A free-streamline boundary-layer model for small-amplitude oscillation regime of square cylinder under vortex-induced rotation

Numerical studies about vortex-induced rotation (VIR) have shown that six regimes exist for the dynamics of square cylinder under VIR at small Reynolds numbers; however, theoretical explanations are still rare. Aiming at stepping a little further, we select one of these regimes, that is, small-amplitude oscillation regime, to develop an analytical model. In the present model, we expand the symmetric free streamline theory to an inviscid flow pasting an inclined plate and introduce the Blasius boundary layer theory in the calculation of viscous torque on a square cylinder. This model is supported by comparing with numerical results using the immersed boundary method. Results explain the mechanism of small-amplitude oscillation regime: the main sources of the out-of-phase torque come from the imbalanced distribution of pressure on the windward face and the asymmetric distribution of pressure and viscous force on the top/bottom face. An alternative way to determine the local flow parameters by global dynamic quantities is also proposed based on this model.