Vortex dynamics of the two-dimensional turbulent shear layer

Abstract

The role of large vortex structures in the evolution of a two-dimensional shear layer is studied numerically. The motion of up to 4096 vortices is followed on a 256 × 256 grid using the cloud-in-cell algorithm. The scaling predictions of self-preservation theory are confirmed for low-order velocity correlations, although the existence of vortex structures produces large fluctuations even in a simulation of this size. The simple picture of the shear layer as a line of vortex blobs, that merge pairwise thus thickening the layer, is not seen. On the contrary, the layer seems to thicken by the scattering of vortex structures of roughly fixed size about the midline. The size of the vortex structures does not scale with the layer thickness. A study of the entrainment of a passive marker shows that flow visualization experiments may have overestimated the size of the vortex structures. It appears that the finite area vortices have time to equilibrate between mergings, and the consequences of applying equilibrium statistical mechanics to their internal structure are explored. A simple model is presented which demonstrates how the size and separation of vortex structures may lock into a fixed ratio. This is precisely the type of mechanism that is needed to produce simple scaling in a flow that has initially several distinct length scales. A number of consistency checks on the numerical results are performed. In particular, the evolution of the same vortex configuration on two grids of different size is compared. This test showed that, although errors on subgrid scales do propagate to small wavenumbers, the dominant wavenumber of vorticity cascades back ahead of the peak in the error spectrum.