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In this Brief Note, we show that shedding frequency data is well collapsed, over a large range of Re from 50 up to at least 140,000, by using a Strouhal number that depends upon an effective wake width, which includes not only the physical body diameter, but also a characteristic width of the separating shear layers. The use of this effective wake width also leads to a new formulation for the relationship between Strouhal number (S) versus Reynolds number (Re) for the cylinder wake, which may be expressed as an expansion in powers of (1/√Re): Equation Truncated two-term or three-term series have much less error-of-fit when compared with the traditional S–Re relationships commonly in use. A good test of any S–Re functional relationship is now made possible by comparison with Henderson's numerical data for two-dimensional laminar shedding, over a much larger range of Re (up to Re=1000) than is possible to obtain experimentally. It seems significant that even a two-term fit, given by S=0·2698 −1·0271/√Re has one order of magnitude less error than the traditional three-term fit. By using such √Re-formulae in both the laminar and 3-D wake turbulent regimes, we may accurately represent S–Re data over a large range of Re, although the validity of these representations at these higher Re needs further support. In summary, this Brief Note not only provides physical support for the use of such S–Re relationships as shown above, but also demonstrates that these formulations fit the data closer than traditional S–Re expressions.
Williamson et al. (Sun,) studied this question.