Nonlinear dynamics of large-scale coherent structures in free shear layers

etc15 Tracking Number 190

It is well known that fully developed turbulent free shear layers exhibit a high degree of order, characterized by large-scale coherent structures, i.e. spanwise vortex rollers. Extensive experimental investigations show that such organised motions 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 paper, we present a mathematical theory to describe the nonlinear dynamics of coherent structures. 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 fast spreading of the mean flow, and (b) the influence of small-scale turbulence on coherent structures. The combination of these factors with nonlinearity leads to an interesting evolution system, consisting of the coupled amplitude and vorticity equations, in which non-parallelism contributes the so-called translational critical-layer effect. Numerical solutions of the evolution system captures vortex roll-up, which is the hallmark of turbulent mixing layer, and the predicted amplitude development closely mimics what was measured in experiments. Key words: turbulence, coherent structures, instability, nonlinearity