DEVELOPMENT OF THE WAKE BEHIND A CIRCULAR-CYLINDER IMPULSIVELY STARTED INTO ROTATORY AND RECTILINEAR MOTION

The temporal development of two-dimensional viscous incompressible flow generated by a circular cylinder impulsively started into steady rotatory and rectilinear motion at Re = 200 (based on the cylinder diameter 2a and the magnitude U of the rectilinear velocity) is studied computationally. We use an explicit finite-difference/pseudospectral technique and a new implementation of the Biot-Savart law to integrate a velocity/vorticity formulation of the Navier-Stokes equations. Results are presented for the four angular: rectilinear speed ratios alpha = OMEGAa/U (where OMEGA is the angular speed) considered experimentally by Coutanceau & Menard (1985). For alpha less-than-or-equal-to 1, extension of the computations to dimensionless times larger than achieved either in the experimental work or in the computations of Badr & Dennis (1985) allows for a more complete discussion of the temporal development of the wake. Using the frame-invariant vorticity distribution, we discuss several aspects of the vortex kinematics and dynamics not revealed by the earlier work, in which vortex cores were identified from frame-dependent streamline and streamfunction information. Consideration of the flow in the absence of sidewalls confirms the artifactual nature of the trajectory of the first vortex reported by Coutanceau & Menard for alpha = 3.25. For alpha greater than unity (the largest value considered by Badr & Dennis), our results indicate that at Re = 200 shedding of more than one vortex does indeed occur for alpha = 3.25 (and possibly for larger alpha), in contrast to the conclusion of Coutanceau & Menard. Moreover, the shedding process is very different from that associated with the usual Karman vortex street for alpha = 0. Specifically, consecutive vortices can be shed from one side of the cylinder and be of the same sense, in contrast to the non-rotating case, in which mirror-image vortices of opposite sense are shed alternately from opposite sides of the cylinder. The results are discussed in relation to the possibility of suppressing vortex shedding by open- or closed-loop control of the rotation rate.