UNSTEADY MODELS FOR THE NONLINEAR EVOLUTION OF THE MIXING LAYER

We investigate several unsteady two-dimensional models of increasing complexity for the nonlinear evolution of the temporally growing mixing layer. In the simplest model, we use a subharmonically perturbed point vortex row which serves initially to identify certain key dynamical and kinematic aspects of the transition process, in which small scales in the flow are rapidly generated as a result of the vortex pairing process. A slightly more realistic vortex blob model is used at the next level. Finally, Navier-Stokes calculations are performed in order to identify which features are artifacts of the earlier models, and which ones are likely to be inherent to the physics. An important kinematic aspect of the transition, present in all of the models for small subharmonic perturbations, is a change in the topology of the streamline pattern when viewed in a rotating reference frame. This topological change contributes to the formation of spiral arm structures seen in other work and consequently to the intense production of small scales. For larger subharmonic perturbation amplitudes, this effect does not occur. We attempt to establish a connection between the aspects of our two-dimensional models and the findings of other authors in three-dimensional computations and experiments.