| Numerical simulation of turbulent shear flows are computationally demanding, but by taking advantage of the mechanics determining the nature of free shear flows, it is possible to develop inviscid vortex methods that permit large-scale flow simulations. The large amplitude Kelvin-Helmholtz instability of a relatively thin vorticity layer is studied in two and three dimensions using numerical simulations. For the two-dimensional problem the goal is the development of a vortex model that correctly includes viscous effects. As a first step, inviscid vortex sheet calculations are compared to fully viscous finite difference calculations of the Navier-Stokes equations. Results show that the inviscid regularization effectively reproduces many of the features associated with the thickness of viscous vorticity layers with increasing Reynolds number, though the simplified dynamics of the inviscid model allows it to accurately simulate only the large scale features of the vorticity field. The results also show that the limiting solution of zero regularization for the inviscid model and high Reynolds number and zero initial thickness for the viscous simulations appear to be the same.; The second step, is the development of a modified vortex sheet model by incorporating real fluid effects in the thin layer model. This model accounts for the effects of viscosity and finite thickness in an approximate way, but retains the major computational advantages of the original vortex sheet model. The results from this improved vortex sheet model show improvements over the constant vortex blob computations. Particularly, the inner structure of the rolled up vortex is much better reproduced by the model and is similar to the viscous results. The results however, are obtained for a relatively large regularization parameter.; In the three-dimensional case, an efficient numerical method, based on the vortexin-cell approach, is developed. The method is used to study the three-dimensional evolution of inviscid jets. The formation of vortex rings, helical vortical structures as well as pairing and three-dimensional vortical structures are followed in time. These vorticity dynamics phenomena have been reported in various experimental studies. |
