On the trajectory of leading-edge vortices under the influence of Coriolis acceleration

Leading-edge vortices (LEVs) can form and remain attached to a rotating wing indefinitely, but the mechanisms of stable attachment are not well understood. Taking for granted that such stable structures do form, a practical question arises: what is the trajectory of the LEV core? Noting that span-wise flow exists within the LEV core, it is apparent that a mean streamline aligned with the axis of the stable LEV must exist. The present work uses the Navier–Stokes equations along such a steady, axial streamline in order to consider the accelerations that act in the streamline-normal direction to affect its local curvature. With some simplifying assumptions, a coupled system of ordinary differential equations is derived that describes the trajectory of an axial streamline through the vortex core. The model is compared to previous work, and is found to predict the trajectory of the LEV core well at span-wise locations inboard of the midspan. This result suggests that Coriolis acceleration is responsible for limiting the span-wise extent of a stable LEV by tilting it into the wake within several chord lengths from the centre of rotation. The downwash due to the tip vortex also appears to play a role, as the only significant differences between model-predicted LEV trajectories and previous results are in the plate-normal direction.