The behavior of the tip vortex behind a square NACA0015 wing was numerically investigated. The problems studied include the stationary and the oscillating wings at static and dynamic stall conditions. Reynolds-averaged Navier-Stokes and detached-eddy simulation schemes were implemented. Vortex structures predicted by Reynolds-averaged Navier-Stokes were mainly diffused while detached-eddy simulation was able to produce qualitatively and quantitatively better results as compared to the experimental data. The breakup of the tip vortex, which started at the end of the upstroke and continued to the middle of the downstroke over an oscillation cycle, was observed in detached-eddy simulation data.