Viscous Magnus force for a transversely rotating sphere undergoing vortex-induced vibration

We have conducted direct numerical simulations of flow past a transversely rotating sphere undergoing vortex-induced vibration. At a Reynolds number of Re=500, we have obtained results for dimensionless rotation speeds α=0.2,1 within the reduced velocity range 3≤U∗≤12, with a fixed mass ratio m∗=2. We have proposed an estimation for the viscous Magnus force on the rotating sphere, which is observed to align with the inviscid limit till U∗≈8, beyond which it grows very fast owing to the thickening of the boundary layer in the advancing side. Boundary layer separation at the top sphere surface promotes a thinner shear layer at the bottom, thereby inducing greater upwash that causes a larger Magnus force. The importance of the boundary layer thickness and their separation, thus, plays a crucial role in shaping the Magnus force at larger transverse rotation rates.