Simulation of vortex pair instabilities behind a split wing

The dynamics of a pair of counter-rotating wingtip vortices formed in the wake of a slotted wing are investigated numerically at Reynolds numbers 3000 to 10 000, considering a NACA12 airfoil with various angles of attack ranging from 5 to 10 degrees. Two parts of the wake are investigated. Firstly, we focus on the von Kármán wake of the wing and explore its properties in reference to inifinite wing results. The finiteness of the wing introduces notable differences. Secondly, we examine the dynamics of the wingtip vortices and the instabilities that are obtained. The influence of the von Kármán wake on this vortex is emphasized. Two behaviors are identified, depending on the angle of attack and Reynolds number. An orthogonal proper orthogonal decomposition (POD) is applied to identify the coherent structures that superimpose upon the mean flow. A Fourier analysis of the vortex centerline is conducted to highlight the dominant wavelengths.