Response of a circular cylinder wake to superharmonic excitation. (Q2761833)

A systematic numerical analysis is performed for superharmonic excitations in a wake where a circular cylinder is rotationally oscillated in time. Emphasis is placed on identifying the secondary and tertiary lock-on in the forced wakes. The frequency responses are scrutinized by measuring the lift coefficient (\(C_L\)). A direct numerical simulation has been conducted to portray the unsteady dynamics of wake flows behind a circular cylinder. The Reynolds number based on the diameter is \(Re = 106\), and the forcing magnitude is \(0.10\leq\Omega_{\max}\leq 0.40\). The tertiary lock-on is observed, where the shedding frequency (\(St_0\)) is one third of the forcing frequency (\(S_f\)), i.e. the 1/3 subharmonic lock-on. The phase shift of \(C_L\) with respect to the forcing frequency is observed. It is similar to that of the primary lock-on. However, in the secondary superharmonic excitation, modulated oscillations are observed, i.e. the lock-on does not exist. As \(\Omega_{\max}\) increases, \(St_0\) is gradually shifted from the natural shedding frequency (\(St^*_0\)) to lower values. The magnitudes and phases of \(S_f\) and \(St_0\) are analysed by the phase diagram. The vorticity contours are employed to examine the vortex formation mode against the forcing conditions.