Bursting process of large- and small-scale structures in turbulent boundary layer perturbed by a cylinder roughness element

Abstract

Hot-wire measurements on a turbulent boundary layer flow perturbed by a wall-mounted cylinder roughness element (CRE) are carried out in this study. The cylindrical element protrudes into the logarithmic layer, which is similar to those employed in turbulent boundary layers by Ryan et al. (AIAA J 49:2210–2220, 2011. doi:10.2514/1.j051012) and Zheng and Longmire (J Fluid Mech 748:368–398, 2014. doi:10.1017/jfm.2014.185) and in turbulent channel flow by Pathikonda and Christensen (AIAA J 53:1–10, 2014. doi:10.2514/1.j053407). The similar effects on both the mean velocity and Reynolds stress are observed downstream of the CRE perturbation. The series of hot-wire data are decomposed into large- and small-scale fluctuations, and the characteristics of large- and small-scale bursting process are observed, by comparing the bursting duration, period and frequency between CRE-perturbed case and unperturbed case. It is indicated that the CRE perturbation performs the significant impact on the large- and small-scale structures, but within the different impact scenario. Moreover, the large-scale bursting process imposes a modulation on the bursting events of small-scale fluctuations and the overall trend of modulation is not essentially sensitive to the present CRE perturbation, even the modulation extent is modified. The conditionally averaging fluctuations are also plotted, which further confirms the robustness of the bursting modulation in the present experiments.

Appendix: Filter scale effects on turbulent intensity and bursting frequency

In this appendix, we will discuss the effect of filter cut-off length on turbulent intensity and bursting frequency. As the vertical lines plotted in Fig. 4, four different length cut-offs (λ _x /δ = 1.5, 2, 3, 4) are selected for the comparison. The large- and small-scale fluctuations are decomposed following the methodology by Mathis et al. (2009a, b) for each filter case.

Figure 13 shows the effect of the different filters on turbulent intensity. The figures in the left and right column present large- and small-scale turbulent intensity (〈u ² _L 〉⁺ and 〈u ² _S 〉⁺), respectively, for the different length cut-offs. As the filter length scale increases, the value of the large-scale turbulent intensity is decreased; meanwhile, the small-scale turbulent intensity is increased. In spite of the variation of the turbulent intensity value, the general trends of turbulent intensity under the impact of the cylinder roughness element are almost identical for the different length cut-offs.

Fig. 13

Effect of filter length cutoff (λ _x /δ = 1.5, 2, 3, 4) on turbulent intensity of large and small scales (left and right column, respectively)

Figure 14 present the bursting frequency of the large and small scales (left and right column) for the different length cut-offs. As similar as the effect on turbulent intensity shown in Fig. 13, it is observed that the large-scale bursting frequency is reduced and small-scale bursting frequency is increased, by increasing the filter length as the plots shown from top to bottom. Under the CRE’s impact, the overall trend of both large- and small-scale bursting frequency does not appear to change with varying the selected filter scales.

Fig. 14

Effect of filter length cut-off (λ _x /δ = 1.5, 2, 3, 4) on bursting frequency of large and small scales (left and right column, respectively)

It can be concluded that the general trends of the turbulent intensity and bursting frequency are weakly depend on the choice of the filter length scales as considered (λ _x /δ = 1.5, 2, 3, 4). Thus, it is reasonable to use λ _x /δ = 2 as the length cut-off, to decompose the large- and small-scale fluctuations in the present study.