3.1. Effect of a mesh on roughness-induced transition

Without the roughness element, the measured Blasius boundary layer thickness and the displacement thickness at $x=300~\text{mm}$ were ${\it\delta}_{B}=5.45~\text{mm}$ and ${\it\delta}_{B}^{\ast }=1.9~\text{mm}$ respectively, for a free-stream velocity of $U_{\infty }=5.3~\text{m}~\text{s}^{-1}$ . The roughness height (of 2 mm) was approximately equal to ${\it\delta}_{B}^{\ast }$ ; that is, the roughness element was within the boundary layer. The Reynolds number based on the roughness height was $\mathit{Re}_{h}$ $(=U_{h}h/{\it\nu})=396$ ; $U_{h}$ is the mean velocity at a height $h$ without the roughness element and ${\it\nu}$ is the kinematic viscosity; this value is higher than the critical value of $\mathit{Re}_{h}=338$ suggested by Bade & Naguib (Reference Bade and Naguib2012) for a single roughness element. Most of the flow parameters are normalized with $U_{\infty }\,(=5.3~\text{m}~\text{s}^{-1})$ and ${\it\delta}_{B}^{\ast }$ in the following.

Downstream of the roughness element, the boundary layer velocity profiles at different streamwise locations are shown in figure 2(a). The flow just behind the roughness element underwent separation and the bubble extended until approximately $x=310~\text{mm}$ . The spanwise variation of $u_{rms}$ , the root-mean-square of the streamwise fluctuating velocity component $u$ due to the roughness element alone showed prominent peaks at ${\rm\Delta}z/{\it\delta}_{B}^{\ast }\approx 0$ , $\pm 3$ , as can be seen in figure 2(b). This indicates the presence of low- and high-speed streaks, as can also be seen in the spanwise variation of $U/U_{\infty }$ in figure 2(c). As $u_{rms}$ variation is significant within ${\rm\Delta}z/{\it\delta}_{B}^{\ast }=\pm 5$ until approximately $x=500~\text{mm}$ , SM (of 21 mm width) was initially considered. Due to the finite mesh width, flow in the mid-plane was slightly contaminated by disturbances generated along its sides. Therefore, to avoid this, LM (which is wider than SM) was mostly used.

Figure 2.

Streamwise velocity and intensity of fluctuations due to roughness. (a) Boundary layer velocity profiles; (b) spanwise variation of the fluctuation intensity; (c) spanwise variation of the streamwise velocity. The values of ${\rm\Delta}z/{\it\delta}_{B}^{\ast }$ in (a) and $y/{\it\delta}_{B}^{\ast }$ in (c) indicate spanwise and wall-normal PIV measurement locations respectively.

Figure 3.

(a) Instantaneous spanwise vorticity contours in the wall-normal plane at $x=450~\text{mm}$ illustrating the inclined high-shear layer in roughness-induced (R) transitional flow. The arrows are fluctuating velocity vectors of $u$ and $v$ seen by an observer moving at a convection velocity of $0.85U_{\infty }$ . The line contours represent the swirl strength. (b) Instantaneous streamwise velocity contours in the spanwise plane showing the varicose instability feature. The arrows are fluctuating velocity vectors of $u$ and $w$ .(c) Correlation contours of the streamwise velocity fluctuation ( $R_{uu}$ ); the white dot indicates the reference location. The wall-normal plane is at ${\rm\Delta}z/{\it\delta}_{B}^{\ast }\approx -0.58$ and the spanwise plane is at $y/{\it\delta}_{B}^{\ast }\approx 1.79$ .

The instantaneous PIV measurements in the wall-normal and spanwise planes in figure 3 show a typical flow picture at $x=450~\text{mm}$ due to the roughness element; here (and in the following), R denotes the roughness-alone case. We may note that the camera centre here (and hereafter) is at ${\rm\Delta}x=0$ . Figure 3(a) shows high-shear layers with detached vortices extending well into the free stream in the wall-normal plane. The colour contours in this figure correspond to the normalized spanwise vorticity, ${\it\Omega}_{z}{\it\delta}_{B}^{\ast }/U_{\infty }$ ; ${\it\Omega}_{z}$ is the dimensional spanwise vorticity. The line contours correspond to vortices, and the superimposed vectors are those seen by an observer moving with a convection velocity ( $U_{C}$ ) of 0.85 $U_{\infty }$ . The breakdown of flow shown in figure 3(b) is similar to that observed by Chernoray et al. (Reference Chernoray, Kozlov, Löfdahl and Chun2006) in varicose instability (see their figure 6) triggered by artificial disturbances introduced on streaks generated by a single roughness element. Bade & Naguib (Reference Bade and Naguib2012) have also observed similar breakdown in their flow visualization. The contours in this figure correspond to the non-dimensional instantaneous velocity ( $U_{I}/U_{\infty }$ ), and the superimposed vectors are fluctuating velocities. In terms of the correlation contours of the streamwise velocity fluctuation, $R_{uu}$ , the breakdown pattern is shown in figure 3(c). The choice of a mesh at $x_{m}=450~\text{mm}$ was based on the fact that it would prevent the lift-up of the inclined high-shear layer seen in figure 3(a) and also distort the symmetric streaky structure (figure 3 b).

Upstream of the mesh, the free-stream velocity at $x$ = 400 mm is slightly lower than the roughness-alone case due to the blockage caused by it, as shown in figure 4(a); note that the velocity is normalized by $U_{\infty }=5.3~\text{m}~\text{s}^{-1}$ (of the roughness-alone case) to show this effect; here (and in the following), R & LM02mm, R & LM04mm, etc., indicate that the large mesh was placed at $y_{m}=2~\text{mm}$ , 4 mm, etc., in roughness-induced transitional flow. Further upstream, this reduction in free-stream velocity was less pronounced (not shown here). However, the $u_{rms}$ profiles in figure 4(b) indicate that the peak fluctuation intensity is not so significantly altered upstream of the mesh.

Figure 4.

Effect of a mesh on the upstream flow. Boundary layer velocity (a) and fluctuation intensity (b) profiles at $x=400~\text{mm}$ and ${\rm\Delta}z/{\it\delta}_{B}^{\ast }\approx 0.47$ .

The instantaneous velocity fields in the spanwise plane at $x=500~\text{mm}$ in figure 5 show the effect of LM at different $y_{m}$ locations. The streak instability in the roughness-alone case can be clearly seen in figure 5(a). The instantaneous velocity field is symmetric along the centreline. The counter-rotating vortices (indicated by black and white lines) at the interface of low- and high-speed streaks (i.e. region of large shear) correspond to the legs of a hairpin vortex (e.g. Chernoray et al. Reference Chernoray, Kozlov, Löfdahl and Chun2006; Zhang et al. Reference Zhang, Pan and Wang2011). The streamwise ( $L$ ) and spanwise ( $W$ ) length scales of the instability determined following Mans et al. (Reference Mans, Kadijk, de Lange and van Steenhoven2005) are also shown in figure 5(a). In FST-induced transition, Mans et al. (Reference Mans, Kadijk, de Lange and van Steenhoven2005) find $L=28{\it\delta}_{0}^{\ast }$ and $W=2.5{\it\delta}_{0}^{\ast }$ for sinuous instability, and $L=19{\it\delta}_{0}^{\ast }$ and $W=5.5{\it\delta}_{0}^{\ast }$ for varicose instability; ${\it\delta}_{0}^{\ast }$ corresponds to $\mathit{Re}_{{\it\delta}_{0}^{\ast }}=300$ . As shown in figure 5(a), the values of $L=38.2{\it\delta}_{0}^{\ast }$ and $W=12.58{\it\delta}_{0}^{\ast }$ are almost twice those reported for the varicose instability in FST-induced transition. On introducing the mesh at $y_{m}=2~\text{mm}$ (figure 5 b), the symmetric streaky structure associated with the instability (including vortices) is completely distorted. The mesh is seen to cause a large number of streaks of smaller spanwise spacing, an increase in instantaneous velocity and a reduction in velocity fluctuations. The velocity fluctuation across streaks is also very small. Vortices are still present, but are not as regular as in figure 5(a). By applying travelling waves with a certain phase shift in the spanwise plane, Bai et al. (Reference Bai, Zhou, Zhang, Xu, Wang and Antonia2014) control the spanwise modulation of streaks to reduce drag in a turbulent boundary layer. The resulting orderly streaky structure is attributed to the frictional-drag reduction. Interestingly, their orderly streaky pattern (see their figure 10b) is qualitatively similar to that in figure 5(b). Thus, one may anticipate that the mesh at $y_{m}=2~\text{mm}$ will reduce the frictional drag, compared with the roughness-alone case, if orderly streaks are responsible for any such reduction. With the mesh further away from the wall, the instantaneous velocity increases (figures 5 c,d); the faint appearance of a low-speed streak in the centre can also be observed. Almost all of the instantaneous velocity fields (with mesh) were similar to those shown here. The spanwise variation of $U$ at $x=500~\text{mm}$ in figure 6(a) shows that the mesh increases the acceleration and reduces the streak amplitude, $(U_{max}-U_{min})$ (Elofsson et al. Reference Elofsson, Kawakami and Alfredsson1999), thus reducing the spanwise gradient of the streamwise velocity; $U_{max}$ and $U_{min}$ are the maximum and minimum of the mean streamwise velocity in the spanwise plane respectively. While a significant reduction in $u_{rms}$ is caused by the mesh (figure 6 b), the greatest reduction is for the mesh at $y_{m}=2~\text{mm}$ .

Figure 5.

Instantaneous streamwise velocity contours in the spanwise plane at $x=500~\text{mm}$ showing the effect of a mesh at different wall-normal locations on roughness-induced transitional flow: (a) R; (b) R & LM02mm; (c) R & LM04mm; (d) R & LM06mm. The arrows are the fluctuating velocity vectors of $u$ and $w$ . The line contours represent the swirl strength (black line, anticlockwise vortex; white line, clockwise vortex). The spanwise plane is at $y/{\it\delta}_{B}^{\ast }\approx 1.84$ and  $h$ is the roughness height.

Figure 6.

Comparison of the spanwise distribution of the streamwise mean velocity (a) and the fluctuation intensity (b) at $x=500~\text{mm}$ and $y/{\it\delta}_{B}^{\ast }\approx 1.84$ with and without the mesh.

The effect of a mesh on the boundary layer velocity profile at $x=750~\text{mm}$ is shown in figure 7(a). Compared with the roughness-alone case, the mesh reduces the free-stream velocity from 5.3 to $3.7~\text{m}~\text{s}^{-1}$ , i.e. a reduction of approximately 30 %. This reduction is due to the pressure drop caused by the mesh. Nearly the same velocity profiles for both the SM and LM cases indicate that the flow history is less significant far downstream; this could be due to the fact that SM and LM differ only in width. Figure 7(b) shows that, compared with the roughness-induced transitional case (filled symbols), both SM and LM reduce $u_{rms}$ considerably; the higher values across the boundary layer for SM are due to the contamination by disturbances from its sides, as mentioned earlier. This significant reduction of $u_{rms}$ indicates transition delay caused by the mesh at $y_{m}=2~\text{mm}$ . A reduced free-stream velocity implies a lower mean flow Reynolds number ( $\mathit{Re}=U_{fs}{\it\theta}/{\it\nu}$ ); $U_{fs}$ is the local free-stream velocity and ${\it\theta}$ is the momentum thickness. Moreover, due to the transition delay, the boundary layer integral parameters at $x=750~\text{mm}$ are reduced, as shown in figure 8; ${\it\delta}^{\ast }$ and ${\it\theta}$ are based on $U_{fs}$ ; ${\it\delta}^{\ast }=\int _{0}^{\infty }[1-(U/U_{fs})]\,\text{d}y$ and ${\it\theta}=\int _{0}^{\infty }(U/U_{fs})[1-(U/U_{fs})]\,\text{d}y$ .

Figure 7.

Effect of a mesh on the roughness-induced transitional flow. Boundary layer velocity (a) and fluctuation intensity (b) profiles at $x=750~\text{mm}$ and ${\rm\Delta}z/{\it\delta}_{B}^{\ast }\approx 0.58$ .

Figure 8.

Effect of a mesh on the boundary layer integral length scales. For R: ▫, ${\it\delta}^{\ast }$ ; △, ${\it\theta}$ . For R & LM02mm: ▪, ${\it\delta}^{\ast }$ ; ▴, ${\it\theta}$ . The mesh is at $x_{m}=450~\text{mm}$ .

Figure 9.

Instantaneous spanwise vorticity contours in the wall-normal plane at $x=750~\text{mm}$ illustrating the effect of a mesh on roughness-induced transitional flow; the arrows are fluctuating velocity vectors of $u$ and $v$ : (a) R; (b) R & LM02mm. The line contours represent the normalized swirl strength ( ${\it\lambda}{\it\delta}^{\ast }/U_{fs}$ ); contour level: (a) $-0.15$ and (b) $-0.1$ . The wall-normal plane is at ${\rm\Delta}z/{\it\delta}_{B}^{\ast }\approx 0.58$ . Note that the inclined high-shear layers caused by roughness in (a) are absent due to the mesh in (b).

The Reynolds number reduction seen here is similar to that in the relaminarization of a fully turbulent flow by a strong streamwise favourable pressure gradient (e.g. Blackwelder & Kovasznay Reference Blackwelder and Kovasznay1972; Narasimha & Sreenivasan Reference Narasimha and Sreenivasan1973; Piomelli, Balaras & Pascarelli Reference Piomelli, Balaras and Pascarelli2000), where the boundary layer integral length scales also reduce. The transition delay reported here can be regarded as near relaminarization of the transitional flow. While an imposed favourable pressure gradient does not alter the shape of the large-scale spanwise structure in the relaminarization of fully turbulent flows (Blackwelder & Kovasznay Reference Blackwelder and Kovasznay1972), a mesh here breaks down many transitional structures, as shown by the instantaneous PIV measurements in the wall-normal and spanwise planes at $x=750~\text{mm}$ in figures 9 and 10 respectively. Compared with figure 9(a), figure 9(b) shows that the downstream evolution of the high-shear layer caused by the roughness alone is completely modified by the mesh (at $x_{m}=450~\text{mm}$ and $y_{m}=2~\text{mm}$ ). The colour contours in figure 9(b) are based on ${\it\delta}_{B}^{\ast }$ and $U_{\infty }\,(=5.3~\text{m}~\text{s}^{-1})$ values used in the roughness-alone case, for a meaningful comparison. The line contours show the normalized swirl strength, ${\it\lambda}{\it\delta}^{\ast }/U_{fs}$ . It can be seen that strong vortices (shown by line contours), which are associated with lifted-up shear layers, are either destroyed or their strength is reduced by the mesh. Similarly, the formation of orderly and less intense low- and high-speed streaks due to the mesh can be seen on comparing figure 10(b) with figure 10(a); we note that the contours in these figures are also based on the $U_{\infty }\,(=5.3~\text{m}~\text{s}^{-1})$ value of the roughness-alone case. Comparing the streak spacing at $x=750~\text{mm}$ in figure 10(b) with that at $x=500~\text{mm}$ (figure 5 b), it is seen to increase downstream, along with increased streak width. The $R_{uu}$ correlation (not shown here) also revealed the same. The strong disturbances at ${\rm\Delta}z/{\it\delta}_{B}^{\ast }\approx \pm 5$ in figure 10(c) are due to the finite mesh width, as mentioned earlier. Therefore, the mesh seems to break up the unsteady activities in the outer high-shear layer region and modify the spanwise structure as well. Interestingly, the lifted-up high-shear layer with negative $u$ fluctuations in figures 3(a) and 9(a) and the streak breakdown via the varicose instability in figures 3(b) and 5(a) are similar to those in bypass transition induced by a high level of FST (e.g. Mandal et al. Reference Mandal, Venkatakrishnan and Dey2010; Hack & Zaki Reference Hack and Zaki2014). While the mesh at $y_{m}=2~\text{mm}$ modifies many transitional events in the spanwise plane, the shape of the large-scale streamwise structure in the wall-normal plane seems to be more or less preserved, as also discussed in § 3.2 below. This is shown in figure 11 in terms of the contours of $R_{uu}$ at $x=750~\text{mm}$ .

Figure 10.

Instantaneous streamwise velocity contours in the spanwise plane at $x=750~\text{mm}$ illustrating the effect of a mesh on roughness-induced transitional flow: (a) R; (b) R & LM02mm; (c) R & SM02mm. The arrows are fluctuating velocity vectors of $u$ and $w$ . The spanwise plane is at $y/{\it\delta}_{B}^{\ast }\approx 1.84$ .

Figure 11.

Contours of $R_{uu}$ showing the effect of a mesh on roughness-induced transition at $x=750~\text{mm}$ and ${\rm\Delta}z/{\it\delta}_{B}^{\ast }\approx 0.58$ : (a) R; (b) R & LM02mm; (c) R & SM02mm. The black dot indicates the reference location.

3.2. Effect of a mesh on FST-induced transition

As mentioned earlier, a grid was used (see figure 1 b) to create a transitional flow by FST. The measured mean flow characteristics are shown in figure 12; here, ${\it\delta}^{\ast }$ and $u_{rms,max}$ are the local displacement thickness and maximum value of $u_{rms}$ respectively. As in Matsubara & Alfredsson (Reference Matsubara and Alfredsson2001), the boundary layer velocity profiles (figure 12 a) become fuller in the inner half and show deficit in the outer half of the boundary layer with increasing downstream distance (indicated by an upward/downward arrow). Figure 12(b), for pre-transitional flow, shows that the variation of $u_{rms}/u_{rms,max}$ compares well with the non-modal growth of Luchini (Reference Luchini2000). The streamwise variations of $u_{rms,max}$ and its wall-normal location in figure 12(c) show that $u_{rms,max}$ in pre-transitional flow occurs at approximately $y/{\it\delta}^{\ast }=1.3$ , and it moves towards the wall with increasing downstream distance (e.g. Westin et al. Reference Westin, Boiko, Klingmann, Kozlov and Alfredsson1994; Matsubara & Alfredsson Reference Matsubara and Alfredsson2001). The maximum value of $u_{rms}$ at the transition onset ( $x=300~\text{mm}$ , ${\it\gamma}\approx 1.3\,\%$ at $y/{\it\delta}^{\ast }\approx 1.1$ ) is approximately $0.12U_{\infty }$ , but its wall-normal location is slightly lower than $y/{\it\delta}^{\ast }=1.3{-}1.4$ reported by others (e.g. Matsubara & Alfredsson Reference Matsubara and Alfredsson2001; Hernon et al. Reference Hernon, Walsh and McEligot2007); here, ${\it\gamma}$ is the flow intermittency.

Figure 12.

Mean flow characteristics in an FST-induced transitional boundary layer. (a) Mean velocity profiles; the arrows indicate the downstream change in profile shape. (b) Comparison of pre-transitional $u_{rms}$ profiles with Luchini (Reference Luchini2000). (c) Streamwise variations of $u_{rms,max}$ (empty symbols) and its wall-normal location (filled symbols). Symbols: ▫, $x=125~\text{mm}$ ; △, $x=180~\text{mm}$ ; ▿, $x=250~\text{mm}$ ; ▹, $x=300~\text{mm}$ ; ◃ , $x=450~\text{mm}$ ; ♢, $x=500~\text{mm}$ ; ○, $x=750~\text{mm}$ .

In terms of the probability density function (p.d.f.) of the normalized instantaneous velocity fluctuations, Imayama, Alfredsson & Lingwood (Reference Imayama, Alfredsson and Lingwood2012) have reported the change in flow structure during transition on a rotating disk. Nolan (Reference Nolan2009) and Patten, Griffin & Young (Reference Patten, Griffin and Young2013) also suggest that such p.d.f. plots provide a good representation of the magnitude of fluctuations at different wall-normal locations in an FST-induced transitional flow. Here, we follow Imayama et al. (Reference Imayama, Alfredsson and Lingwood2012). After normalizing the p.d.f. amplitude at each wall-normal location by its maximum value, such plots for streamwise instantaneous velocity fluctuations at different streamwise locations are shown in figure 13(a–f); here, ${\it\delta}$ is the local boundary layer thickness. Only $u$ fluctuations are considered, as $u\gg v$ in FST-induced transition (e.g. Jacobs & Durbin Reference Jacobs and Durbin2001; Mandal et al. Reference Mandal, Venkatakrishnan and Dey2010). The asymmetry in the p.d.f. distributions inside the boundary layer can be attributed to the presence of negative $u$ fluctuations in the inclined shear layer away from the wall and positive $u$ fluctuations in the shear layer close to the wall (e.g. Jacobs & Durbin Reference Jacobs and Durbin2001; Mandal et al. Reference Mandal, Venkatakrishnan and Dey2010; Nolan & Zaki Reference Nolan and Zaki2013). Downstream, the p.d.f. seems to be more skewed to the left near the boundary layer edge. This might be due to the lifting up of low-speed streaks to the boundary layer edge. The p.d.f. is symmetric in the free stream as the flow is isotropic there. The peak negative velocity fluctuation is higher than the peak positive fluctuation; the increase in their magnitudes and the movement of the peak positive fluctuation towards the wall on approaching the transition onset are in agreement with Hernon et al. (Reference Hernon, Walsh and McEligot2007). The movement of the peak negative fluctuation towards the boundary layer edge is not so clear. At $x=250~\text{mm}$ , i.e. near the transition onset, the locations of the peak negative and positive fluctuations at $y/{\it\delta}\approx 0.5$ and 0.2 respectively in figure 13(c) are also close to those reported by Hernon et al. (Reference Hernon, Walsh and McEligot2007). On approaching the transition onset, two peaks in the p.d.f. plots appear near the location of $u_{rms,max}$ . This might be due to the secondary instability of streaks. Imayama et al. (Reference Imayama, Alfredsson and Lingwood2012) have also reported double peaks in p.d.f. plots at the wall-normal location of maximum disturbance in transitional flow on a rotating disk. By conditional sampling of positive and negative $u$ fluctuations (e.g. Kähler Reference Kähler2004), the distributions of $u_{rms,p}$ (for positive fluctuation) and $u_{rms,n}$ (for negative fluctuation) are shown in figure 13(g–l), along with $u_{rms}$ . It can be seen that the peak values of $u_{rms,p}$ and $u_{rms,n}$ are higher than $u_{rms}$ . Interestingly, the wall-normal locations of peak $u_{rms,p}$ and $u_{rms,n}$ nearly correspond to the peaks of the instantaneous velocity fluctuations in the p.d.f. plots (figure 13 a–f).

Figure 13.

Probability density functions of the instantaneous streamwise velocity fluctuation (a–f) and corresponding distributions of the root-mean-square values across the boundary layer (g–l) at different streamwise locations in FST-induced transitional flow: (a,g) $x=125~\text{mm}$ ; (b,h) $x=180~\text{mm}$ ; (c,i) $x=250~\text{mm}$ ; (d,j) $x=300~\text{mm}$ ; (e,k) $x=450~\text{mm}$ ; (f,l) $x=500~\text{mm}$ . The empty circle denotes the $u_{rms,max}$ location. Lines: ——, $u_{rms}$ ; - - - -, $u_{rms,p}$ ; — ⋅ —, $u_{rms,n}$ . Contours levels in (a–f): 10 %–90 % of the local p.d.f. value with increment of 10 %.

An inclined high-shear layer is always present in FST-induced transition, irrespective of whether a turbulent spot appears at the boundary layer edge (e.g. Jacobs & Durbin Reference Jacobs and Durbin2001; Zaki & Durbin Reference Zaki and Durbin2005) or at the interface of low- and high-speed streaks (e.g. Nolan & Walsh Reference Nolan and Walsh2012). A similar inclined high-shear layer was also seen in the instantaneous PIV measurements at $x=450~\text{mm}$ (not shown here). Here, again, the mesh was introduced at $x_{m}=450~\text{mm}$ and at different wall-normal locations to study its effect on FST-induced transitional flow, including possible transition delay, as in § 3.1.

The effect of a mesh on the boundary layer flow characteristics at $x=500~\text{mm}$ is shown in figure 14; dimensional quantities are shown for clarity. Here (and hereafter), the FST-alone case is denoted by G, and G & LM02mm, G & LM04mm, etc. indicate that LM was placed at $y_{m}=2~\text{mm}$ , 4 mm, etc., in this transitional flow. The mean velocity in figure 14(a) shows a mild acceleration near the wall and an overshoot in the outer region, followed by a reduced free-stream velocity. Bi et al. (Reference Bi, Zhao, Dong, Xu and Gui2014) have also reported similar variation of the boundary layer velocity downstream of a flexible net of finite size. Moreover, the velocity overshoot seems to be similar to that observed by He, Pan & Wang (Reference He, Pan and Wang2013) in flow over a flat plate with a cylinder placed above it; the overshoot is much smaller in their case. The large velocity gradients ( $\text{d}U/\text{d}y$ ) near the wall and in the outer region, compared with the FST-alone case, are better seen in figure 14(b). The wall-normal location corresponding to the peak of negative $\text{d}U/\text{d}y$ is denoted by $y_{G}$ . The pressure drop caused by the mesh reduces the free-stream velocity by almost 30 % from $U_{\infty }=3$ to $2.1~\text{m}~\text{s}^{-1}$ , irrespective of its location. This reduction is similar to that in the roughness-induced transition discussed in § 3.1. The velocity overshoot increases rapidly as the mesh is moved from $y_{m}=2$ to 8 mm and then slowly for higher mesh location. The variation of $u_{rms}$ in figure 14(c) shows a large reduction of it by the mesh, compared with the FST-alone case, and the greatest reduction occurs when the mesh is close to the wall. For the mesh at $y_{m}>4~\text{mm}$ , the large value of $u_{rms}$ in the outer region is due to the large velocity gradient there. Moreover, for the mesh at $y_{m}\geqslant 4~\text{mm}$ , the peak $u_{rms}$ near the wall occurs at about the same wall-normal location. Therefore, on introduction of the mesh at $x_{m}=450~\text{mm}$ downstream of the leading edge, the location of peak $u_{rms}$ near the wall is not significantly altered when compared with the FST-alone case.

Figure 14.

Effect of a mesh on the boundary layer flow characteristics at $x=500~\text{mm}$ . (a) Mean velocity, (b) velocity gradient and (c) intensity of fluctuation. Symbols: ▪, G; ▫, G & LM02mm; △, G & LM04mm; ▿, G & LM08mm; ♢, G & LM12mm. Here, $y_{G}$ denotes the location of maximum negative $\text{d}U/\text{d}y$ .

Typical instantaneous PIV measurements depicting the effect of a mesh near the wall on FST-induced transitional flow at $x=500~\text{mm}$ are shown in figure 15. For the FST-alone case, figure 15(a) represents a typical breakdown scenario, similar to that reported by Mandal et al. (Reference Mandal, Venkatakrishnan and Dey2010). The clockwise vortex (white line) slightly above and to the right of an anticlockwise vortex (black line), and strong negative velocity fluctuations over the positive vorticity region in this figure are similar to those reported by Hladík, Jonáš & Uruba (Reference Hladík, Jonáš and Uruba2011) for a turbulent spot in a non-bypass (natural) type transitional flow. This is possibly expected as the breakdown via turbulent spots may be common in bypass, natural or controlled (by a vibrating ribbon, for example) transition. A similar relative arrangement of clockwise and anticlockwise vortices also prevails in turbulent flows (e.g. Wu & Christensen Reference Wu and Christensen2006; Natrajan, Wu & Christensen Reference Natrajan, Wu and Christensen2007). Compared with the FST-induced transition case in figure 15(a), the mesh at $y_{m}=2$ and 4 mm causes the negative spanwise vorticity and clockwise vortices to be confined very close to the wall, as shown in figures 15(b) and 15(c) respectively; the non-dimensional contours in these figures are based on the ${\it\delta}^{\ast }\,(=2.86~\text{mm})$ and $U_{\infty }\,(=3~\text{m}~\text{s}^{-1})$ values of the FST-alone case. Importantly, the inclined shear layers in figure 15(a) are now absent in the presence of a mesh, as was also seen earlier in figure 9(b), and the velocity fluctuation is also less. Almost 98 % of the instantaneous PIV measurements (in the case of a mesh at $y_{m}=2~\text{mm}$ ) were found to be identical to figure 15(b); however, being instantaneous, the fluctuating velocity vectors were not of the same sign. The anticlockwise vortices at $y/{\it\delta}^{\ast }\approx 1.4$ in figure 15(c) are those generated by the bottom edge of the mesh at $y_{m}=4~\text{mm}$ . The instantaneous velocity ( $U_{I}/U_{fs}$ ) profiles at ${\rm\Delta}x/{\it\delta}^{\ast }=-1.3$ in figure 15(a–c) are compared with the Blasius profile in figure 15(d–f); note that ${\it\delta}$ and $U_{fs}$ are the local values. These clearly show acceleration near the wall. Noting the absence of inclined high-shear layers in figure 15(b,c), the large reduction of $u_{rms}$ by the mesh at $y_{m}=2$ and 4 mm (figure 14 c) is due to the suppression of such shear layers and the associated transitional structure.

Figure 15.

Instantaneous spanwise vorticity contours in the wall-normal plane at $x=500~\text{mm}$ illustrating the effect of a mesh placed near the wall (b,c) on FST-induced transitional flow (a): (G (a); G & LM02mm $(y_{m}/{\it\delta}^{\ast }=0.7)$ (b); G & LM04mm $(y_{m}/{\it\delta}^{\ast }=1.4)$ (c)). The arrows are fluctuating velocity vectors of $u$ and $v$ , and the line contours represent the swirl strength (white line, clockwise vortex; black line, anticlockwise vortex). (d–f) Comparison of instantaneous velocity profiles at ${\rm\Delta}x/{\it\delta}^{\ast }=-1.3$ (in a–c) with the Blasius profile (——). Note that the inclined high-shear layers caused by FST alone (a) are absent due to LM in (b,c).

Figure 16.

Instantaneous spanwise vorticity contours in the wall-normal plane at $x=500~\text{mm}$ illustrating the effect of a mesh located away from the wall on FST-induced transitional flow: (a) G & LM08mm $(y_{m}/{\it\delta}^{\ast }=2.8)$ ; (b,c) G & LM12mm $(y_{m}/{\it\delta}^{\ast }=4.2)$ . The arrows are the fluctuating velocity vectors of $u$ and $v$ . The line contours represent the swirl strength (white line, clockwise vortex; black line, anticlockwise vortex). Note that shear layer is near the wall in (a,b) while it is inclined in (c).

Figure 16 shows some typical instantaneous PIV measurements in flows with the mesh away from the wall at $y_{m}=8$ and 12 mm; the non-dimensional contours in these figures are also based on the ${\it\delta}^{\ast }\,(=2.86~\text{mm})$ and $U_{\infty }\,(=3~\text{m}~\text{s}^{-1})$ values of the FST-alone case. We note that figures 16(b) and 16(c) are representative of two different events – a large shear near the wall and a lifted-up shear layer. Figure 16(a) shows that strong negative spanwise vorticity and clockwise vortices are confined close to the wall, similar to those in figures 15(b) (for $y_{m}=2~\text{mm}$ ) and 15(c) (for $y_{m}=4~\text{mm}$ ). The number of such PIV frames was found to decrease with increasing $y_{m}$ . For example, although similar instantaneous PIV measurements were found for the mesh at $y_{m}=12~\text{mm}$ (figure 16 b), the lifted-up shear layer (figure 16 c) and breakdown, similar to those for FST-induced transition (figure 15 a), were found to be greater; the only difference was the presence of anticlockwise vortices in the free stream. Figure 16(c) then suggests that the lift-up of the high-shear layer in FST-induced transition is not entirely suppressed by a mesh placed away from the wall even though it reduces the free-stream velocity by 30 % and accelerates the flow (figure 14 a). Consequently, the higher $u_{rms}$ inside the boundary layer in flow with the mesh at $y_{m}=12~\text{mm}$ (figure 14 c) is due to transitional flow that prevails there. Therefore, unless the lift-up is disturbed, as in the case of the mesh at $y_{m}=2$ and 4 mm, by manipulating the outer region, transition delay over a large downstream distance may not be possible, even with a reduced free-stream velocity and flow acceleration.

The hot-wire signals at $x=750~\text{mm}$ in figure 17 show the effect of the mesh at different $y_{m}$ locations; here, $e^{\prime }$ is the voltage fluctuation and $t$ is the time in seconds. These signals were taken at the wall-normal location corresponding to $u_{rms,max}$ . Figure 17(b) shows that the mesh at ( $x_{m}=450~\text{mm}$ and) $y_{m}=2~\text{mm}$ inhibits the high-frequency fluctuations seen in figure 17(a). In fact, figure 17(b) is a typical low-intermittency signal (between 0.15 to 0.25 s) associated with the passage of incipient turbulent spots. Thus, compared with the FST-alone case in figure 17(a), one finds that transition delay has been caused by the mesh at $y_{m}=2~\text{mm}$ . However, this does not occur for the mesh at $y_{m}>8~\text{mm}$ , and high-frequency fluctuations still persist (figure 17 d). The flow intermittency increases with increasing $y_{m}$ .

Figure 17.

Hot-wire signals at $x=750~\text{mm}$ showing the effect of a mesh at different wall-normal locations on FST-induced transition: (a) G; (b) G & LM02mm; (c) G & LM04mm; (d) G & LM12mm.

The mean flow characteristics in the boundary layer at $x=750~\text{mm}$ are shown in figure 18. Corresponding to the hot-wire signal in figure 17(a), the boundary layer velocity profile is compared with the $(1/7)$ th power law for turbulent flows in figure 18(a); $H\,(={\it\delta}^{\ast }/{\it\theta})$ denotes the shape factor. It can be seen that the flow due to FST is not fully turbulent yet. Figure 18(b) shows that, although the near-wall acceleration is reduced, the velocity overshoot persists even at $x=750~\text{mm}$ . Interestingly, the velocity profile corresponding to the hot-wire signal in figure 17(b) is a near-Blasius one, as shown in figure 18(c). That is, the mesh at $y_{m}=2~\text{mm}$ has caused a near relaminarization of the FST-induced transitional flow; this also reflects in lower fluctuation intensities in flows with the mesh at $y_{m}=2$ and 4 mm than the FST-alone case (figure 18 d), even 300 mm downstream of the mesh. This may be due to the fact that as the upper part of the transitional boundary layer is affected by the mesh, a rapid recovery of streamwise streaks is prevented, unlike in the control of streaks near the wall (e.g. Lundell Reference Lundell2007; Monokrousos et al. Reference Monokrousos, Brandt, Schlatter and Henningson2008). For the mesh at $y_{m}=12~\text{mm}$ , the peak $u_{rms}$ value is slightly greater than in the FST-alone case, possibly indicating a faster transition due to the increased disturbances in the outer region by the mesh.

Figure 18.

Mean flow characteristics at $x=750~\text{mm}$ . (a) Comparison of the boundary layer velocity profile with the $(1/7)$ th profile for turbulent flows. The measured profile corresponds to the hot-wire signal in figure 17(a). (b) Effect of a mesh on boundary layer velocity profiles. (c) Comparison of the measured boundary layer velocity profile corresponding to the hot-wire signal in figure 17(b) with the Blasius profile. (d) Effect of a mesh on the intensity of fluctuations. The symbols are as in figure 14.

Figure 19.

Effect of a mesh on the Reynolds stresses and turbulence production at $x=500~\text{mm}$ : (a) $\overline{uv}$ , (b) $-\overline{uv}\,\text{d}U/\text{d}y$ , (c) $\overline{vv}$ and (d) $-\overline{vv}\,\text{d}U/\text{d}y$ . The symbols are as in figure 14.

Along with a reduction of the free-stream velocity (figures 14 a and 18 b), transition delay caused by the mesh also reduces the integral length scales like ${\it\theta}$ and ${\it\delta}^{\ast }$ ; therefore, there is a reduction in the flow Reynolds number. Although we have not measured the skin friction, we consider the low-intermittency flow in figure 17(b), for the mesh at $y_{m}=2~\text{mm}$ , to infer the skin-friction coefficient, $C_{f}$ , using the transition zone model of Dhawan & Narasimha (Reference Dhawan and Narasimha1957). The skin friction in this linear combination model is, $C_{f}=C_{f,L}\,(1-{\it\gamma})+{\it\gamma}C_{f,T}$ , where the subscripts $L$ and $T$ denote the laminar and turbulent states respectively. For the hot-wire signal in figure 17(b), ${\it\gamma}\rightarrow 0$ . Thus, one expects a reduction in $C_{f}$ during the delay of transition by the mesh at $y_{m}=2~\text{mm}$ .

Figure 19 shows the effect of a mesh on the Reynolds stresses, $\overline{uv}$ , $\overline{vv}$ , and the turbulence production, $-\overline{uv}\,\text{d}U/\text{d}y$ , $-\overline{vv}\,\text{d}U/\text{d}y$ , at $x=500~\text{mm}$ . It can be seen that, compared with the FST-alone case (filled squares), a mesh reduces these quantities in the boundary layer, and the greatest reduction occurs with the mesh at $y_{m}=2~\text{mm}$ . As the mesh is moved away from the wall, Reynolds stresses and turbulence production increase considerably in the outer region due to the large velocity gradient there (see figure 14 b). The variations of these quantities in the wall and outer regions with increasing $y_{m}$ are similar to those for $u_{rms}$ , described above. Moreover, quadrant decomposition of the Reynolds shear stress (Wallace, Eckelmann & Brodkey Reference Wallace, Eckelmann and Brodkey1972) shows a reduction of this during $Q_{2}$ (ejection: $-u,~v$ ) and $Q_{4}$ (sweep: $u,~-v$ ) events, as shown in figures 20(b) and 20(d) respectively. For the FST-alone case, the peak value of $\overline{uv}$ in $Q_{2}$ is in the middle of the boundary layer, and it is close to the wall in $Q_{4}$ , as in Nolan, Walsh & McEligot (Reference Nolan, Walsh and McEligot2010); however, near the wall, $\overline{uv}$ in $Q_{3}$ is different from these authors. While the mesh at all $y_{m}$ locations reduces these events, the maximum reduction is again for the mesh at $y_{m}=2~\text{mm}$ . With increasing $y_{m}$ , Reynolds stresses in $Q_{1}~(u,v)$ and $Q_{3}~(-u,-v)$ increase rapidly in the outer region in the same way as in figure 19(a). The reduction in the turbulence production and Reynolds stresses by the mesh at $y_{m}=2~\text{mm}$ can be attributed to the absence of lifted-up low-speed streaks or interaction between inclined low- and high-speed streaks (figure 15 b) and the associated transitional events. On the other hand, the increased Reynolds shear stress in the boundary layer (during $Q_{2}$ and $Q_{4}$ events) with increasing $y_{m}$ is due to the prevailing transitional flows, as discussed earlier (in the context of figure 16).

Figure 20.

Effect of a mesh on the quadrant decomposed Reynolds shear stress at $x=500~\text{mm}$ : (a) $Q_{1}~(u,v)$ , (b) $Q_{2}$ (ejection: $-u,~v$ ), (c) $Q_{3}~(-u,-v)$ and (d) $Q_{4}$ (sweep: $u$ , $-v$ ). Lines: ——, G; $\cdots \cdots$ , G & LM02mm; - - - -, G & LM04mm; — ⋅ —, G & LM08mm; — — —, G & LM12mm.

Figure 21.

Fraction of PIV frames with negative (a) and positive (b) swirl strength at $x=500~\text{mm}$ . (c) Mean non-zero swirl strength.

In a turbulent boundary layer, hairpin vortices contribute to the Reynolds stresses (e.g. Ganapathisubramani, Longmire & Marusic Reference Ganapathisubramani, Longmire and Marusic2003; Tomkins & Adrian Reference Tomkins and Adrian2003; Guala, Hommema & Adrian Reference Guala, Hommema and Adrian2006). Here, a mesh is seen to reduce these stresses in the wall region and increase them in the outer region as it is moved away from the wall, along with a reduction of the free-stream velocity. Thus, it may be worthwhile to find out the effect of a mesh on the population of vortices in the boundary layer. Following Volino, Schultz & Flack (Reference Volino, Schultz and Flack2007), who compare smooth- and rough-wall turbulent boundary layers in terms of the swirl strength, such a quantification is shown in figure 21; for clarity, the two cases of mesh at $y_{m}=4$ and 12 mm are shown separately in figure 22. Here, of the total number of PIV frames acquired, those associated with only negative ( $N_{n}$ ) and positive ( $N_{p}$ ) swirl strength are counted separately at each wall-normal location at $x=500~\text{mm}$ , and are shown as a fraction of the total number of frames; ${\it\lambda}_{n}$ and ${\it\lambda}_{p}$ are the corresponding mean swirl strengths, and $\overline{{\it\lambda}}=({\it\lambda}_{n}N_{n}+{\it\lambda}_{p}N_{p})/(N_{n}+N_{p})$ . Figure 21(a) shows that the mesh at $y_{m}=4~\text{mm}$ reduces the number of PIV frames associated with negative swirl strength (i.e. the population of clockwise vortices) in the outer region and confines them to a very small region close to the wall, compared with the FST-alone case. In other words, clockwise vortices are confined close to the wall by the mesh at $y_{m}=4~\text{mm}$ , as also seen in figure 15(c). For $y_{m}>4~\text{mm}$ , although the number of such frames increases with increasing $y_{m}$ , it is still lower than the FST-alone case. This is due to the prevalence of transitional flows when the mesh is away from the wall. It is also interesting to note that $N_{n}$ is maximum (i.e. the highest population of clockwise vortices) near the wall at approximately $y=2~\text{mm}$ , irrespective of the type of flow; this location nearly corresponds to the maximum of $u_{rms}$ (see figure 14 c). This might be due to the absence of the leading-edge effect, as the mesh was placed downstream. Moreover, different mean velocity profiles caused by the mesh at $y_{m}\geqslant 4~\text{mm}$ do not seem to affect this near-wall result. In other words, the number of vortices with negative swirl strength seems to be almost fixed by the leading-edge effect arising from FST alone. Figure 21(b) shows that, while the number of PIV frames with positive swirl strength (i.e. the population of anticlockwise vortices) is negligible across the boundary layer for the FST-alone case, the effect of a mesh on $N_{p}$ appears only when it is away from the wall, as also observed in instantaneous PIV measurements in figures 15(c) and 16, and the maximum of such vortices occurs at approximately $y_{G}$ . A mesh in the region $4\leqslant y_{m}\leqslant 8~\text{mm}$ causes an increase in the number of these anticlockwise vortices before attaining an almost constant value. For $y_{m}\geqslant 8~\text{mm}$ , the fraction of PIV frames with positive swirl strength is more than those with negative swirl strength. Figure 21(c) shows the variation of the mean non-zero swirl strength ( $\overline{{\it\lambda}}$ ) across the boundary layer. Here again, the near-wall feature is the same, irrespective of the mesh location, and its change away from the wall is due to the positive swirl shown in figure 21(b). Thus, suppression of the lift-up of the high-shear layer (and associated transitional events) by the mesh when placed near the wall causes clockwise vortices to be confined to the wall region. Otherwise, apart from a small change in the clockwise vortices, the anticlockwise vortices formed at the bottom edge of the mesh become significant in the outer region.

Figure 22.

Fraction of PIV frames with positive and negative swirl strength at $x=500~\text{mm}$ for a mesh at $y_{m}=4~\text{mm}$ (a) and $y_{m}=12~\text{mm}$ (c). The corresponding products with their mean swirl strengths are shown in (b) and (d) respectively.

The p.d.f. plots of the normalized instantaneous $u$ fluctuations in figure 23 show the change in flow structure at $x=500~\text{mm}$ by the mesh. The non-dimensional quantities are based on the ${\it\delta}\,(=12~\text{mm})$ and $U_{\infty }\,(=3~\text{m}~\text{s}^{-1})$ values of the FST-alone case, for a meaningful comparison. The reduced spread of the p.d.f. across the boundary layer in figure 23(b), compared with the FST-alone case in figure 23(a), further confirms the transition delay caused by the mesh at $y_{m}=2~\text{mm}$ ; for the other mesh locations, decreased spread of the p.d.f. near the wall can be seen in figure 23(c–e). As $y_{m}$ increases, the negative p.d.f. region away from the wall also increases. This might be due to the lift-up of the high-shear layer not being entirely suppressed (figure 16). Two clear peaks in the p.d.f. appear near $y_{G}$ (indicated by a dashed line) for the mesh at $y_{m}=8$ and 12 mm; at $y_{G}$ , the maximum number of anticlockwise vortices (figure 21 b) and a second peak in $u_{rms}$ (figure 14 c) appear. As shown in figure 23(e), the line connecting two peaks near the wall and a similar line at $y_{G}$ are almost perpendicular to each other. From the direction of the inclination of these lines, one may infer from a p.d.f. plot itself whether clockwise or anticlockwise vortices are dominant at those locations.

Figure 23.

Probability density functions of the instantaneous streamwise velocity fluctuations at $x=500~\text{mm}$ for various mesh locations. The dashed line indicates the $y_{G}$ location: (a) G; (b) G & LM02mm; (c) G & LM04mm; (d) G & LM08mm; (e) G & LM12mm. The contour levels are as in figure 13.

In the relaminarization process of a turbulent boundary layer by a strong streamwise pressure gradient (Blackwelder & Kovasznay Reference Blackwelder and Kovasznay1972) and in near-wall control of FST-induced transition (Lundell Reference Lundell2007), the shape of the spanwise structure is not altered. This may not be so downstream of the mesh, as orderly streaks, similar to those in figure 5(b) for the roughness-induced transition, will occur. However, the streamwise structure in the wall-normal plane in FST-induced transition seems to be preserved even in the presence of a mesh, as indicated by the $R_{uu}$ contours at $x=500~\text{mm}$ in figure 24; correlation contours at two different reference locations (indicated by black dots) are shown in this figure. Although the mesh seems to distort the streamwise structure slightly when located close to the wall, its overall shape is largely unchanged. The mild increase in size and inclination of the streamwise structure with increasing $y_{m}$ (figure 24 c–e) might be due to the reduced effect of acceleration on transitional flow events. From the cross-correlation between ‘wall wire’ and streamwise velocity fluctuations, Lundell (Reference Lundell2007) reports that the size of the structure decreases mainly near the wall in control of an FST-induced transition, but the overall shape seems to remain similar. Elsewhere, Dixit & Ramesh (Reference Dixit and Ramesh2010) find that in a turbulent boundary layer subjected to high acceleration, the streamwise structure elongates with decreasing inclination towards the wall. However, the shape seems to be preserved in this case as well. In the case of a mesh at $y_{m}\geqslant 8~\text{mm}$ , the weak negative correlation region might be due to the interaction or presence of vortices of opposite sign. On the whole, the shape of the streamwise structure in the wall-normal plane is largely preserved even in the presence of a mesh, with possibly mild change in size and inclination, as in flows with a mesh in roughness-induced transition (figure 11).

Figure 24.

Contours of $R_{uu}$ at $x=500~\text{mm}$ : (a,f) G; (b,g) G & LM02mm; (c,h) G & LM04mm; (d,i) G & LM08mm; (e,j) G & LM12mm. The black dot indicates the reference location; note that the reference locations in (a–e) and ( f–j) are different.

Figure 25 shows the correlation of signed swirl strength with itself, $R_{{\it\lambda}{\it\lambda}}$ , and unsigned swirl strength with the wall-normal velocity fluctuation, $R_{{\it\lambda}v}$ , at $x=500~\text{mm}$ ; the reference location ( ${\rm\Delta}x=0$ , $y=y_{G}$ ) is indicated by an empty circle. Although such correlations in a turbulent boundary layer correspond to hairpin vortices (e.g. Christensen & Adrian Reference Christensen and Adrian2001; Volino et al. Reference Volino, Schultz and Flack2007), here they refer to vortices generated by the bottom edge of the mesh (see figures 15 c and 16). While the correlation contours of $R_{{\it\lambda}{\it\lambda}}$ compare the size of these vortices and separate the regions of clockwise and anticlockwise vortices in the entire measurement area, the $R_{{\it\lambda}v}$ correlation compares the spatial extent and strength of the velocity field associated with them. Figures 25(a) and 25(b) show $R_{{\it\lambda}{\it\lambda}}$ contours for the mesh at $y_{m}=4$ and 12 mm respectively, whereas figure 25(c) shows a comparison of its wall-normal variation at ${\rm\Delta}x=0$ for different $y_{m}$ . As only anticlockwise vortices are present at $y_{G}$ (figure 21), the regions associated with anticlockwise and clockwise vortices in these contour maps are indicated by positive and negative correlation values respectively. These show that the entire measurement region can be separated into two distinct regions of negative (near the wall) and positive (around $y_{G}$ ) swirl. The strong negative correlation region seen around $y=2~\text{mm}$ corresponds to the wall-normal location having the maximum number of vortices with negative swirl strength (figure 21 a). The larger positive correlation region ( $R_{{\it\lambda}{\it\lambda}}>0.4$ ) for $y_{m}=12~\text{mm}$ in figure 25(b) indicates a larger vortex than that for $y_{m}=4~\text{mm}$ (figure 25 a). Figure 25(c) also shows an increase in length of the positive and negative correlation regions with increasing $y_{m}$ . Figures 25(d) and 25(e) show $R_{{\it\lambda}v}$ contours for the mesh at $y_{m}=4$ and 12 mm respectively, while its streamwise variation at $y_{G}$ for different $y_{m}$ is shown in figure 25( f). The positive and negative correlation regions to the right and left of the reference location in these plots indicate the presence of an anticlockwise vortex. Similar correlation regions below and above the reference location were also seen in $R_{{\it\lambda}u}$ plots (not shown here). While the positive and negative correlation regions ( $R_{{\it\lambda}v}>\pm 0.1$ ) are small for $y_{m}=4~\text{mm}$ (figure 25 d), these are significant for $y_{m}=12~\text{mm}$ (figure 25 e). The weak correlation regions in figure 25(d) can be attributed to the fact that the mesh at $y_{m}=4~\text{mm}$ is partly inside the boundary layer and also to the smaller size (figure 25 a), strength (figure 21 c) and number (figure 21 b) of vortices, compared with the mesh at $y_{m}=12~\text{mm}$ . Figure 25( f) also shows maximum and minimum values of the correlation and their streamwise spacing increase with increasing $y_{m}$ . This indicates that the spatial extent and strength of the velocity field associated with the anticlockwise vortex increase as the mesh is moved away from the wall.

Figure 25.

Swirl correlations at $x=500~\text{mm}$ : (a,b) $R_{{\it\lambda}{\it\lambda}}$ contours; (d,e) $R_{{\it\lambda}v}$ contours. Wall-normal variation of $R_{{\it\lambda}{\it\lambda}}$ at ${\rm\Delta}x=0$ (c) and streamwise variation of $R_{{\it\lambda}v}$ at $y_{G}$ ( f) for different $y_{m}$ . The empty circle denotes the reference location ( ${\rm\Delta}x=0$ , $y=y_{G}$ ).

Figure 26.

The plane mixing layer feature in the outer region of the boundary layer at $x=500~\text{mm}$ for the mesh at $y_{m}=8$ (▿) and 12 (♢) mm. (a) Mean velocity. (b) Reynolds stress of the streamwise velocity fluctuations. Mixing layer data: ——, Rogers & Moser (Reference Rogers and Moser1994); ●, Loucks & Wallace (Reference Loucks and Wallace2012) for $\mathit{Re}_{{\it\theta}^{\ast }}=432$ .

As noted earlier, the mesh reduces the free-stream velocity and accelerates the boundary layer flow, even causing an overshoot when located away from the wall (figure 14 a). Now the mesh is expected to cause a mixing layer type discontinuity near its bottom edge, and this effect may continue downstream. It is found that, in flows with the mesh at $y_{m}=8$ and 12 mm, the mean velocity profile between the overshoot and free stream at $x=500~\text{mm}$ is of the plane mixing layer type reported by Rogers & Moser (Reference Rogers and Moser1994) and Loucks & Wallace (Reference Loucks and Wallace2012), as shown in figure 26(a). Here, following these authors, the similarity variables used are $U_{c}=(U_{p}+U_{l})/2$ and ${\rm\Delta}U=U_{p}-U_{l}$ ; $U_{p}$ is the peak velocity, and $U_{l}=U_{fs}$ ; ${\it\theta}^{\ast }=\int _{-(y_{l}-y_{c})}^{-(y_{p}-y_{c})}[(1/4)-((U-U_{c})/{\rm\Delta}U)^{2}]\,\text{d}y$ and ${\it\xi}=-(y-y_{c})/{\it\theta}^{\ast }$ ; $y_{c}=y(U=U_{c})$ , $y_{p}=y(U=U_{p})$ and $y_{l}=y(U=U_{l})$ ; ${\it\xi}$ is negative here due to the opposite sense of low- and high-speed fluids from those in Rogers & Moser (Reference Rogers and Moser1994) and Loucks & Wallace (Reference Loucks and Wallace2012). Similarly, the Reynolds stress, $\overline{uu}/{\rm\Delta}U^{2}$ , variation in this region also compares well with those reported by these authors (figure 26 b). This mixing layer feature could be the reason why vortices from the bottom edge of the mesh remain prominent downstream of $x_{m}=450~\text{mm}$ , as shown in figures 15(c) and 16. However, it should be noted that there was no wall effect in the studies of Rogers & Moser (Reference Rogers and Moser1994) and Loucks & Wallace (Reference Loucks and Wallace2012); in fact, the similarity seen here is only in the outer region of the boundary layer in the case of a mesh away from the wall. Moreover, the increase in peak Reynolds stress values (figures 19 and 26 b) and the strength of the vortex (figure 21 c) with increasing $y_{m}$ (and, equivalently, decreasing velocity ratio, $r=U_{l}/U_{p}=0.84$ –0.67) are in agreement with those reported by Wiecek & Mehta (Reference Wiecek and Mehta1998) for plane mixing layers. Thus, the vortices downstream of the mesh seen along $y_{m}$ in figures 15(c) and 16 possibly correspond to spanwise rollers (e.g. Bernal & Roshko Reference Bernal and Roshko1986; Rogers & Moser Reference Rogers and Moser1992).

Control of streaks near the wall in FST-induced transition may not inhibit rapid recovery of streaks downstream, as the outer region of the boundary layer is less affected (Monokrousos et al. Reference Monokrousos, Brandt, Schlatter and Henningson2008). On the other hand, the present study suggests that, if the inclined high-shear layer or its lift-up and the associated structures are suppressed/distorted, transitional streaks fail to recover over a large downstream distance. Now, a grid/screen is used either to break large vortices (at the inlet of a wind tunnel, for example) or in generating FST in many experimental studies. Here, disturbances from a mesh that is placed close to the wall are small, due to the small velocity gradient there, and are damped by viscosity. However, when it is away from the wall, disturbances from its bottom edge are large (figure 14 c) and may enhance transition of the flow under mild acceleration; that is, mild in the sense that the flow is not under an accelerating free stream.