A nonlinear oscillator model for vortex shedding from cylinders and cones in uniform and shear flows

Abstract

An elastically coupled Van der Pol oscillator is introduced as a model for vortex shedding from uniform cylinders in shear flows. It is found that the elastically coupled oscillator is incapable of modeling vortex shedding in this situation. The oscillator fails to produce the cellular vortex-shedding pattern observed experimentally. The basic effect of the elastic coupling between the fluid layers is to modify, unacceptably, the vortex-shedding frequency. A diffusively coupled Van der Pol oscillator, that has been previously used successfully to model vortex shedding from uniform cylinders in linearly sheared flows, is then extended to model vortex shedding from tapered cylinders and cones in uniform and sheared flows. We find that the diffusively coupled oscillator replicates the cellular nature of vortex shedding that was observed experimentally. The number and axial extent of the frequency cells from the model are in excellent agreement with experimental results. The model further displays the experimentally observed low-frequency modulation of the near wake at low Reynolds numbers. ©1996 Academic Press Limited.