BIFURCATION FOR FLOW PAST A CYLINDER BETWEEN PARALLEL PLANES

Numerical experiments are described to ascertain how the steady flow p ast a circular cylinder loses stability as the Reynolds number is incr eased. A novel feature of the present study is that the cylinder is co nfined between parallel planes, allowing a more definitive specificati on of the flow, both experimentally and computationally, than is possi ble for the unbounded case. Since the structure of the bifurcation is unclear from the extant literature, with the experimental and computat ional evidence not in good agreement, a critical appraisal of both set s of evidence is presented. A study has been made of the formation of the steady vortex pair behind the cylinder, and it has been determined that the first appearance of the vortices is not associated with a bi furcation of the full dynamical problem but instead it is probably ass ociated with a bifurcation of a restricted kinematical problem. A set of numerical experiments has been made in which the steady flow past t he cylinder was perturbed slightly and the ensuing time-dependent moti ons were computed. These experiments revealed that, for a given blocka ge ratio, the perturbation would die away at small Reynolds numbers bu t that, above a critical Reynolds number, the disturbance would be amp lified and the flow would eventually settle down to a new state compri sing a time-periodic motion. Experiments were also carried out to dete rmine the bifurcation point numerically by considering an eigenvalue p roblem based on a linearization about the computed steady flow past th e cylinder. The calculations showed that stability is lost through a s ymmetry-breaking Hopf bifurcation and that, for a given blockage ratio , the critical Reynolds number was in very good agreement with that es timated from the time-dependent computations.