C. Jin, I. Potts, D. C. Swailes, M. W. Reeks 18 measurement as well as the present predicted value fall well within the range 95% of the universal Strouhal number for the sub-critical range of Reynolds number. To examine the spatial structure of vortex shedding behind the cylinders, figure 15 presents the auto-correlation functions for the streamwise and crosswise velocity components for the 40- sampling stations ( x/D = 0 . 55 ,y/D = 0 . 65) with respect to the axis of the cylinder the across the homogeneous spanwise direction. It is defined as From figure 15a, it can be observed for the first column cylinder C1 that R$_{u}$ $^{′}$u′ and R$_{v}$ $^{′}$v ′ are decreasing monotonically to zero within the range of L/D = 1. This implies that the spanwise length of the biggest eddy from vortex shedding approximately equals to the diameter of the cylinder. This feature has been demonstrated for an unconfined single circular cylinder by previous researchers. Nonetheless, the fact that R$_{u}$ $^{′}$u′ and R$_{v}$ $^{′}$v ′ do not tend asymptotically towards zero at large separation distance is concerned with the periodic boundary condition employed for the homogeneous spanwise direction in the present LES study. Nevertheless, from figure 15b,c d, it can be observed that the downstream cylinders C1, C2 and C3 display distinct behaviors with respect to the auto-correlation as a function of the spanwise length for the streamwise and crosswise velocity fluctuations. First, within the length of L/D = 1, R$_{u}$ $^{′}$u′ and R$_{v}$ $^{′}$v ′ do not decease to zero. Secondly, R$_{v}$ $^{′}$v ′ wiggles across the middle part of the R$_{ii}$ ( x ; z ,t ) = u ′ $_{i}$( x ; t ) u ′ $_{i}$( x + z ; t ) u ′ i $^{2}$( x ; t ) . (29) 3.5 Correlation length for vortex shedding Table 3: Comparison of St with the universal Strouhal number Case St Present LES ( Re$_{g}$ = 15270) C1 0.153 C2 0.153 C3 0.153 C4 0.153 Experiments [27] 0.152 Experiments [42] ( Re = 1 . 5 × 10 $^{4}$) St ∗ 0.151 Theoretical Value [48]( Re < 2 × 10 $^{5}$) St ∗ 0.16