A systematic numerical analysis is performed for superharmonic excitations
in a wake where a circular cylinder is rotationally oscillated in time. Emp
hasis is placed on identifying the secondary and tertiary lock-on in the fo
rced wakes. The frequency responses are scrutinized by measuring the lift c
oefficient (C-L). A direct numerical simulation has been conducted to portr
ay the unsteady dynamics of wake flows behind a circular cylinder. The Reyn
olds 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 terti
ary 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 simi
lar 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 conditio
ns.