Figure 11 presents a statistically significant sample of time histories of velocity fluctuations at a point ( x/D = 0 . 55 , y/D = 0 . 65) with respect to the center of the cylinder that lies in the near wake. The power spectrum density is obtained by an ensemble average across the 40 sampling stations in the homogeneous spanwise direction. The fairly sharp peaks, the Strouhal frequency f$_{St}$ , characterize the predominant vortex shedding. Moreover, it can be observed that there is another peak ( f$_{sl}$ ) that represents the frequency of shear-layer vortexes and is significantly higher and is of a relatively broader band than f$_{St}$ . For this broadband feature of shear layer vortexes, Dong et al.[43] ascribed this complex phenomena to a few factors, e.g. the Karman vortex formation, the varying momentum thickness and the oscillation of the separation line. However, the value for f$_{sl}$ predicted for the first column cylinder fails to match the well-known Re 0 . 67 law for an unconfined circular cylinder ([44]. This is consistent with the observations from Brun et al.[45] that indicate there is no universal Reynolds number dependence of f$_{sl}$/f$_{St}$ for two cylinders placed side by side. 

The time histories and corresponding power spectrum densities for the three downstream cylin- ders are presented in figure 12, figure 13 and figure 14. The fundamental frequency of vortex shedding is well pronounced for the three cylinders. From Gerrard[46] and Gerrard[47], the funda- mental shedding frequency behaviors like a mean rather than a fluctuating quantity because the strengths of the vortexes depend most strongly on the mean rate of shedding of vorticity, which is governed by the mean behavior of the separated shear layer. Consequently, it is reasonable to ex- pect that the fundamental shedding frequency will show little variations for downstream cylinders in the sub-critical range of Reynolds number. Nonetheless, there is no signature for the shear layer vortexes observed. This may result from the feature of significant inhomogeneity in the crosswise direction associated with the wake from the upstream cylinders. 

It is worthwhile noting that the dominant frequency of vortex shedding predicted in the present study is evaluated in terms of the mean velocity across the gap u$_{g}$ . It is of interest to compare the predicted value with the experimental observations, especially with the universal Strouhal number St ∗ proposed by Roshko[48] that is defined fd $^{∗}$/u∗ in terms of the wake width between the rows of vortexes d ∗ and the wake velocity u ∗ obtained from the free-streamline theory. These are summarized in the table 3 along with an extrapolated value from the measurements for a confined circular cylinder by Richter and Naudascher [42]. It can be observed that Shim[27]’s 

