Three-Dimensional Large-Scale Coherent Structures in a Developing Plane Mixing Layer.

A theoretical investigation of the role of three-dimensional large-scale structures and their mutual interactions in a developing, plane mixing layer subjected to external forcing is presented. Large-scale structures are decomposed into 3 fundamental and 2 subharmonic wave modes. Two fundamentals and one subharmonic are three-dimensional. Linear stability of the three-dimensional, viscous shear layer is formulated and solved as the basis for the solution of a nonlinear formulation based on an energy method. This method leads to a set of nonlinearly-coupled, ordinary differential equations governing the evolution of modal energies and phases, and of the shear layer thickness. A parametric study is carried out examining effects of a multitude of initial conditions. It is found that the evolution of the forced three-dimensional shear layer and the associated local entrainment can be influenced greatly by the initial amplitudes and phases of the large-scale modes. The presence of three-dimensional modes may have a profound effect on shear layer growth when forced at amplitudes comparable or larger than those of the two-dimensional ones. This effect is more pronounced at low spanwise wave numbers. Nonlinear interactions between the fundamentals and subharmonics indicate that subharmonics of the most amplified frequency of the shear layer are usually produced during the early stages of flow development, while its harmonics are always produced far downstream, regardless of initial conditions. Experimental observations regarding the appearance of three-dimensional large-scale structures, spanwise wave-length doubling and three-dimensional vortex merging phenomena have been given qualitative interpretation under the light of the theoretical results. Measurements of initial conditions and individual two- and three-dimensional mode energies are presently not available. Therefore, quantitative comparisons of our results with experiments have not been possible. However, this study provides guidelines for future experiments that can clarify the influence of initial conditions and three-dimensional structures on the flow evolution. The results of this study also provide useful parametric information for the control, through multi-mode forcing, of shear layers in practical applications, aiming at mixing and transport augmentation