  We investigate the spatial distributions and production mechanisms of
vorticity and turbulent kinetic energy around a finite NACA 0018 wing with
square wingtip profile at $Re_c=10^4$ and $10^{\circ}$ angle of attack with the
aid of Direct Numerical Simulation (DNS). The analysis focuses on the highly
inhomogeneous region around the tip and the near wake; this region is highly
convoluted, strongly three-dimensional, and far from being self-similar. The
flow separates close to the leading edge creating a large, open recirculation
zone around the central part of the wing. In the proximity of the tip, the flow
remains attached but another smaller recirculation zone forms closer to the
trailing edge; this zone strongly affects the development of main wing tip
vortex. The early formation mechanisms of three vortices close to the leading
edge are elucidated and discussed. More specifically, we analyse the role of
vortex stretching/compression and tilting, and how it affects the strength of
each vortex as it approaches the trailing edge. We find that the
three-dimensional flow separation at the sharp tip close to the leading edge
plays an important role on the subsequent vortical flow development on the
suction side. The production of turbulent kinetic energy and Reynolds stresses
is also investigated and discussed in conjunction with the identified vortex
patterns. The detailed analysis of the mechanisms that sustain vorticity and
turbulent kinetic energy improves our understanding of these highly three
dimensional, non-equilibrium flows and can lead to better actuation methods to
manipulate these flows.
