Characteristic spanwise length scales of streamwise vortical structures in the wake of a circular cylinder at Re = 1500 measured via global and local approaches

Abstract

Wake characteristics of the flow past a circular cylinder are analysed in detail at Reynolds number Re=1500 via direct numerical simulation. A periodic spanwise domain of length 1.5πD has been found to yield correct first- and second-order wake statistics in remarkable agreement with published results at the same and closeby Re. A Kelvin–Helmholtz instability with a frequency fKH≃0.666 is observed to occur intermittently in the shear layers issued from the top and bottom of the cylinder. The three-dimensional patterns in the wake have an estimated spanwise length scale lz1/D≃0.70 (D is the cylinder diameter) in the near-wake at (x,y)/D=(3,0.5), downstream from the cylinder, when quantified by autocorrelation (global approach). When using the Hilbert-transform (local approach) instead, the predicted length scale of streamwise vortical structures is distributed around λz/D≃0.33 at the same sampling location. Our results show that the two approaches measure different aspects of three-dimensionality: while the former informs of the typical spanwise spacing of streamwise vortices, the latter quantifies the local spanwise size of these same flow structures.