Nonlinear Instabilities and Large Scale Structures in Mixing Layers
NEW YORK UNIV NY DEPT OF APPLIED SCIENCE
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The dynamics of the large scale structuresvorticity concentrations observed in two-dimensional transitional and turbulent mixing layers are described in terms of a nonlinear inviscid two-dimensional instability model. According to the model, the formation and repetitive pairing of the structures reflect a deterministic cyclic mechanism wherein the nonlinear evolution of the finite amplitude instability, which dominates the flow at any one stage, intrinsically provides first excitation of, and then energy transfer to, the bound 12 subharmonic. The key to identifying and modeling the mechanism resides in a realistic description of the concurrent changes in the mean flow and in the structure of the wave motion during the amplification, saturation and subsequent modulation of the individual nonlinear instability. Models based on weakly nonlinear stability theory prove inadequate to this task. The cause of the failure is identified, and attendant criteria for estimating the applicability of the theory to the present as well as other problems are indicated. By contrast, several salient features of transitional and turbulent mixing layer development are reproduced by the repeated application of a nonlinear model, which describes the life cycle of the individual structure only in terms of the interactive evolution of the mean flow and of the wave motions associated with an appropriate finite amplitude fundamental together with its bound second harmonic.
- Fluid Mechanics