2. Experimental set-up

Experiments were carried out in a low turbulence wind tunnel at City, University of London, whose test section measured 0.91 m (height) by 0.91 m (width) by 1.8 m (length). The tunnel was housed in a temperature-controlled laboratory, where the air temperature change was kept within ±0.5 °C. The wind tunnel speed was set at 18 m s⁻¹ in all tests, which corresponded to the unit Reynolds number of 1.2 × 10⁶ per metre. The turbulence level was less than 0.005 % at this speed for the frequency range between 2 Hz and 2 kHz (Gaster Reference Gaster, Hussaini and Voigt1990). A 1.537-m long and 0.91-m wide flat test plate was made of a 12.7-mm thick aluminium cast tooling plate, which was vertically installed in the centre of the test section. It had a modified asymmetric super-elliptic shaped leading edge skewed towards the working surface, with a thickness ratio of 0.41 and a length of 127 mm (Bosworth Reference Bosworth2016). The surface roughness (Ra) of the test plate was less than 8 μm, where the flatness was less than 50 μm per 50-mm length anywhere in both the streamwise and spanwise directions. The pressure gradient of the boundary layer was set to zero by adjusting the trailing edge flap and tab, see figure 1(a). Mean velocity profiles of the laminar boundary layer over a flat plate at various streamwise locations are shown in figure 2, which indicate that they were well represented by the Blasius profile up to at least x = 1000 mm.

Figure 1. Schematic of a flat test plate (a) and the mounting arrangement of a miniature speaker (b). Dimensions are in millimetres. There are, in total, 19 orifices and miniature speakers across the span of the test plate, but only the centre speaker is used in this study. Two unused circular instrumentation plates are also shown.

Figure 2. Mean velocity profiles of the laminar boundary layer over a flat plate at various streamwise locations, which are compared with the Blasius profile. Here, $\eta = y{({U_e}/\nu x)^{1/2}}$ is the non-dimensional distance from the wall.

The laminar boundary layer was excited by a 12-mm diameter miniature speaker (IMO Precision Controls 41.T70L015H-LF), which was embedded on the centreline of the flat plate at 325 mm from the leading edge as shown in figure 1(b). The speaker was driven by a random broadband signal (0 to 1 kHz), as shown in figure 3(a), which issued jets through a 1-mm diameter orifice. Figure 3(b) shows the corresponding power spectrum. Here, a 400-ms long signal was repeated 20 times while the streamwise velocity was sampled at a rate of 10 kHz by a single hot-wire probe using a DISA 55M CTA unit. The sampled data were converted to a digital form by a 16-bit analogue-to-digital convertor before they were stored on a computer for subsequent analysis. The velocity measurements were taken across the whole boundary-layer thickness along the central plane, which covered a streamwise range of 325–800 mm. Flow velocities were also measured in spanwise planes at several streamwise positions in a fine spanwise step of z = 0.5 mm to reveal the detailed flow structures. The total experimental uncertainty in velocity measurements was ±1.2 %, which was composed of a ±1.0 % error in hot-wire measurements and calibration, a ±0.6 % error owing to freestream velocity change during the run and a ±0.2 % error owing to flow uniformity in the test section of the wind tunnel. The spatial uncertainties associated with hot-wire measurements were ±0.2, ±7.5 and ±1.6 μm in the streamwise (x), wall-normal (y) and spanwise (z) directions, respectively, which arose from step motor resolutions (±0.2 μm in x and y and ±1.6 μm in z) and the laser displacement sensor accuracy (±7.5 μm) of the wall positioning of the hot-wire probe.

Figure 3. Time series (a) and power spectrum (b) of a random broadband voltage signal applied to a miniature speaker at x = 325 mm.

3. Experimental results

The streamwise velocity fluctuation in the laminar boundary layer measured by a single hot-wire probe immediately above the disturbance source (x = 325 mm) at y = 0.5 mm is shown in figure 4(a). Here, the velocity fluctuations leading to turbulent spots, Spot I, Spot II and Spot III are labelled by I, II and III, respectively. Because the velocity is the time derivative of displacement, the jet velocity from the orifice should be linearly proportional to the frequency of the voltage signal that sets the diaphragm displacement, i.e. $\textrm{sin}^{\prime}(2{{\rm \pi} }ft) = 2{{\rm \pi} }f \cdot \cos (2{{\rm \pi} }ft)$. Indeed, the power spectrum shown in figure 4(b) demonstrates that the measured velocity fluctuation is dominated by high frequency components of around 1 kHz. Therefore, the flow disturbance applied to the boundary layer can be considered as amplitude modulated jet pulses operating at the high end of the excitation frequency (1 kHz). Because these frequencies are located outside the neutral stability curve of the boundary layer, as shown in figure 5 (Wang & Gaster Reference Wang and Gaster2005), they are linearly stable.

Figure 4. Time series (a) and power spectrum (b) of the hot-wire signal immediately above the disturbance source (x = 325 mm) at y = 0.5 mm.

Figure 5. Neutral stability curve of a flat-plate boundary layer with a zero pressure gradient. The streamwise location of the disturbance source is indicated by a dotted line. Horizontal axis is the Reynolds number based on the displacement thickness, $Re = {\delta^\ast }{U_e}/\nu$ and the vertical axis is the non-dimensional frequency, $F = 2{{\rm \pi} }f\nu/U_e^2$.

The downstream development of the ensemble-averaged streamwise fluctuating velocity is shown in figure 6. Here, the measurements were taken along the centreline of the test plate between x = 350 and 700 mm. The time sequence is reversed through the use of Taylor's frozen-flow hypothesis, so that the flow structures correspond to physical space in the x–y plane. An early development of turbulent spots was seen at x = 350 mm (see figure 6a). These were incipient turbulence spots, which looked like heads of hairpin eddies. The pattern of these velocity fluctuations was very similar to the velocity signal at the disturbance source (see figure 4a). For example, five such low-speed structures were seen for Spot II at t = 110 ms, which grew in size and strength downstream. These structures will eventually ‘merge’ together, creating a large low-speed lump accompanied by a thin high velocity region near the wall, which is very similar to that observed for the turbulent spots studied by Zilberman, Wygnanski & Kaplan (Reference Zilberman, Wygnanski and Kaplan1977) and Fransson (Reference Fransson2010), see figure 6(g) at x = 700 mm.

Figure 6. Downstream development of the ensemble-averaged streamwise fluctuating velocity: (a) x = 350 mm, (b) x = 380 mm, (c) x = 400 mm, (d) x = 450 mm, (e) x = 520 mm, (f) x = 600 mm and (g) x = 700 mm. I, II and III indicate the turbulent spots being investigated in detail.

Only the disturbance with an initial velocity fluctuation (x = 325 mm at y = 0.5 mm) greater than 10 % of the freestream velocity U_e, as indicated by the red horizontal bar in figure 4(a), developed to turbulent spots downstream. For example, the velocity disturbances at times t = 85 ms and 110 ms developed to the turbulent spots, Spot III and Spot II, respectively, while those with lower velocity fluctuations (Spot I) decayed downstream. This agreed with the finding of previous studies (Elder Reference Elder1960; Wygnanski et al. Reference Wygnanski, Sokolov and Friedman1976), which indicated that only disturbance above a ‘critical intensity’ will breakdown to turbulence to form turbulent spots. However, the threshold value in our study was less than that of the critical intensity obtained before.

Figure 7(a) shows the colour velocity contours of three incipient turbulent spots in a plan view (t–z plane) at y = 0.2, 0.5 and 1.0 mm, 25 mm downstream from the disturbance source (x = 350 mm). Again, the time sequence is reversed in this figure so that the turbulent spots’ orientation corresponds to physical space in the x–y plane. The low-speed streaks that are shown in each figure were induced by a pair of necklace vortices from the disturbance source (Jabbal & Zhong Reference Jabbal and Zhong2008; Qayoum et al. Reference Qayoum, Gupta, Panigrahi and Muralidhar2010). Here, the low-speed streaks were seen on the upwash side of each pair of necklace vortices. The streaks seemed to be undisturbed everywhere except where velocity disturbance was applied.

Figure 7. Ensemble-averaged streamwise velocity contours in the t–z plane at t = 170 ms (Spot I), 115 ms (Spot II) and 90 ms (Spot III): (a) x = 350 mm, y = 0.2 mm, 0.5 mm and 1.0 mm; (b) x = 380 mm, y = 0.2 mm, 0.5 mm and 1.0 mm; (c) x = 400 mm, y = 0.2 mm, 0.5 mm, 1.0 m and 1.5 mm.

The incipient structure of Spot I was generated when the disturbance was applied to the boundary layer in two successive velocity pulses at t = 170 ms, see figure 4(a), where a pair of high velocity streaks lasting approximately 2 ms is shown at y = 0.2 mm. These are believed to be the legs of a hairpin vortex that extends from the orifice (Acarlar & Smith Reference Acarlar and Smith1987; Haidari & Smith Reference Haidari and Smith1994). Because the ratio of velocity disturbance to the freestream velocity was low in our experiment, only the downstream part of the ring vortex from the orifice will develop into a hairpin (Sau & Mahesh Reference Sau and Mahesh2008, Reference Sau and Mahesh2010). The vorticity of the upstream part cancelled out that of the on-coming boundary layer. A low-speed fluid (shown in blue) was pumped up from the wall region within the hairpin head. At y = 1.0 mm, the incipient structure consisted of two nested hairpins as a result of two successive pulsed disturbances. As shown later, this flow structure decayed downstream as the initial disturbance level (about 0.07 U_e) was less than the threshold value of 0.1 U_e to cause a breakdown to turbulence.

However, the initial structure of Spot III was created by a series of pulsed velocity disturbances at t = 80 ms. Here, ‘wavy’ pairs of high-speed streaks (as shown in red) were seen close to the wall (y = 0.2 and 0.5 mm). Three successive hairpin legs were developed from an orifice where the velocity disturbance had been applied. Further away from the wall at y = 1.0 mm, the head of the hairpin was seen slightly enlarged in the spanwise direction. A low-speed region (as shown in blue) was also observed in this figure, which was induced (upwashed) by the hairpin vortex. The level of applied disturbance (0.12 to 0.17 U_e) was large enough to breakdown the laminar boundary layer to develop a turbulent spot. A similar sequence of events was observed for Spot II after a sequence of five strong-pulsed disturbances was applied to the laminar boundary layer at t = 110 ms. This structure was nearly identical to that of Spot III, except that the number of wavy pairs were greater, which made this structure much longer in the streamwise direction.

What is interesting to observe in the initial structure of Spot III is that there were extra streaks outside of the original hairpin legs as compared with the incipient structure of Spot I, whose development was in its early stage owing to a weak disturbance. This suggested that lateral growth of the flow structure resulted from generation of secondary vortices by the original hairpin legs. Lateral growth of the flow structure through secondary vortices was also evident in the initial structure of Spot II, which indicated that this was one of the mechanisms for turbulent spot growth, as suggested by Asai et al. (Reference Asai, Sawada and Nishioka1996). Similar mechanisms for lateral growth were proposed by Gad-el-Hak et al. (Reference Gad-el-Hak, Blackwelder and Riley1981), Perry et al. (Reference Perry, Lim and Teh1981) and Sankaran et al. (Reference Sankaran, Sokolovs and Antonia1988).

These results indicate that the development of a turbulent spot depends on the initial level of disturbance as well as the number of velocity pulses. For example, Spot II and Spot III are already in an advanced stage of development only 25 mm downstream of the disturbance. They have strong velocity defect regions away from the wall (shown in blue) together with velocity excess regions near the wall (shown in red). However, Spot I is still in its infancy, showing no or little development in the velocity defect or excess regions. Downstream developments of incipient turbulent spots are shown in figures 7(b) and 7(c) at x = 380 and 400 mm, respectively. Spot I grew in size (height, width and length) until x = 380 mm, but started to decay after x = 400 mm. However, Spot II and Spot III grew, both in size and intensity, through an increase in the number of velocity pulses during the development. The increase in the spot height seemed to arise from the increase in the boundary layer thickness, which will be shown later.

Results shown in figure 7 were obtained by ensemble-averaged x-component velocities when a 400-ms long disturbance signal was repeated 20 times. Here we show the effect of the number of ensemble averages on the velocity contour of Spot II at x = 380 mm in figure 8, which suggests that the repeatability of the velocity measurements in the present experiment was excellent at least in the near field where the early development of artificially initiated turbulence is investigated. This demonstrates that the velocity pattern does not effectively change as the number of ensemble averages is reduced from 20 to 1. This arises from the ‘deterministic turbulence’ technique (Shaikh Reference Shaikh1997; Borodulin et al. Reference Borodulin, Kachanov and Roschektayev2011) employed in our test, which was carried out in an extremely low-turbulence wind tunnel (Gaster Reference Gaster, Hussaini and Voigt1990). All results reported here were ensemble averaged using 20 repeated data, except for those shown in figures 10–13 where the velocity signals and associated wavelet spectra are shown using a single realisation.

Figure 8. Effect of the number of ensemble average on the streamwise velocity contour of Spot II at x = 380 mm, y = 1.0 mm: (a) 20 ensembles, (b) 10 ensembles, (c) 5 ensembles and (d) no ensembles (a single realisation).

The development of incipient turbulent spots is demonstrated further in figure 9, where the three-dimensional structure of Spot II is depicted by iso-surfaces of the x-component velocity fluctuation at 10 % (shown in coral) and −5 % (cyan) of the freestream velocity. Figures 9(a), 9(b) and 9(c) correspond to the spot structure at x = 350, 380 and 400 mm, respectively. They demonstrate that the incipient turbulent spot was composed of a number of low-speed pillars that were anchored at the wall, which stretched out to the edge of the boundary layer. A high-speed region of the turbulent spot was also visible near the wall in between the low-speed pillars. These pillars represent the low-speed regions that were pumped up within each hairpin-like structures of the incipient turbulent spot. The structural development of an incipient turbulent spot shown in figure 9 reveals that the number of hairpin-like structures increased in both the streamwise and spanwise directions during the development. Low-speed pillars of incipient turbulent spots seem to be amalgamated at x = 400 mm (see figure 9c), which suggested that hairpin-like structures merged together during the spot development. The early development of turbulent spots that is shown in figure 9 is similar to that of Wu et al. (Reference Wu, Moin, Wallace, Skarda, Lozano-Durán and Hickey2017) in their DNS simulation of the turbulent boundary layer during transition.

Figure 9. Three-dimensional structure of Spot II depicted by iso-surfaces of ensemble-averaged x-component velocity fluctuations at 10 % (coral) and −5 % (cyan) of the freestream velocity, where colour contour slices at y = 1 mm are superimposed: (a) x = 350 mm; (b) x = 380 mm; (c) x = 400 mm.

Figures 10(a), 10(b) and 10(c) present the streamwise velocity fluctuations in the near-wall region (y = 0.5 mm) at x = 350, 380 and 400 mm, respectively, showing the downstream development of incipient turbulent spots. They show that Spot I decayed downstream, and its initial disturbance nearly disappeared by x = 400 mm. Meanwhile, Spot II developed downstream by generating a large number of high-frequency spikes. These spikes were positively skewed, which suggested that they were associated with a downwash of higher momentum fluid towards the wall. A similar development of Spot III is shown in figures 10(a), 10(b) and 10(c), although the development of this turbulent spot seemed to be slower than that of Spot II. The main difference between Spot II and Spot III was in the number of initial disturbances above the critical intensity. While Spot II had five velocity pulses in the initial disturbance, Spot III only had two. It seems, therefore, the speed of development of incipient turbulent spots depends on the number of velocity pulses or the duration of the initial disturbance.

Figure 10. Streamwise velocity signals (a single realisation) in the boundary layer at y = 0.5 mm, showing the downstream development of Spot I, II and III: (a) x = 350 mm, (b) x = 380 mm, (c) x = 400 mm.

The downstream change in the turbulence energy distribution within incipient turbulent spots can be studied by wavelet spectra using Matlab. Here, we used generalised Morse wavelets defined by ${\varPsi _{P,\gamma }}(\omega ) = U(\omega ){a_{P,\gamma \textrm{\; }}}{\omega ^{{P^2/ \gamma}}}{\textrm{e}^{ - {\omega ^\gamma }}}$ in the frequency domain $\omega $, where $U(\omega )$ is the unit step function and ${a_{P,\gamma }}$ is a normalising constant (Lilly & Olhede Reference Lilly and Olhede2012). The symmetry parameter and the time-bandwidth product were set to γ = 3 and P ² = 60, respectively. Figures 11(a), 11(b) and 11(c) show the wavelet spectra of the streamwise velocity signals in figures 10(a), 10(b) and 10(c), respectively. Figure 11(a) shows that the turbulence energy of Spot II and Spot III at x = 350 mm was contained between f = 0.5 and 2 kHz. With a downstream development of incipient turbulent spots, the wavelet spectrum spread to cover a wider frequency range up to f = 3 kHz. At x = 400 mm, much of the turbulence energy within Spot II and Spot III can be found between f = 1 and 3 kHz, see figure 11(c), as a result of high-frequency spikes being generated within incipient turbulent spots (see figure 10c). Figure 11 clearly shows that the turbulence energy in Spot I had nearly disappeared by x = 400 mm.

Figure 11. Wavelet spectra of streamwise velocity signals (a single realisation) in the boundary layer at y = 0.5 mm, showing the downstream development of Spot I, II and III: (a) x = 350 mm, (b) x = 380 mm, (c) x = 400 mm.

Figures 12(a), 12 (b) and 12(c) are similar to figures 10(a), 10(b) and 10(c), which show the streamwise velocity fluctuations at x = 350, 380 and 400 mm, respectively, near the edge of the boundary layer at y = 1.5 mm. Again, an increase in the number of high-frequency spikes was evident for Spot II and Spot III, while the initial disturbance was almost gone by x = 400 mm for Spot I. In contrast to figure 10, the high-frequency spikes at y = 1.5 mm were negatively skewed, which suggested that they were associated with an upwash of lower momentum fluid from the near-wall region. The downstream development of this low momentum region is clearly seen in figure 6. A strong shear layer between the low-speed region and the high-speed region produces high frequency velocity spikes (Wygnanski et al. Reference Wygnanski, Sokolov and Friedman1976) as we observe in figures 10 and 12. Figures 10 and 12 also show that velocity pulses within the structure started to shape into an envelope of turbulent spots at around x = 400 mm. This could be a result of a beating effect of high-frequency velocity pulses generated within the developing spot structure, which is similar to the generation process of very large-scale motions (VLSMs) from the hairpin packets in a turbulent boundary layer (Sharma & McKeon Reference Sharma and McKeon2013).

Figure 12. Streamwise velocity signals (a single realisation) in the boundary layer at y = 1.5 mm, showing the downstream development of Spot I, II and III: (a) x = 350 mm, (b) x = 380 mm, (c) x = 400 mm.

The wavelet spectra of streamwise velocity signals at y = 1.5 mm are shown in figures 13(a), 13(b) and 13(c) at x = 350, 380 and 400 mm, respectively. The turbulence energy of Spot I was reduced downstream very quickly as shown in figures 13(a), 13(b) and 13(c). However, the turbulence energy of Spot II and Spot III near the edge of boundary layer, which was initially concentrated between f = 1 kHz and 3 kHz owing to high-frequency spikes as shown in figure 12(a), shifted towards lower frequency downstream between f = 0.5 and 2.5 kHz at x = 380 mm and then to between f = 0.5 and 2 kHz at x = 400 mm. This shift of turbulence energy coincided with the formation of a turbulent spot envelope, as observed in figures 12(b) and 12(c). Indeed, we observed a low frequency peak (175 Hz) in the wavelet spectrum of Spot III at x = 400 mm in figure 13(c), which corresponded to the duration (6 ms) of the turbulent spot envelope being formed as shown in figure 12(c). A similar downshift in energy peak frequency was observed by Casper et al. (Reference Casper, Beresh, Henfling and Spillers2014a), who used the wavelet transform of wall-pressure traces to identify the location of turbulent spots on a 7° hypersonic cone.

Figure 13. Wavelet spectra of streamwise velocity signals (a single realisation) in the boundary layer at y = 1.5 mm, showing the downstream development of Spot I, II and III: (a) x = 350 mm, (b) x = 380 mm, (c) x = 400 mm.

Integral boundary-layer parameters, which include the displacement thickness δ*, the momentum thickness θ and the shape factor H, at x = 350, 380 and 400 mm are given in figures 14(a), 14(b) and 14(c), respectively. We observe that δ* and θ increased and the shape factor H = δ*/θ reduced as expected with the development of the boundary layer downstream. We can also observe that the integral parameters δ* and θ increased within incipient turbulent spots at each downstream location. Here, the relative increase in the momentum thickness within incipient turbulent spots was greater than that of the displacement thickness, therefore the shape factor H = δ*/θ was reduced. For example, the shape factor in Spot II was reduced to H = 1.9, 1.6 and 1.4 at x = 350, 380 and 400 mm, respectively, as shown in figures 14(a), 14(b) and 14(c). Therefore, the boundary layer flow within Spot II was already fully developed turbulence at x = 400 mm as the shaper factor reached to H = 1.4. The shape factor of the boundary layer outside incipient turbulent spots was reduced from H = 2.5 at x = 350 mm to H = 2.15 at x = 400 mm. This suggested that the ‘non-turbulence’ region of the boundary layer was already affected by the development of incipient turbulent spots even when the intermittency factor was only 22 % at x = 400 mm. It is interesting to observe that the shape factor of the boundary layer at this streamwise location was reduced from H = 2.15 to H = 1.4 very quickly when the front (downstream end) of the turbulent spot approached. However, the process of getting back to the ‘laminar’ region from the ‘turbulent’ region at the back (upstream end) of the turbulent spot, which is called the ‘calmed region’ by Schubauer & Klebanoff (Reference Schubauer and Klebanoff1956), was much slower. This arose from the elongated high-speed region affecting the ‘laminar’ region.

Figure 14. Integral boundary-layer parameters: (a) x = 350 mm; (b) x = 380 mm; (c) x = 400 mm.

Ensemble-averaged velocity profiles of the boundary layer between t = 113 and 130 ms are given in figure 15, which show the temporal structure of Spot II at x = 400 mm. Here, the boundary layer profiles are shown from left to right with an interval of 1 ms. This indicates that the boundary layer starts to develop a strong inflexional profile at t = 115 ms only a few milliseconds after the spot front had passed. Then, a velocity retardation region develops, moving towards the boundary-layer edge for the next 3 ms (t = 116–118 ms). This is followed by a flow acceleration near the wall. These temporal changes in the boundary-layer profile within Spot II can be further examined by the velocity fluctuations recorded between 110 and 130 ms at y = 0.2, 0.5, 1.0, 1.5, 2.0 and 2.6 mm, as shown on the right-hand side of the figure. Here, the velocity fluctuations were mostly negative away from the wall (y > 1.5 mm) and positive close to the wall (y < 0.5 mm), which suggested that a strong shear layer was created at around y = 1 mm by the inflexional velocity profile. This seems to be the location where the turbulence energy was produced in the boundary layer to maintain turbulent spots. This behaviour of turbulence energy generation in turbulent spots is very similar to the burst events in the turbulent boundary layer, where the ejection event (−u and +v velocity fluctuations) is followed by the sweep event (+u and -v velocity fluctuations), see figure 9 of Blackwelder & Kaplan (Reference Blackwelder and Kaplan1976).

Figure 15. Ensemble-averaged velocity profiles of the boundary layer at x = 400 mm. Solid lines are perturbed velocity profiles in Spot II between 110 and 130 ms at an interval of 1 ms, while dotted lines indicate the ‘laminar’ velocity profile outside incipient turbulent spots (t = 105 ms). The velocity fluctuations in Spot II between 110 and 130 ms are shown on the right at y = 0.2, 0.5, 1.0, 1.5, 2.0 and 2.6 mm (from bottom to top).