Randomization And Spectrum Broadening In Free Shear Layers

It has been observed experimentally that when a free shear layer (such as a mixing layer or a wake) is perturbed by a disturbance consisting of two waves with frequenciesω1 andω2, components with combination frequencies mω1±nω2 develop to a significant level, thereby causing flow randomization. In this thesis, such flow randomization process is investigated theoretically for the case whereΔω=ω1 ?ω2 is small. The perturbation can then be treated as modulated wave train. A nonlinear system governing its evolution is derived by using the non-equilibrium nonlinear critical-layer theory.The evolution system is solved numerically using a third-order Adams'predictor-corrector scheme to study the interaction of sideband instability waves introduced to the flow. The following findings are made.1. Due to the interaction among the sideband instability waves, one of the waves would amplify at a rate significantly larger than its linear growth rate.2. Because of the interaction of two waves with frequencies ofω1 andω2, a wave with the difference frequencyΔω=ω1 ?ω2 is first generated and grows rapidly, confirming the experimental observation.3. As the wave with the difference frequency ofΔω=ω1 ?ω2 grows, it interacts with the two waves with frequencies ofω1 andω2 as well as with their harmonics. This leads to rapid development of components at various combination frequencies, mω1±nω2. Such a spectral broadening may cause flow randomization.