Development of the wake behind a circular cylinder impulsively started into rotatory and rectilinear motion: Intermediate rotation rates

Abstract

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 an 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 alpha = (omega x a)/U (where omega is the angular speed) up to 3.25. Several aspects of the kinematics and dynamics of the flow not considered earlier are discussed. For higher values of alpha, the results indicate that for Re = 200, vortex shedding does indeed occur for alpha = 3.25. The shedding process is; however, very different from that which gives rise to the usual Karman vortex street for alpha = 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