WAVELET-DECOMPOSED THREE VORTICITY COMPONENTS IN A TURBULENT NEAR WAKE

The purpose of the present study is to examine the characteristics of the vortical structures using the orthogonal wavelet multi-resolution technique by decomposing the vorticity into a number of wavelet components based on different central frequencies. The three vorticity components were measured simultaneously using an eight-wire probe in the near wake of a circular cylinder at three Reynolds numbers, namely 1,600, 6,500 and 10,000. It is found that the dominant contributions to the vorticity variances are from the intermediate and relatively small-scale structures. The contributions from the large and intermediate-scale structures to the vorticity variances decrease with the increase of Reynolds number, while the contributions from the small-scale structures to all three vorticity variances jump significantly, which is connected to previous observations in the near wake that there is a significant increase in the generation of smallscale structures. The result reinforces the conception that turbulence ‘remembers’ its origin. INTRODUCTION Flow around a circular cylinder is of significant importance for engineering applications. The topology and transport characteristics of the turbulent structure in the wake that depend on the initial conditions have been well established studied. Especially the Reynolds number has a significant effect on the formation of vortices behind the circular cylinder and attracted a large amount of investigation in the past several decades particularly in the range of Re = 1,000 to 10,000 (Lin et al., 1995). Recently, Yiu et al. (2004) examined the Reynolds number effects on the turbulent near wake over the Re range of 2,500 – 10,000 using a 4-X-wire 3-dimentional vorticity probe. They found that the streamwise vorticity component “jump” significantly as Re is increased from 5,000 to 10,000. Correspondingly, the contributions from the large-scale structures to the spanwise vorticity variance decline appreciably, suggesting an increased 3-dimentionality of the flow. However, due to the limitation of their detection scheme, they could not provide any information on the relationship between initial conditions and organized structures other than the large-scale ones. One interesting question to be asked is how these variations with Re would affect the contribution of various scales to the threedimensional vorticity in the near wake. This motivates the present investigation. In the past decade there has been a growing interest in the use of wavelet analysis for extracting new information on the turbulence structures of various scales. Recently, an orthogonal wavelet multi-resolution technique was applied to the analysis of the turbulent structures of various scales in the near-wake of a circular cylinder by Rinoshika and Zhou (2005). It is observed for the first time that the spanwise vorticity contours of the wavelet component at the averaging frequency of Kármán vortices display a secondary spanwise structure near the saddle point in the near wake of a circular cylinder. Using the same technique, Rinoshika & Zhou (2005, 2007) further investigate the dependence of the turbulent structures of various scales on various wake-generating bodies in the near and far wakes. Their results indicate that the intermediateas well as the large-scale structures depend on the initial conditions. One objective of this work is to explore further the possible dependence of the near-wake turbulence on Re, in particular, focusing on the aspects of vorticity. For this purpose, a probe that used by Zhou et al. (2006) was employed to measure the three-dimensional vorticity components of far wake simultaneously at two Reynolds Sixth International Symposium on Turbulence and Shear Flow Phenomena Seoul, Korea, 22-24 June 2009