Secondary motions downstream of pipe curvatures are widely studied for low and moderate Reynolds numbers, where the secondary flows are driven by the centrifugal pressure gradient. For these Reynolds numbers, there exists two cell vortex that is symmetric around the center plane of the pipe known as the Dean motion. However, when the Reynolds number is increased the flow becomes turbulent, and instabilities are introduced to the two-cell structure. These instabilities cause the flow to alternate between a dominating upper cell and lower cell. The two cells coexist in the transition between the modes, Figure 1.
The instantaneous streamwise vorticity does not reveal a Dean motion at high Reynolds numbers. Rather we see locally strong vortices. However, the mean streamwise vorticity field shows that the Dean motion is hidden in the instantaneous vorticity field. While present, it is considerably weaker than the unstable motions, Figure 2.