Long Time Evolution of Optimally Perturbed Wing-Tip Vortices

We numerically investigate the effectiveness of optimal perturbations in exciting instabilities in the wake of flow past a finite aspect ratio wing at Re=1000. Analysis of the long-term evolution of perturbed wing-tip vortices is done in a frame of reference that moves roughly at the speed of the perturbation ( \(\sim U_\infty \) ; free stream speed). We simulate the scenarios in which the optimal perturbation is periodically injected into the wake. The wing-tip vortices displacement in response to the perturbation serves as a model for the actual perturbation. The maximum displacement experienced by perturbed wing-tip vortices as a function of time is analysed. The maximum displacement displays short time growth (up to 10-time units) after initial decay for the scenario where a single perturbation is present over a length of \(\sim \) 8b (where ‘b’ is the separation between the wing-tip vortices at \(x=50c\) (c: chord length) from the leading edge of the finite wing in the wake) along the wing-tip vortices. Additionally, the impact of altering the spacing between the wing-tip vortices has been investigated. When the separation is reduced to \(\sim \) 0.37b, the initial rate of decay of maximum displacement slows down by \(\sim 40\%\) . Increased perturbations and further narrowing of the space between the wing-tip vortices are predicted to produce intriguing findings.