Transient growth associated with secondary vortices in ground/vortex interactions

Abstract

The interaction of an isolated trailing vortex and the ground is investigated. An unsteady unperturbed flow is first calculated through a two-dimensional direct numerical simulation and then used as base flow for linear transient growth studies. The transient growth increases with Reynolds number and maximizes at streamwise wave number 3∼53∼5 over the parameters considered. The most energetic initial perturbation is found to be located aside of the main vortex and convected by the base flow to the ground to interact with the separating boundary layer and the secondary vortex. Finally, the calculated perturbation is used to perturb the base flow in three-dimensional direct numerical simulation. It is observed that the secondary vortex and the rebound motion of the main vortex are both significantly suppressed. This observation indicates that the secondary structures are sensitive to external noise, and the widely reported secondary vortex and its induced rebound motion of the main vortex in two-dimensional direct numerical simulation would not appear or become much weaker in real conditions.