Nonlinear Dynamics Of Large-scale Coherent Structures In Free Shear Layers

It is well known that fully developed turbulent free shear layers, such as mixing layer, wake and(plane and circular) jet, exhibit a high degree of order, characterized by large-scale coherent structures, i.e. spanwise vortex rollers. Such organized motions play an important role in momentum and heat transport, entrainment and mixing of species and generation of noise. Extensive experimental investigations show that coherent structures bear remarkable resemblance to inviscid instability waves, and their main characteristics, including the length scales, propagation speeds and transverse structure, are reasonably well predicted by inviscid linear stability analysis of the mean flow.In this thesis, we present a mathematical theory to describe the nonlinear dynamics of coherent structures in a turbulent mixing layer. The theory is adapted from the nonlinear non-equilibrium critical-layer approach for laminar-flow instabilities by accounting for(a) the enhanced non-parallelism associated with the fast spreading of the mean flow, and(b) the influence of small-scale turbulence on coherent structures. The combination of these extra physical factors with nonlinearity leads to a new and interesting evolution system, consisting of the coupled amplitude and vorticity equations, in which non-parallelism contributes the so-called translational critical-layer effect as well as the usual direct influence on the growth rate. Numerical solutions of the evolution system capture vortex roll-up, which is the hallmark of turbulent mixing layer, and the predicted amplitude development closely mimics what was measured in experiments.