Numerical visualization of boundary layer transition when negative Magnus effect occurs

We previously identified the appearance of negative Magnus lift on a sphere rotating about an axis perpendicular to an incoming flow at a critical Reynolds number using large-eddy simulation and obtained the statistically time-averaged lift and pressure coefficients around the sphere. We have now numerically investigated the unsteady characteristics of the boundary layer around a rotating sphere at three Reynolds numbers (1.0 x 10^[4], 2.0 x 10^[5], and 1.14 x 10^[6]). At a Reynolds number in the subcritical or supercritical region, the direction of the lift force followed the Magnus effect independent of the rotational speed. In contrast, at the critical Reynolds number when a particular rotational speed was imposed, negative lift was observed and a boundary-layer transition occurred only on one side of the sphere, as indicated by the visualization of the vortical structures around the sphere. A change in these structures and a shift of the separation points along with a change in the Reynolds number or rotational speed of the sphere were investigated in the context of boundary layer transition by using visualization around the sphere