A model for the formation of oblique shedding and ‘‘chevron’’ patterns in cylinder wakes

Abstract

It is demonstrated that many features of flow visualizations involving oblique vortex shedding from two-dimensional bluff bodies, cylinders in particular, are qualitatively well described by a one-dimensional model, which represents diffusively coupled oscillators arranged along a line parallel to the cylinder. In mathematical terms, the idealized model consists of a transverse Ginzburg–Landau equation, in which the coefficients are determined experimentally. In physical terms, the model describes the formation of a pattern of tracer particles (e.g., smoke) over a very short streamwise interval which is subsequently only convected downstream. It is shown that, as in impulsively started experiments, ‘‘vortex shedding’’ in the model starts parallel to the cylinder. Regions of oblique shedding then develop from the cylinder ends and lead to steady-state chevrons for symmetric end conditions. Selection rules for the shedding angle as a function of Reynolds number are derived from the model and compared to experiments.