frequencies in strictly two-dimensional incompressible flow subject to monochromatic disturbance input is developed by joint use of matched asymptotic expansion and stretched coordinates techniques. The predictions of the model are compared favorably with relevant experimental data for mixing layers. Model extensions required for the analysis of modulated three-dimensional non-linear disturbances in non-homogeneous compressible flows are outlined, and the role of those results in describing the evolution of quasi-ordered events/structures in practical turbulent flows are discussed. (Author)