Description of transient states of von Kármán vortex streets by low-dimensional differential equations

Abstract

Aperiodic time series of hot-wire signals can be described as trajectories in a state space representation. The flow vector field is calculated by numerical differentiation of these trajectories and then each component of the flow vector field is approximated by a polynomial of order p. This approximation provides a model for the dynamics of the von Kármán vortex street by a low-dimensional system of ordinary differential equations. At a Reynolds number of 114 a compact description of the complex dynamics of the vortex street by a set of only ten parameters can be obtained. It will be shown that these parameters are independent of the probe position for distances greater than two-and-one-half cylinder diameters.