Nonlinear evolution and acoustic radiation of instability waves/coherent structures in transitional/turbulent free shear flows

Prof. Xuesong Wu (Imperial College London)

Frank Adams 1,

Free shear flows, such as mixing layers, jets and wakes, are inviscidly unstable due to their inflectional velocity profiles. Instability modes, which are usually excited by external perturbations, amplify on the shear flow, leading to vortex roll-up and randomization in the nonlinear stage. Interestingly, in turbulent state free shear flows exhibit a high degree of order, characterised by the prevalent presence of the so-called coherent structures, the most striking of which are 'Brown-Roshko rollers'. There structures bear remarkable resemblance to instability modes, raising the prospect that their dynamics might be understood and predicted by instability theory.

Instability waves and coherent structures are known to be dynamically significant for entrainment and mixing, noise generation as well as for turbulence modelling. In this talk, I will present a unified nonlinear critical-layer theory to describe the development of instability modes/coherent strictures on transitional/turbulent free shear layers. The effects of non-parallelism and small-scale fluctuations are accounted for. The theory predicts nonlinear saturation, randomisation through a generalized side-band instability mechanism and formation of 'Brown-Roshko rollers'. Furthermore, by analyzing the far-field asymptotic behaviour of the coherent structures, we are able to explain and predict, on the first-principle basis, how coherent structures radiate sound.

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