A laser-Doppler velocimetry study of ensemble-averaged characteristics of the turbulent near wake of a square cylinder

TLDR

The study distinguishes a near‑wake region with mature, distinct vortices from a base region where vortices grow to maturity before shedding, and examines how flow topology, including vorticity and streamline saddles, relates to turbulence. The authors propose scaling arguments based on circulation discharged into the near wake to explain observed differences between square‑cylinder and circular‑cylinder flows. Phase was defined using a pressure‑sensor signal at the cylinder sidewall midpoint, and the scaling arguments were applied to the resulting phase‑locked laser‑Doppler data. Laser‑Doppler measurements at Re≈21400 yielded ensemble‑averaged near‑wake statistics that differ from circular‑cylinder flow in length, velocity scales, and vortex celerities, reveal high Reynolds shear stresses near peak vorticity, asymmetries near streamline saddles, and show that base‑region vorticity structures change importance during shedding.

Abstract

Ensemble-averaged statistics at constant phase of the turbulent near-wake flow (Reynolds number ≈ 21400 around a square cylinder have been obtained from two-component laser-Doppler measurements. Phase was defined with reference to a signal taken from a pressure sensor located at the midpoint of a cylinder sidewall. The distinction is drawn between the near wake where the shed vortices are ‘mature’ and distinct and a base region where the vortices grow to maturity and are then shed. Differences in length and velocity scales and vortex celerities between the flow around a square cylinder and the more frequently studied flow around a circular cylinder are discussed. Scaling arguments based on the circulation discharged into the near wake are proposed to explain the differences. The relationship between flow topology and turbulence is also considered with vorticity saddles and streamline saddles being distinguished. While general agreement with previous studies of flow around a circular cylinder is found with regard to essential flow features in the near wake, some previously overlooked details are highlighted, e.g. the possibility of high Reynolds shear stresses in regions of peak vorticity, or asymmetries near the streamline saddle. The base region is examined in more detail than in previous studies, and vorticity saddles, zero-vorticity points, and streamline saddles are observed to differ in importance at different stages of the shedding process.