A study on the vortex shedding and lock-on behind a square cylinder in an oscillatory incoming flow

Vortex shedding behind a square cylinder in an oscillatory incoming flow is studied at Reynolds numbers of 80, 100 and 200 by numerical solutions. The forcing frequencies investigated for the oscillatory incoming flow are f(f)/f(so)=0.4similar to4.0 and the, forcing amplitudes normalized by the mean incoming velocity are 0.1, 0.2 and 0.4, where A. is the vortex shedding frequency under steady incoming flow and f(f) is the forcing frequency of the oscillatory incoming flow. In the lock-on region, the flow is in a periodic state and there is a strong regularity between the drag and lift forces. The different phase diagram between the drag and lift forces is brought on by the different lift mode. The phase difference between the incoming velocity and the drag is nearly the same magnitude of 65similar to70 degrees in the lock-on region. The time-averaged mean recirculation region in the oscillatory incoming flow is smaller than that for the steady one and is inversely proportional to the forcing amplitude or the Reynolds number. The time-averaged streamwise mean velocity in the oscillatory incoming flow recovers more quickly than that in the steady incoming flow.