Initial growth of a disturbance in a boundary layer influenced by a circular cylinder wake

Abstract

The initial growth of a disturbance induced by a near-wall circular cylinder in a flat-plate boundary layer is experimentally investigated using both particle image velocimetry and hydrogen bubble visualization techniques. The secondary spanwise vortices appear in the near-wall region as a direct response to the outside passing wake vortices, consistent with previous studies on similar models (Pan et al., J. ). The streamwise variation of the total disturbance energy within the boundary layer shows a two-stage growth, which characterizes the initial transition process: the first exponential growth stage, followed by a region with slower growth rate. It is revealed that these two stages of growth are related to the formation and the destabilization of the secondary vortex in the near-wall region. The technique of dynamic mode decomposition is used to decompose the total disturbance into temporally orthogonalized modes, and it shows that the first growth stage largely results from the increased disturbance at the same frequency as that of the wake vortex shedding, while the second growth stage comprises the disturbance growth in a number of frequencies, especially the lower ones.

Evolution of Lagrangian coherent structures in a cylinder-wake disturbed flat plate boundary layer

“…In a recent experimental study of He, Wang & Pan (2013), secondary vortices were also observed in the near-wall region for Re D = 1118. In this case the cylinder was not placed near the leading edge but downstream and right above the boundary layer in order to avoid problems of leading edge receptivity.…”

“…Further downstream, the profile near the wall surpasses that of the Blasius profile, indicating a boundary layer transition. As no uniform outer flow can be observed due to the existence of the wake, we adopt a definition of boundary layer thickness used in the studies of Sarkar & Sarkar (2009) and He et al (2013). In this definition, the height of the maximum streamwise velocity between the wall and the wake deficit region is the boundary layer edge (as indicated by the horizontal dashed lines for the profiles at x/D = 5 and 25).…”

“…It has been pointed out in an earlier study of He & Wang (2015) that the three-dimensional destabilization is triggered by the spanwise instability of wake vortices. As Λ vortices are stretched in the streamwise direction, their counter-rotating streamwise-stretched legs would induce a streamwise elongated low-speed region in the boundary layer, so low-frequency disturbances associated with them will gradually become dominant in the growth of disturbances in the boundary layer (He et al 2013). Corresponding to the formation and destabilization of the secondary vortices, the total disturbance experiences a fast growth, as shown in figure 3(a).…”

“…They investigated the initial growth of disturbances associated with the evolution of secondary vortices in the boundary layer. By adopting a novel flow diagnostic method proposed by Rowley et al (2009) and Schmid (2010), called dynamic mode decomposition (DMD), He et al (2013) found that the disturbance level in the boundary layer was at first manifested as the dominant growth of disturbance at the wake vortex shedding frequency, which corresponded to the formation of secondary vortices. In the subsequent growth stage, the disturbance had a broader spectrum, and the low-frequency components associated with destabilization of the secondary vortices were dominant.…”

On the accuracy of dynamic mode decomposition in estimating instability of wave packet

“…Recently, an de-biasing noise-robust method based on solving the total least-squares problem was proposed by Hemati and Rowley (2015), which provides the unbiased dynamical approximations in the noise contamination circumstance. On the other hand, the fluid community has seen a vast boost of DMD applications in both numerical and experimental studies Schmid 2011;Pan et al 2011;Muld et al 2012;Ghommem et al 2014;He et al 2013;Tang and Jiang 2012;Sampath and Chakravarthy 2014).…”