VLES of aircraft wake vortices in a turbulent atmosphere : a study of decay

Very Large-Eddy Simulations (VLES) of aircraft wake vortices in various atmospheric turbulence conditions are carried out. The turbulence level is characterized by the eddy dissipation rateand ranges from very strong to weak. The turbulence is assumed isotropic. Two LES models are considered. Most simulations were done using explicit gaussian filtering and a mixed model: thetensor-diffusivity model supplemented by a dynamic Smagorinsky term. As a point of comparison, some simulations were done using the classical dynamic Smagorinsky model alone (thus without explicit filtering). Initially, the wake vortices are assumed to follow the fairly “universal” circulation profile shortly after rollup. The vortex global circulation is investigated: its decay exhibits a similar behavior in all cases, leading to the exponential decay model based on the eddy dissipation rate. The present model differs from others by the presence of a time delay before the exponential decay. The constant defining the decay rate is also found to be quite different from that found in the literature. This lack of agreement is partially explained by the differences in the definitions of circulations.