Development of the wake behind a circular cylinder impulsively started into rotatory and rectilinear motion

Ns,.... 4L The temporal development of two-dimensional viscous incompressible flow generated by a circular cylinder started impulsively into steady rotatory and rectilinear motion is studied by integration of a velocity/vorticity formulation of the governing equations, using an explicit finite-difference/pseudo-spectral technique and a new implementation of the Biot-Savart law. Results are presented for a Reynolds number of 200 (based on the cylinder diameter 2a and the magnitude U of the rectilinear velocity) for several values of the angular/rectilinear speed ratio a = Qa/U (where fQ is the angular speed) up to 3.25. For values of a < 1, our extension of the computations to larger dimensionless times than those possible in the experimental work of Coutanceau & Mdnard (1985) or considered in the computational work of Badr & Dennis (1985) allows for a more complete discussion of the long-term development of the wake. We also discuss several aspects of the kinematics and dynamics of the flow not considered earlier. For higher values of a, our results indicate that for Re = 200, vortex shedding does indeed occur for a = 3.25 (and possibly for higher values of a also), in contrast to the conclusion of Coutanceau & M6nard (1985). The shedding process is, however, very different from that which gives rise to the usual KArm n vortex street for a = 0. In particular, consecutive vortices shed by the body can be shed from the same side, and be of the same sense, in contrast to the nonrotating case, in which mirror-image vortices of opposite sense are shed alternately on opposite sides of the body. The implications of the results are discussed in relation to the possibility of suppressing vortex shedding by open- or closed-loop control of the rotation rate.