Response of a circular cylinder wake to superharmonic excitation

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 less than or equal to Ohm (max) less than or equal to 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 Ohm (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.