Bluff, unstreamlined bodies have been working on so many places. People had been unconsciously ignoring the most interesting part for thousands years until the wire was vibrating so hard with the Aeolian tone coming out. Strouhal at 1878 started the experiment of the interaction between bluff bodies and the blowing wind. Even the wind went smoothly and uniformly, the existence of fluctuating forces which was exciting Rayleigh so much at 1896 was attributed to the vortex shedding from the leeward surface of the circular cylinder body into the wake with the alternating motion periodically to the downstream [1]
once Reynolds number went beyond a certain number otherwise a pair of symmetric vortices stayed right behind the body steadily [2]. Vortex shedding phenomena were caused by the separated boundary layers from the upper and lower surfaces of the bluff body [3]. Lots of scientists and engineers were getting the researches begun after the fascination had been widely spread.
Strouhal number was, hence, theoretically defined by Roshko [4], Bearman [5], and Griffin [6] for scaling the vortex street. Due to the computer had not been sufficiently well-performance yet, people were so much hitting the road from the experimental parts. The fluctuating vortex street was experimentally found to be
complex and varied along the increase of Reynolds number from 40 to 10,000 while the phenomena changed from stable to transition, and then to the irregular movement [4]. Furthermore, Hama [7] visually found out the three-dimensionality in the wake of a circular cylinder. The decreasing span-wise frequency was observed with the increasing Reynolds number great than 150. Despite the wake instability interested many researchers devoting their sophisticated experimental skills, the Strouhal-Reynolds number relation from different labs somehow deviated from each other by about 20 percent still. Until 1988, Williamson and Roshko proposed that the three-dimensional effect introduced by the so-called oblique shedding mode happened to be the critical reason of those disagreements for years. Although they all brought us the different experimental data, the contributions were still made. The discontinuities of Strouhal frequency along the increase of Reynolds number were reported by Trittin [8]. The causes of these discontinuous variations were explained to be attributed to the unskilled flow control which did not maintain the flow uniformly [9]. The forced cylinder vibration was told to be one of the possible reasons by observing the existence of quasi-periodic state in the laminar wake and the transformation to chaotic state [10]. The cylinder vibration triggering the discontinuities was still supported [11]. The quasi-periodic state was actually confirmed but the flow non-uniformity and the forced vibration were on the contrary examined not to be exact the main reasons causing the discontinuities [12]. Williamson and Roshko [12] indicated an intrinsic three dimensional wake instability which potentially caused the discontinuities of Strouhal frequency as the Reynolds number went beyond 178 and 260 even under a controlled parallel shedding, i.e. two-dimensional flow, of circular cylinder. This critical Reynolds number 178 was said to be the onset point of the
transition of wake from two-dimensional to three-dimensional. Although the wire was the research topic, the bluff body does not have to be always a circular cylinder. The shape of interest was thought to be sharp-corners or to be something not that smooth. The mechanism responsible for vortex shedding of rectangular cylinder was sort of different from the one of circular cylinder. The development of Vortex Street was triggered by the separation from the leading edge of a square cylinder instead of from the leeward side of circular one while Reynolds number was sufficiently high. The data of square and of other rectangular cylinders reported in detail and systematical were achieved by Okajima [13] although the width-to-height ratio of a rectangular cylinder had already been considered to be the contributing factor by Nakaguchi et al. since 1968 [14]. The vortex street had been a popular topic with Reynolds number staying high, whereas the finding of the onset critical Reynolds number for the vortices turning from symmetric to asymmetric and from steady to unsteady was the topic as well. Works had never been too easy even the numerical analysis came to be the one doing the prediction of the phenomena of interests. The onset Reynolds number turned out to be more than just one certain number due to the blockage effect. A bigger blockage ratio brought a higher value of onset Reynolds number [15, 16] as well as the higher Strouhal frequency and drag coefficient [17]. Two critical values of Reynolds number are mentioned so far.
One is the onset point for flow turning from steady to unsteady and the other one is the onset point of three-dimensionality. The 2D simulation would over predict the drag and lift coefficient once the flow goes beyond the critical Reynolds number of three-dimensionality [18]. Many researchers were quite focusing on the second onset point with the interest of three-dimensionality and they defined
Once the flow features turn into three-dimensional, span-wise instabilities appear with different wavelengths which classify the particular features with modes A and B [12]. Mode A was characterized by longer span-wise wavelength by about two to four diameters of cylinder with larger vortex dislocations while second onset Reynolds number was achieved. Mode B happened with shorter wavelength by about one diameter instead while Reynolds number was about 230 whose value was higher than the one of second onset point. Although these measurements or predictions of mode classification were done with circular cylinder flow, those of rectangular or sharp-corners cylinders possessed the similarities as well [19]. Even a new Mode S with span-wise wavelength of 2.8 diameter between those of Mode A and B was observed in the wake of square cylinder while Reynolds number equaled 200 [20]. More complex phenomena could be found once people were doing the studies of the Karman vortex street in the wake of the rectangular or square cylinder. The nonlinear dynamic system of the wake was truly interesting. The frequency spectrum was studied from first onset Reynolds number to what induced the chaos. This transition process was somehow indicating the existence of three-dimensionality.