Multiple-contour-dynamic simulation of eddy scales in the plane shear layer

Abstract

The method of contour dynamics (CD) is applied to several inviscid prototype flows typical of the motions found in the transition region of the free shear layer. Examples of the interaction between the fundamental streamwise-layer perturbation and its first subharmonic are presented that illustrate the events of pairing and tearing of two rolled-up cores and also the coalescence of three rolled-up cores. The present simulations of the temporally unstable two-dimensional layer, at effectively infinite Reynolds number, support the hypothesis that the dynamics of the large-scale roll-up is only weakly dependent on Reynolds number. However, we find fine-scale structure that is not apparent in previous simulations at moderate Reynolds number. Spiral filaments of rotational fluid wrap around the rolled-up vortex cores producing 'spiky' vorticity distributions together with the entanglement of large quantities of irrotational fluid into the layer. Simulations proceeded only until the first such event because we were unable to resolve the fine detail generated subsequently. The inclusion of prescribed vortex stretching parallel to the vortex lines is found to accelerate the initial roll-up and to enhance the production of spiral vortex filaments. In the fundamental-subharmonic interaction, vortex stretching slows but does not prevent pairing.

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