2.1. Wind tunnel facility, swept wing model and surface irregularities

Experiments have been conducted at the atmospheric closed return low-turbulence tunnel (known as LTT) located at the Delft University of Technology. The wind tunnel features a contraction ratio of 17 : 1. The design and construction of the wind tunnel results in a low turbulence intensity level ($Tu = (1/U_\infty )\sqrt {(U'^{2} + V'^{2})/2} \leqslant 0.03\,\%$, single hot-wire measurement, bandpass filtered between 2 and 5000 Hz) at the nominal conditions employed in this study (Serpieri Reference Serpieri2018). All reported measurements were performed on the pressure side of the wing, for a fixed angle of attack of $\alpha = 3^{\circ }$ and a Reynolds number of $Re_{c_X} = 2.3 \times 10^{6}$, based on the free stream velocity ($U_\infty$) and the streamwise chord length ($c_X$). To be noted, the free stream velocity and corresponding Reynolds number used throughout the present work refer to a corrected wind tunnel velocity of $26.5 \ \textrm {m}\ \textrm {s}^{-1}$ based on a calibrated static pressure drop across the tunnel contraction. Due to blockage effects, the free stream velocity just upstream of the wind tunnel model was measured at $27.5 \ \textrm {m}\ \textrm {s}^{-1}$ using a Pitot-static tube.

The M3J swept wing model designed by Serpieri & Kotsonis (Reference Serpieri and Kotsonis2015), was installed in the wind tunnel octagonal test section ($2.6\ \textrm {m}\times 1.80\ \textrm {m}\times 1.25\ \textrm {m}$; $\textrm {length}\times \textrm {width}\times \textrm {height}$). Extensive research conducted on the development of CFI (Serpieri & Kotsonis Reference Serpieri and Kotsonis2015, Reference Serpieri and Kotsonis2016), boundary layer control (Serpieri et al. Reference Serpieri, Yadala Venkata and Kotsonis2017; Serpieri & Kotsonis Reference Serpieri and Kotsonis2018; Yadala et al. Reference Yadala, Hehner, Serpieri, Benard, Dörr, Kloker and Kotsonis2018) and surface irregularities (Rius-Vidales & Kotsonis Reference Rius-Vidales and Kotsonis2020) has shown that the combination of this wind tunnel and model offers the necessary conditions for the study of the development of stationary CFI and ensuing transition.

The swept wing model features a streamwise chord of $c_X = 1.27\ \textrm {m}$, a span of $b = 1.25\ \textrm {m}$ and a sweep angle of $45^{\circ }$. The airfoil shape, a modified symmetric NACA 66018 (figure 1a) is designed to enhance the amplification of CFI while suppressing TS waves, Görtler type instabilities and attachment line contamination as shown by Serpieri & Kotsonis (Reference Serpieri and Kotsonis2016) at mild angles of attack ($\alpha \approx 3^{\circ }$). Furthermore, during the experiments, considerable care was taken to ensure a consistent and polished surface near the leading edge, due to the extreme sensitivity of CFI to surface roughness. To this end, a Mitutoyo SJ-310 profilometer was used to examine the swept wing surface. The measured root mean square surface roughness is $R_{q} = 0.20\ \mathrm {\mu }\textrm {m}$.

Figure 1. Experimental set-up: (a) swept wing airfoil shape; (b) streamwise pressure coefficient distribution at two spanwise locations measured on the pressure side at $\alpha = 3^{\circ }$ and $Re_{c_X} = 2.3 \times 10^{6}$; (c) general schematic (flow direction from left to right $b = 1.25$ m) showing the FFS location, the IR analysis regions (IR-A, IR-B), planar PIV set-up and details of DRE.

The static pressure distribution on the model was measured using a multichannel scanner connected to two rows of 46 streamwise ($X$) oriented taps at $24\,\%$ and $76\,\%$ of the model span. At the nominal conditions of this study ($Re_{c_X} = 2.3 \times 10^{6},\alpha = 3^{\circ }$) the streamwise pressure distribution (pressure side of the wing) shows a favourable gradient up to $X/c_X \approx 0.65$ as shown in figure 1(b). The nearly invariant pressure along the span, in agreement with Serpieri & Kotsonis (Reference Serpieri and Kotsonis2016), confirms the adequacy of the infinite swept wing assumption for the boundary layer and stability calculations in the measurement region.

The steady and incompressible 2.5D (i.e. spanwise invariant infinite span conditions) laminar boundary layer equations are solved numerically for the pressure side of the model along the $x$ component (i.e. orthogonal to the leading edge, figure 1c) using the measured pressure distribution for a reference case with no surface irregularity and no artificial forcing of CFI. The stability of the calculated boundary layer is evaluated by solving the Orr–Sommerfeld equation using the spatial theory formulation, which is simplified by assuming a zero spanwise growth rate ($\beta _i$) due to the infinite swept wing assumption. Subsequently, the $N$-factor is calculated for a combination of a given spanwise wavelength ($\beta _r$) and frequency $\omega = 0$ (stationary) by integrating the spatial growth rate ($\alpha _i$) along the $x$-coordinate (Arnal & Casalis Reference Arnal and Casalis2000).

As summarised in the previous section, the main objective of the present study is to elucidate the interaction between an FFS irregularity and the incoming stationary CF vortices. However, the quest for experimentally simulating a representative scenario raises the question regarding which particular mode is more relevant. Several options are available; these entail focusing on the CFI mode most amplified (i.e. highest $N$) at the step location (Tufts et al. Reference Tufts, Reed, Crawford, Duncan and Saric2017; Rius-Vidales & Kotsonis Reference Rius-Vidales and Kotsonis2020), or the most unstable mode (i.e. highest growth rate) at the step. Another option is to investigate the overall most unstable mode (Tufts et al. Reference Tufts, Reed, Crawford, Duncan and Saric2017; Eppink Reference Eppink2020b). Considering the sensitivity of transition location to step height, the latter option can be further narrowed down to investigating the transition-inducing mode at clean conditions (i.e. no FFS). Following these considerations, the present work is indeed focusing on the transition-inducing mode at clean conditions. Preliminary stability analysis results at the tested conditions, identified a stationary CFI mode featuring a spanwise wavelength close to $\lambda _z = 7.5\ \textrm {mm}$ as the most amplified prior to transition and exhibiting a monotonic growth upstream and downstream of the step location ($x_h/c_x = 0.2$).

To study the impact of an FFS on this unstable stationary CFI mode, discrete roughness elements (DREs) are used (Reibert et al. Reference Reibert, Saric, Carrillo and Chapman1996; Saric, Carrillo & Reibert Reference Saric, Carrillo and Reibert1998; Serpieri & Kotsonis Reference Serpieri and Kotsonis2016) to force a single fundamental CFI mode featuring a nominal spanwise wavelength of $\lambda _{z,D} = 7.5\ \textrm {mm}$ in the vicinity of the leading edge. Motivated by a lack of experimental or numerical evidence pertaining to interaction of strongly amplified CFI with steps and in line with previous experiments (Rius-Vidales & Kotsonis Reference Rius-Vidales and Kotsonis2020), DREs with a relatively large nominal height of $k_D = 100 \ {\rm \mu}\textrm{m}$ and a diameter of $d_D = 2\ \textrm {mm}$ were manufactured in-house from an adhesive transfer vinyl film using a custom laser cutting system. The DREs were installed at $x_D/c_x = 0.02$, which is just upstream of the forced mode neutral point according to linear stability theory calculations.

Surface add-ons have been commonly used to create FFS surface irregularities on existing wind tunnel models (Holmes et al. Reference Holmes, Obara, Martin and Domack1985; Perraud & Seraudie Reference Perraud and Seraudie2000; Rius-Vidales et al. Reference Rius-Vidales, Kotsonis, Antunes and Cosin2018; Rius-Vidales & Kotsonis Reference Rius-Vidales and Kotsonis2020). Following a similar approach in this study, a polyethylene terephthalate (known as PET) foil is used to simulate a sharp edge FFS on the surface of the existing swept wing model. Foils of different thicknesses were cut to size using a CNC DCS 2500 Gerber machine, and each was installed on the model, as illustrated by the grey region in figure 1(c).

The resulting FFS step height was characterised in situ by traversing a Micro-Epsilon 2950-25 laser profilometer (reference resolution of $2\ {\mathrm {\mu }}\textrm {m}$) along $200\ \textrm {mm}$ of the spanwise extent of the surface irregularity, centred at midspan. Table 1 indicates the resulting average step height ($\bar {h}$), standard deviation ($\sigma _{h}$) and streamwise location ($x_{h}/c_x$) of the FFS surface irregularity for all tested configurations. As an indication of the relative size of the FFS inside the boundary layer flow, the displacement thickness ($\delta ^{*}_h$) is computed based on the aforementioned 2.5D numerical boundary layer solution for the streamwise velocity ($u$) at the nominal step location ($x_h/c_x = 0.2$). Similarly, from the linear stability theory analysis the estimated CF vortex core height ($y_c$) based on Tufts et al. (Reference Tufts, Reed, Crawford, Duncan and Saric2017) at the step location (indicated in table 1) is extracted from the $v$-perturbation eigenfunction corresponding to the CFI mode featuring the spanwise wavelength enforced by the DREs ($\lambda _{z,D}=7.5\ \textrm {mm}$).

Table 1. Geometrical parameters of tested configurations. For all cases the nominal DRE settings are: $\lambda _{z,D}=7.5\ \textrm {mm}$; $d_D = 2\ \textrm {mm}$; $k_{D} = 100\ \mathrm {\mu }\textrm {m}$; $x_{D}/c_x =0.02$.

Finally, two different coordinate systems are used throughout this study with their origin at the intersection between the leading edge and the wing midspan. As illustrated in figure 1(c), the first coordinate system spatial coordinates ($X, Y, Z$) and velocity components ($U, V, W$) are referenced according to the $X$-coordinate being parallel to the wind tunnel floor. On the second coordinate system, the spatial coordinates are given by ($x,y,z$) and the velocity components ($u,v,w$). In this case, the $x$-coordinate is perpendicular to the leading edge.

2.2. Measurement techniques

2.3. Boundary layer flow stability metrics

The changes in the stability of the CF vortices induced by the FFS are studied by analysing the streamwise evolution of the experimental spanwise steady disturbance profile based on the time-averaged planar PIV velocity measurements described in § 2.2.2.

The methodology described by White & Saric (Reference White and Saric2005) and Downs & White (Reference Downs and White2013) indicates that the experimental steady disturbance profile is equivalent to the spanwise root mean square ($\langle \rangle _z$) of the time-average perturbation, which for the spanwise component is given by $\langle \hat {w}(y)\rangle _z = (({1}/{n})\sum _{j=1}^{n}(w(y,z_j) - \bar {w}(y))^{2})^{1/2}$. Subsequently, the streamwise change in the steady disturbance can be determined by calculating the mathematical maximum of the profiles along the $y$-coordinate as $A_{M} = \max (\langle \hat {w}(y)\rangle _z)$.

It is important to note that according to perturbation analysis used in stability theory, the velocity perturbation ($w'$) should be calculated by subtracting a basic state or baseflow ($W$) to the mean velocity component ($w$). Hence, in this context, $\hat {w} \ne w'$ since the experimentally measured spanwise average $\bar {w}(y)$ corresponds to a mean-flow distorted flow and not to a baseflow. Nevertheless, this approach has been traditionally used as a metric to determine the growth and decay of CFI modes in experimental conditions and is accordingly followed in the present study as well.

3.1. Global influence of the FFS on transition location

The laminar–turbulent boundary layer transition location was determined for each configuration based on the camera IR-B surface thermal maps. The time-averaged thermal maps presented in figure 2(Ia) reveal a jagged transition front pattern which extends along the span of the wing. The nature of this jagged pattern has been traced to the breakdown process typical of stationary CF vortices (Dagenhart et al. Reference Dagenhart, Stack, Saric and Mousseux1989; Bippes Reference Bippes1999; Saric et al. Reference Saric, Reed and White2003; Downs & White Reference Downs and White2013). As the stationary CF vortices saturate, a rapidly growing secondary instability leads to a local breakdown of the CF vortices characterised by contiguous turbulent wedges forming along the span creating the so-called ‘jagged’ or ‘sawtooth’ transition front pattern. Therefore, the appearance of this pattern indicates the dominance of stationary CFI modes over travelling modes. In contrast, when the latter dominate, a more smooth (i.e. non-wedged) time-average transition front is observed due to the movement of CF vortices along the span.

Figure 2. The IR-B thermal maps (flow from left to right) displaying the effect of an FFS (orange line) on the transition front pattern, dashed white line indicates transition linear fit and ($\bullet$) marks its projection to the mid-domain of the measurement: (Ia) clean; (Ib) $A_3$; (IIa) $B_3$; (IIb) $C_3$; (IIIa) $D_3$.

The transition front location and variance along the span is identified from the surface thermal maps of camera IR-B following the DIT technique mentioned in § 2.2.1 and employed in Rius-Vidales & Kotsonis (Reference Rius-Vidales and Kotsonis2020). It is particularly noteworthy that the linear fit of the identified transition front locations (white dashed line in figure 2Ia) forms an angle with the leading edge, which reduces with increasing step height. This behaviour is related to the non-uniform wind tunnel blockage along the height of the wind tunnel (i.e. along the $Z$-direction in figure 1c) which leads to slightly stronger favourable pressure gradients near the outboard side of the wing. Consequently, to quantify the effect of the FFS height the transition location is extracted from the linear fit at the middle of the measurement domain ($\bullet$ marker in figure 2Ia). The results presented in figure 3 show that for the clean configuration (table 1) laminar-turbulent transition occurs at $x_t/c_x \approx 0.42$ (solid black line in figure 3a).

Figure 3. Transition location: (a) fixed step ($x_{h}/c_x = 0.2$) location for different FFS; (b) variation of the step location ($0.15\leqslant x_{h}/c_x \leqslant 0.225$) for small FFS ($A$).

The addition of a moderate FFS ($B_3$ and $C_3$ in figure 3a) results in a critical regime behaviour, as the boundary layer transition front shifts upstream of the clean configuration as illustrated in figure 2(IIa–IIb). A further increase in step height ($D_3$) leads to a supercritical regime behaviour with a substantial reduction in the extent of laminar flow as shown in figure 2(IIIa). These results indicate a gradual degradation of the laminar flow with increasing step height analogous to the behaviour observed by Crawford et al. (Reference Crawford, Duncan, Tufts, Saric and Reed2015a) and Rius-Vidales & Kotsonis (Reference Rius-Vidales and Kotsonis2020), and somewhat different to the one presented in Duncan et al. (Reference Duncan, Crawford, Tufts, Saric and Reed2014a) and Eppink (Reference Eppink2020b) which showed that with increasing step height the transition location more abruptly shifts towards the FFS location.

An important note must be made regarding the use of the terms critical and supercritical, which vary significantly in previous works on roughness effects on transition. Throughout the present study, the term critical is assigned to cases in which the step has an identifiable effect on transition location, while the term supercritical refers to cases in which transition location is very near or at the step location. A supercritical behaviour essentially denotes flow ‘tripping’ due to the step. Therefore, the critical step height definition used in this work is compatible with the one presented in Tufts et al. (Reference Tufts, Reed, Crawford, Duncan and Saric2017).

Notwithstanding the general adverse effects of an increasingly high FFS on transition, it is remarkable to note that a new transition behaviour is revealed when adding a small FFS ($A_3$ in figure 3a,b) at these conditions. Counter-intuitively, the addition of the FFS results in a favourable effect as transition postponement is observed instead of advancement. At first glance, this unexpected result is in disagreement with most of previous experimental or numerical observations on surface irregularities, and common wisdom alike. However, observations recently presented by Ivanov & Mischenko (Reference Ivanov and Mischenko2019) based on the concept presented by Ustinov & Ivanov (Reference Ustinov and Ivanov2018) suggested a transition delay effect under the influence of rectangular (i.e. FFS followed by a BFS) surface reliefs. Nonetheless, regarding surface irregularities in the form of only FFS the behaviour observed in this work contrast with previous studies (Perraud & Seraudie Reference Perraud and Seraudie2000; Duncan et al. Reference Duncan, Crawford, Tufts, Saric and Reed2014a; Crawford et al. Reference Crawford, Duncan, West and Saric2015b; Saeed et al. Reference Saeed, Mughal and Morrison2016; Eppink Reference Eppink2017; Tufts et al. Reference Tufts, Reed, Crawford, Duncan and Saric2017; Eppink Reference Eppink2018; Rius-Vidales et al. Reference Rius-Vidales, Kotsonis, Antunes and Cosin2018; Eppink & Casper Reference Eppink and Casper2019; Eppink Reference Eppink2020a,Reference Eppinkb), as to the best of the authors’ knowledge the present case is the first report of a transition delay in a boundary layer dominated by CFI in the presence of an FFS.

Given the novelty of this result and the potential such delay behaviour can offer in a LFC strategy, three additional configurations ($A_{1,2,4}$, table 1) have been tested. The objective of such variation was to exclude random and systematic measurement errors that might bias the result, as well as to establish a range of governing parameters for which the transition delay effect is observed. Figure 3(b), shows the effect of varying the streamwise position of this small FFS ($A$) on the laminar–turbulent boundary layer transition. When the FFS is located at the most upstream location $A_1$ a slight transition advancement is measured. However, as the FFS is translated downstream the detrimental effect of the step reduces for the case $A_2$ until a clear transition delay effect is observed for the position of case $A_3$ ($x_{t,{Clean}}/c_x - x_{t,A_3}/c_x = -0.038$). The consistent behaviour of transition location with the location of the step further confirms the validity and physicality of the transition delay effect. Nevertheless, the non-monotonic trend and rather narrow range of streamwise FFS locations for which the transition delay effect is observed points to the existence of possibly conflicting mechanisms governing the observed transition location.

Towards further probing the effect, a subtraction of thermal maps pertaining to the $A_{1-4}$ FFS positioned at several streamwise locations from the thermal map of the clean case ($\Delta I_{A_{1-4}} = I_{{Clean}} - I_{A_{1-4}}$) for these conditions are shown in figure 4. The subtracted thermal maps confirm that the transition delay (dark regions) is not a localised or outlier-dominated effect but occurs over a considerable spanwise extent of the measurement region. Note that the differences in the delay effect on the outboard and inboard section of the wing are again related to the non-uniform blockage along the height of the wind tunnel (i.e. $Z$-direction figure 1c).

Figure 4. The IR-B differential thermal maps (flow from left to right) displaying transition advance and postponement effects by FFS $A$ (orange line): (Ia) $\Delta I_{A_1}$; (Ib) $\Delta I_{A_2}$; (IIa) $\Delta I_{A_3}$; (IIb) $\Delta I_{A_4}$.

The global behaviour of transition location with varying FFS height highlights the intricate flow dynamics, which results from the interaction between the FFS and the CF vortices, necessitating high-resolution velocity measurements for further analysis. Notwithstanding the present observations, caution needs to be exercised when interpreting or generalising these results since, in addition to local parameters (i.e. step height, boundary layer displacement thickness and CF vortex core height) the influence of the FFS also depends on the stability characteristics of the incoming CFI mode (Rius-Vidales & Kotsonis Reference Rius-Vidales and Kotsonis2020).

3.2. Local influence of the FFS on the organisation of the CF vortices

The thermal maps of camera IR-A (figure 1c) provide a more detailed visualisation near the step region by showing the thermal footprint of the CF vortices on the surface of the wing model as alternating streaks of high (i.e. lighter) and low (i.e. darker) temperature as presented in figure 5(Ia). This particular temperature distribution originates from a variation in the heat transfer of the near-wall fluid due to a change in the magnitude of local skin friction coefficient induced by the high and low shear regions on the baseflow modulated by the CF vortices. Therefore, the local influence of the FFS on the CF vortex thermal footprint is evaluated by calculating the spatial PSD, as indicated in § 2.2.1, from a series of spanwise ($z$-direction) temperature profiles extracted at different streamwise locations.

Figure 5. Comparison of IR-A thermal maps (I and III, flow from left to right) and spatial PSD analysis (II and IV, 20 levels of $\ln (P/\bar {P}_{max_z})$ from $-3$ to 1): (Ia–IIa) clean; (Ib–IIb) $A_3$; (Ic–IIc) $B_3$; (IIIa–IVa) $C_3$; (IIIb–IVb) $D_3$; (IIIc) CF vortices trajectories; (IVc) change in CF vortices trajectory due to FFS. (Here $\lambda _{z,D} = 7.5 \ \textrm {mm}$).

The results for the clean configuration in figure 5(IIa), identify a series of CF vortices monotonically spaced at the spanwise wavelength of the forcing DREs ($\lambda _{z}/\lambda _{z,D} = 1$, $\lambda _{z,D} = 7.5\ \textrm {mm}$) for the entire measurement region. Upon the addition of a small FFS ($A_3$, figure 5IIb) a clear peak at the forced wavelength is observed at the step location ($x_h/c_x = 0.2$ and $\lambda _{z}/\lambda _{z,D} = 1$). In addition, a second peak centred at the wavelength of the forced mode first harmonic ($\lambda _{z}/\lambda _{z,D} = 0.5$) at the step location is also present. This behaviour occurs in all step cases in figures 5(IIb–IIc,IVa–IVb) and is in agreement with Eppink (Reference Eppink2020b) where an amplification of the harmonics of the primary CFI mode has been reported near the FFS.

A close inspection of the thermal maps for the small ($A_3$) and moderate ($B_3$) FFS (figure 5IIb–IIc), reveal a non-monotonic amplification pattern which develops along the $x$-direction downstream of the FFS step edge at the wavelength of the primary CFI mode ($\lambda _{z}/\lambda _{z,D} = 1$). This non-monotonic pattern corresponds to the observations by Eppink & Casper (Reference Eppink and Casper2019) and Eppink (Reference Eppink2020b) where it was found that as the CF vortices interact with the step they experience a first region of strong amplification, followed by an equally strong reduction and a second region of amplification thus creating a growth–decay–growth pattern of the CF vortices. The first maximum in intensity is located close to the step for all cases, while the first minimum and second maximum move closer to the step with increasing step height. Here, it is important to note that for cases $C_3$ and $D_3$, a different mechanism is responsible for the appearance of the second maxima. More specifically, in these cases, laminar–turbulent transition occurs within the measurement domain. The pattern of the transition reveals spanwise modulations at the same wavelength as the forced CF vortices. At breakdown, the increased thermal contrast between adjacent laminar and turbulent regions effectively produces the observed second maxima. Therefore, the analysis of the non-monotonic pattern is restricted exclusively to the cases $A_3$ and $B_3$ for which the boundary layer flow remains in a laminar condition for the entire measurement region. In addition, it must be stressed here that although the IR imaging has been performed in radiometric conditions (i.e. surface temperature is measured), the non-uniformity of irradiated energy from the halogen lamps as well as the varying curvature and thermal conductivity of the wing model do not allow for direct extraction of the surface heat transfer coefficient. Nevertheless, the narrow field of view of IR-A largely mitigates these effects allowing for a qualitative estimation of the amplitude of spanwise modulations in the near-wall shear around the step. In order to draw conclusions on the origin of this behaviour in the thermal maps, quantitative velocity measurements are essential, as described in the following sections.

The spatial spectral analysis employed here can be further exploited to gain insight into the organisation of the incoming CF vortices near the step. As previously discussed, the thermal maps are representative of the local magnitude of the skin friction coefficient, which in turn is related to the local velocity shear near the wall. In the cases discussed above, the flow near the step is predominantly laminar and is being actively heated. As such, regions of high temperature (i.e. brighter colour) represent low shear areas and vice versa. The characteristic streaky pattern is then qualitatively correlated with the modulation of the laminar boundary layer typical of stationary CFI. Based on the aforementioned, by unwrapping the spectral phase angle ($\phi$) of successive (in streamwise direction) temperature profiles, a reconstruction of the trajectory ($d_z$) of the coherent structures near the wing surface can be inferred.

Figure 5(Ia) presents for the clean configuration a comparison of the trajectory of the CF vortices (solid black line) with a reference line (dashed black line) featuring a streamline angle of $\varPsi ^{*} = 45^{\circ }$ (i.e. parallel to streamwise $X$-direction). The results indicate that the axis of the CF vortices is slightly tilted towards the inboard side of the wing resulting in a near-wall streamline angle of approximately $\bar {\varPsi }_{w}^{*} = 42.6^{\circ }$, which closely matches the one predicted by linear stability theory $\bar {\varPsi }_{LST}^{*} = 41.2^{\circ }$ (dash–dotted line in figure 5Ia). This behaviour is in agreement with previous experiments by Serpieri & Kotsonis (Reference Serpieri and Kotsonis2016) which for similar conditions showed that the inclination of the near-wall streamline differs also by a few degrees from the streamwise $X$-direction in the measurement region.

The collected trajectories for all cases are presented in figure 5(IIIc). As a reference for all cases, the clean configuration is given as a solid black line. Evidently, the interaction with the FFS results in a modification of the trajectory of the CF vortices given by the colour-coded lines. Figure 5(IVc), shows the relative trajectory changes ($\varDelta _z = d_{z,SI} - d_{z,C}$) between the clean ($d_{z,C}$) and the FFS ($d_{z,SI}$) cases. For the small FFS case ($A_3$), as the vortices reach the FFS, their trajectory strongly curves towards the outboard side of the wing (i.e. positive $z$ direction). Shortly downstream of the step edge, the trajectory shows a very sharp turn towards the inboard side of the wing (i.e. negative $z$ direction) before bending outboard again and relaxing to a direction almost parallel to the trajectory pertaining the clean configuration. Qualitatively, the observed behaviour is similar for all the tested FFS cases, albeit intensifying with increasing step height. A similar behaviour has been reported by Eppink (Reference Eppink2018) when analysing the inviscid and near wall streamlines. In addition, Eppink (Reference Eppink2018) showed that near the FFS the bending of the near-wall streamline is more pronounced than the one experienced by the inviscid streamline.

The outboard–inboard–outboard trajectory near the step can be traced to a local modification of the pressure gradient by the FFS. Numerical simulations by Tufts et al. (Reference Tufts, Reed, Crawford, Duncan and Saric2017) and experimental measurements by Duncan et al. (Reference Duncan, Crawford, Tufts, Saric and Reed2014a) showed that the addition of an FFS results in strong modification of the pressure gradient near the step. Hence, as the laminar boundary layer and developing CF vortices approach the step, they will first encounter an adverse pressure gradient upstream of the step, followed by a localised favourable pressure gradient at the step position and a second region of adverse pressure gradient as the flow recovers downstream of the step. The influence of the FFS on the near-step development and the modification to the structure of the CF vortices will be further analysed in § 4.

4.1. Impact of the FFS on the spanwise-averaged flow

As discussed in the previous section, the numerical simulations by Tufts et al. (Reference Tufts, Reed, Crawford, Duncan and Saric2017) and experimental measurements by Duncan et al. (Reference Duncan, Crawford, Tufts, Saric and Reed2014a) indicate that the addition of the FFS results in a local modification of the pressure field which results in strong regions of adverse and favourable pressure gradient. In this work, limitations on the experimental set-up (figure 1) restrict the static pressure measurements to the clean configuration. Nevertheless, the effects of the pressure gradient near the step are well captured in the change of the near-wall flow trajectories (figure 5IIIc,IVc) and the streamwise evolution of the boundary layer investigated using PIV measurements of the spanwise ($w$) and vertical ($v$) velocity components presented in this section.

The velocity measurements are conducted in $z - y$ planes (i.e. parallel to the leading edge and normal to the wing surface, figure 1) at various $x/c_x$ stations. The mean flow $\bar {w}_z$ and $\bar {v}_z$ is calculated by averaging the time-average velocity components along the spanwise direction at each $x/c_x$ station. Note, that based on the experimental set-up (see figure 1c) a positive $\bar {w}_z$ value indicates an average outboard (i.e. from the root towards the tip of the wing) flow movement. For clarity, the vertical $y^{*}$-coordinate is referenced to the clean baseline model surface, while the $y$-coordinate offsets the step height at its location. In addition, the vertical coordinates are non-dimensionalised with the displacement thickness $\delta ^{*}_{w,r} = 514\ {\mathrm {\mu }}\textrm {m}$, extracted from the $w$ spanwise velocity PIV measurements at the most upstream plane ($x/c_x = 0.176$) for the clean baseline case.

A comparison of the FFS cases with the clean configuration at selected stations (figure 6) reconciles the existence of an adverse pressure gradient upstream of the step which causes a deceleration in the boundary layer flow and a reduction in the spanwise $\bar {w}_z$ average velocity component (figure 6Ib). This effect intensifies as the step height increases, and results in growth of the boundary layer displacement ($\delta ^{*}_{w}$) and momentum ($\theta _w$) thickness upstream of the FFS location, as shown in figure 6(c). Conversely, due to the favourable pressure gradient downstream of the FFS edge at $x/c_x = 0.204$ (figure 6IIa) there is an acceleration of the boundary layer flow which leads to a reduction in $\delta ^{*}_{w}$ and $\theta _w$. Farther downstream, at $x/c_x = 0.239$ (figure 6IIb), the velocity profiles collapse to the clean baseline condition except for the case $D_3$ (i.e. highest FFS), not shown in the figure since it transitions to turbulent flow around $x_t/c_x \approx 0.22$ (figure 3a).

Figure 6. Selected profiles of spanwise mean flow velocity $\bar {w}_z$ (a,b) upstream and downstream of the FFS and (c) boundary layer properties (Here $\delta ^{*}_{w,r} = 514\ \mathrm {\mu }\textrm {m}$). The dashed black line in (a) and (b) denotes the numerical boundary layer solution calculated from the pressure distribution in the clean configuration.

Experimental observations by Eppink (Reference Eppink2020b) in the streamline-oriented reference frame, indicate a decrease in the velocity component tangent to the streamline ($u_s$) and a decrease in the CF component ($w_s$) upstream of the FFS, which leads to a strong reversal of the CF velocity profile. These observations are in agreement with the near-wall trajectories presented in figure 5(IIIc,IVc), which shows that an outboard spanwise motion occurs upstream of the FFS. In the present work, it becomes evident that the face of the FFS forms the equivalent of an attachment line. As expected, due to the sharp FFS geometry near the step location, the incoming boundary layer experiences a deceleration in $\bar {u}_z$. Although no surface irregularity or pressure gradient can form in the $z$ direction, the modification of $\bar {u}_z$ directly couples to changes of $\bar {w}_z$, through momentum coupling. As such, a strong conversion of wall tangent velocity components (explicitly $\bar {u}_z$ and by consequence $\bar {w}_z$) into a wall normal velocity component ($\bar {v}_z$) is occurring. Evidence of this behaviour is shown in figure 7(IIa–IIe) in which all FFS cases lead to a considerable increase in the spanwise-averaged time-averaged vertical velocity $\bar {v}_z$ at the step. For the highest FFS case $D_3$, the maximum vertical velocity reaches a value of approximately 10 per cent of the external spanwise velocity. These results are in agreement with Eppink (Reference Eppink2020b) where similar levels of amplification are reported. This rigorous upward flow movement by the FFS which affects the boundary layer flow will be analysed in more detail on the following sections.

Figure 7. Contours of spanwise mean flow velocity (flow direction from left to right) $\bar {w}_z$ (I) and $\bar {v}_z$ (II): (a) clean; (b) $A_3$; (c) $B_3$; (d) $C_3$; (e) $D_3$. The solid black line denotes $\delta _{99,w}$ (Here $\delta ^{*}_{w,r} = 514\ \mathrm {\mu }\textrm {m}$).

4.2. Impact of the FFS on the time-averaged total flow

As elaborated in § 2.1, the investigation of the influence of an FFS on the development and breakdown of CFI is facilitated using DREs near the leading edge to condition the wavelength and amplitude of the disturbances. This conditioning allows for a highly periodic and uniform amplitude distribution for the ensuing CF vortices (figure 5), which further facilitates the extraction of pertinent information from the velocity fields in terms of spanwise spectral modes.

More specifically, for the analysis of the PIV measurements, the time-average and standard deviation of the velocity components have been spatially filtered using Fourier transformations. As indicated on the diagram in figure 8, at each wall-normal position in the measurement plane, a fast Fourier transform (FFT) has been applied on extracted velocity profiles along the $z$-direction. Subsequently, a pertinent set of Fourier modes are selected to reconstruct the velocity through the inverse fast Fourier transform (IFFT). In addition to enhancing the velocity fields by reducing the measurement noise (which typically appears at small wavelengths), this technique offers the possibility to isolate the effect of the FFS on a particular harmonic of the CFI mode. Hence, for the remainder of the analysis, the reconstructed velocity fields (subscript $R$) are used unless otherwise noted. Moreover, the notation $m(0,n)$ (Bippes Reference Bippes1999; Wassermann & Kloker Reference Wassermann and Kloker2002) is used to indicate the Fourier modes used during the reconstruction. Note that the first index in parenthesis corresponds to the frequency of the mode, which for the present study is zero, and indicates a stationary CFI mode while the second index ($n$) denotes multiples of the spanwise wavenumber of the CF vortices forced by the DRE. In addition, when indicated by the summation convention ($\sum ^{5}_n m(0,n$)), the velocity fields have been partially reconstructed using the wavelengths contained between the primary force CFI mode ($\lambda _{z,D} = 7.5\ \textrm {mm}$) and its fifth harmonic ($\lambda _{z,D} = 1.5\ \textrm {mm}$).

Figure 8. Schematic of spatial filtering of time-averaged spanwise velocity $w$ contours (10 levels from 0 to 1, $z^*$ positive direction outboard) for the clean case: (a) original velocity field; (b) spectral decomposition; (c) reconstructed velocity field.

Figures 9 and 10 show the reconstructed fields for the spanwise ($\bar {w}_{R}$) and vertical ($\bar {v}_{R}$) time-average velocity, respectively, for the clean and FFS cases at selected locations upstream and downstream of the step. Note that the $z^{*}$-coordinate features a shift with respect to the $z$-coordinate origin such that the CF vortices align between presented streamwise stations. In the clean configuration, the spanwise velocity contours $\bar {w}_{R}$ presented in figure 9(Ia), show a pair of stationary corotating vortices. These stationary vortices are evenly spaced at the forced wavelength ($\lambda _{z,D} = 7.5\ \textrm {mm}$) for the entire measurement region as shown by the spatial spectral analysis on the thermal maps presented in figure 5(IIa). These CF vortices develop inside the boundary layer, where they transfer high momentum flow towards the wall (downwelling region, $\oplus$ in figure 9Ia) and low momentum flow away from it (upwelling region, $\ominus$ in figure 9Ia). As these structures evolve downstream, their amplitude and inherent distortion they impart on the mean flow increases (Wassermann & Kloker Reference Wassermann and Kloker2002; White & Saric Reference White and Saric2005; Downs & White Reference Downs and White2013). For the condition under study, the initial amplitude provided by the DREs results in a set of nonlinearly amplified vortices when reaching the step location.

Figure 9. Contours of time-averaged spanwise velocity ($z^*$ positive direction outboard), spatially filtered between $\sum ^{5}_n m(0,n)$: (a) clean; (b) $A_3$; (c) $C_3$; (d) change in trajectory of the CF vortices due to the FFS. The solid black line denotes $\delta _{99,w}$ (Here $\delta ^{*}_{w,r} = 514\ \mathrm {\mu }\textrm {m}$ and $\lambda _{z,D} = 7.5\ \mathrm {\mu }\textrm {m}$).

Figure 10. Contours of time-averaged vertical velocity and spanwise velocity (grey line 10 levels from 0 to 1) $z$ positive direction outboard, spatially filtered between $\sum ^{5}_n m(0,n)$: (a) clean; (b) $A_3$; (c) $C_3$; (d) $D_3$. (Here $\delta ^{*}_{w,r} = 514\ \mathrm {\mu }\textrm {m}$ and $\lambda _{z,D} = 7.5\ \mathrm {\mu }\textrm {m}$).

The interaction of the stationary CF vortices with the FFS results in topological modifications within the boundary layer as shown in figure 9. As the CF vortices reach the FFS ($x/c_x = 0.196$, figure 9Ib–Ic) there is an evident increase of the transfer of low momentum flow away from the wall (i.e. upwelling region). This corresponds well with the general upward deflection and streamwise deceleration of the incoming flow evident in figures 6 and 7, as well as the observations of Eppink (Reference Eppink2020b) which indicate an amplification of the vertical velocity component near the FFS. At the same streamwise location, the vertical velocity contours ($\bar {v}_R$) in figure 10(Ib–Ic) indicate a strong increase, especially on the inner section of the upwelling region. Henceforth, the overall increase of vertical velocity at the step location is suggestive of the underlying amplification of the instabilities as a result of the flow modifications incurred by the step.

The near-wall structures trajectory identified in § 3 revealed an outboard–inboard– outboard motion near the wall. In contrast to IR imaging, the PIV measurements facilitate the inspection of this flow deflection away from the wall. Specifically, profiles of spanwise velocity perturbation ($\hat {w}_R$) are extracted along the $z$-direction at the height of the stationary disturbance profile maxima (calculated as described in § 2.3) for each measurement plane. Successive spanwise profiles are compared using a vector convolution (i.e. cross-correlation). The result of this analysis is referenced to the most upstream measurement plane and yields the relative location ($d_z$) along the $z$-direction assumed by the CF vortices as they evolve downstream. Figure 9(d) shows the relative change of trajectory ($\varDelta _z = \textrm {d}z_{SI} - \textrm {d}z_{C}$) between the FFS cases ($\textrm {d}z_{SI}$) and the clean configuration ($\textrm {d}z_{C}$), confirming that the outboard–inboard–outboard motion described by the near-wall trajectory also occurs away from the wall, in proportional intensity to the FFS height.

Eppink (Reference Eppink2018) reported an abrupt change of the near-wall streamline angle as the boundary layer flow intercepts the FFS. Henceforth, to evaluate the spanwise motion effect as a function of the distance from the wall, figure 11(Ia–IIb) shows a set of wall-parallel $\overline {w_R}$ and $\overline {v_R}$ planes extracted away from the wall ($400\ \mathrm {\mu }\textrm {m}$ above the height of the stationary disturbance profile maxima). The dashed lines in figure 11(c) indicate the relative shift ($\varDelta _z$) along the $z$ direction calculated for each configuration. Additionally, wall-parallel planes extracted at a vertical location closer to the wall ($200\ \mathrm {\mu }\textrm {m}$ below the height of the stationary disturbance profile maxima) are presented in figure 11(IIIa–IVb) with $\varDelta _z$ in figure 11(d). A comparison of the $\varDelta _z$ above and below (figure 11c,d) the stationary disturbance profile maxima confirm that the outboard–inboard–outboard motion intensifies closer to the wall.

Figure 11. Wall-parallel contour maps of time-averaged spanwise and vertical velocity spatially filtered between $\sum ^{5}_n m(0,n)$. The contours in rows I and II are extracted at $400\ \mathrm {\mu }\textrm {m}$ above the height of the steady perturbation maxima ($y_{A_M}$), while the contours in rows III and IV are extracted closer to the wall at $200\ {\mathrm {\mu }}\textrm {m}$ below $y_{A_M}$: (I,III) clean case; (II,IV) $C_3$ case; and panels (c,d) the corresponding relative change of trajectory ($\varDelta _z = \textrm {d}z_{SI} - \textrm {d}z_{C}$).

Summarising up to this point, the observed influence of the FFS on the developing boundary layer reveal topological changes in both spanwise averaged flow as well as stationary CF vortices. As the incoming flow approaches the step, a strong outboard–inboard–outboard spanwise motion of the CF vortices is evident. This reflects the non-monotonic changes in pressure imposed by the step (Duncan et al. Reference Duncan, Crawford, Tufts, Saric and Reed2014a; Tufts et al. Reference Tufts, Reed, Crawford, Duncan and Saric2017). This effect is stronger near the wall, where the deceleration in the base flow is larger. Consequentially, an intense ejection of vertical velocity is documented at the vicinity of the step in agreement with Eppink (Reference Eppink2020b), resulting from the upward deflection of incoming wall-tangent flow as the latter engages with the step. The role of the spanwise motion on the overall transition scenario cannot be conclusively inferred by the presented measurements. However, potential candidate mechanisms can be proposed. A simple interpretation of this motion can be traced simply on the underlying changes of the base flow, which in turn can lead to modifications of the wavenumber vector of an incoming instability. A different effect could be the potential appearance of non-modal effects, in a mechanism similar to the well known lift-up effect (Landahl Reference Landahl1980; Marxen et al. Reference Marxen, Lang, Rist, Levin and Henningson2009; Brandt Reference Brandt2014) active in regions of strong shear changes. Notwithstanding the active mechanism, the relation between the outboard–inboard–outboard motion and the growth of the instability remains a point of interest. To elucidate this, fully three-dimensional velocity measurements or detailed numerical simulations of these flows are deemed necessary.

4.3. Impact of the FFS on the primary stationary CFI and harmonics

As described in § 2.3, the experimentally measured mode-shape of the stationary disturbance profile is equivalent to the spanwise root mean square ($\langle \rangle _z$) of the time-average perturbation ($\hat {w}_{R}$ or $\hat {v}_{R}$). Previous experimental studies on CFI (White & Saric Reference White and Saric2005; Downs & White Reference Downs and White2013; Serpieri & Kotsonis Reference Serpieri and Kotsonis2016) have used this metric in the analysis of the Euclidean sum of the vertical and streamwise velocity components measured by hot-wire anemometers. By merit of the chosen imaging planes in the present study, the disturbance profiles have been calculated independently for each measured velocity component.

Figure 12 presents contour plots of the stationary disturbance profiles $\langle \hat {w}_{R}\rangle _z$ and $\langle \hat {v}_{R}\rangle _z$ calculated on the partial reconstructed fields (i.e. $\sum ^{5}_n m(0,n)$) for all FFS cases. The results for the spanwise disturbance profiles ($\langle \hat {w}_{R}\rangle _z$) in figure 12(Ia–Ie) show a distinguishable lower lobe upstream of the FFS at $x/c_x = 0.18$, situated near the wall at $y/\delta ^{*}_{w,r} \approx 1$, which corresponds to the wall-normal maxima of these profiles ($\bullet$ markers in figure 12Ia–Id). In addition, a second upper lobe is also identified ($\blacktriangle$ markers in figure 12Ia–Id). The appearance of this feature has been linked to the mean flow distortion typical in the nonlinear stages of stationary CFI development (Haynes & Reed Reference Haynes and Reed2000; White & Saric Reference White and Saric2005). Near the step location at $x/c_x = 0.2$ there is an evident amplification of the spanwise disturbance profiles ($\langle \hat {w}_{R}\rangle _z$) followed by a decay ($x/c_x > 0.21$) in all measured cases. Moreover, for $x/c_x > 0.22$ the second upper lobe ($\blacktriangle$ markers in figure 12Ia–Id) becomes increasingly evident, indicating a strong mean flow distortion as shown in figure 9(IVa–IVc).

Figure 12. Contours of steady disturbances profiles (flow direction from left to right) $\langle\hat{w}_R\rangle_z$ (I) and $\langle\hat{v}_R\rangle_z$ (II) spatially filtered between $\sum ^{5}_n m(0,n)$. Location of lower ($\bullet$) and upper lobe ($\blacktriangle$): (a) clean; (b) $A_3$; (c) $B_3$; (d) $C_3$; (e) $D_3$. (Here $\delta ^{*}_{w,r} = 514\ \mathrm {\mu }\textrm {m}$).

Previous studies (Tufts et al. Reference Tufts, Reed, Crawford, Duncan and Saric2017; Cooke et al. Reference Cooke, Mughal, Sherwin, Ashworth and Rolston2019; Eppink Reference Eppink2020b) have reported the development of a strong peak near the wall in the disturbance profiles downstream of the step location (see figure 10 in Eppink (Reference Eppink2020b) and figure A5a in Tufts et al. (Reference Tufts, Reed, Crawford, Duncan and Saric2017)). In this work, a second peak near the wall is not evident in the spanwise perturbation profiles $\langle \hat {w}_{R}\rangle _z$, since as shown in figure 12(Ia–Ie) only one lower lobe is present upstream and downstream of the FFS for all the configurations. The lack of the near-wall structure in the present study can be attributed to unresolved regions in the PIV planes, originating from wall reflections. Nevertheless, the vertical perturbation profiles $\langle \hat {v}_{R}\rangle _z$ (figure 12IIa–IId) for the highest step case $D_3$ do reveal a clear peak near the wall at the location of the FFS in agreement with Eppink (Reference Eppink2020b).

Figure 13 presents the spanwise disturbance $\langle \hat {w}_{R}\rangle _z$ profiles extracted at selected streamwise locations upstream and downstream of the FFS for the partial reconstructed field ($\sum ^{5}_n m(0,n$), figure 13Ia–IVa), primary forced mode ($m(0,1$), figure 13Ib–IVb) and first harmonic ($m(0,2$), figure 13Ic–IVc). In all FFS cases there is a considerable upstream effect which leads to a substantial increase in the profiles maxima ($\max (\langle \hat {w}_{R}\rangle _z)$, figure 13IIa). It is noteworthy that the amplitude increase coincides with the localised increase in the vertical velocity component ($v$), the region of outboard spanwise motion of the CF vortices (figures 9d and 5IVc) and possible reversal of the CF velocity component (Eppink Reference Eppink2020b, figures 8 and 9).

Figure 13. Selected profiles (a–c) of the steady disturbance $\langle\hat{w}_R\rangle_z$ upstream and downstream of the FFS for the primary CFI modes and its first harmonic. (d) Streamwise evolution of the steady disturbance maxima wall-normal height ($y_{A_M}$) (Here $\delta ^{*}_{w,r} = 514\ \mathrm {\mu }\textrm {m}$).

Figure 13(d), shows the streamwise evolution of the wall-normal location of the lower lobe (i.e. closer to the wall) maxima ($y_{A_M}$) of the spanwise steady disturbance profiles $\langle \hat {w}_{R}\rangle _z$ for the partial reconstructed field. Note that the $y$-coordinate reference is the model surface and therefore it has been offset by the step height. In agreement with Eppink (Reference Eppink2018, Reference Eppink2020b) as the CF vortices approach the step they experience an increase in $y_{A_M}$, essentially lifting off the surface before reaching the FFS edge. Just downstream of the step edge ($x/c_x = 0.204$, figure 13IIIa) there is a decrease in $y_{A_M}$ as there is a reduction in the boundary layer displacement thickness ($\delta ^{*}_{w}$ in figure 6c) and a sudden sharp increase in the maximum amplitude of the primary stationary disturbance ($m(0,1$), figure 13IIIb). The highest step height ($D_3$) is responsible for the maximum amplification. Similarly, the $\langle \hat {w}_{R}\rangle _z$ profiles corresponding to the reconstructions using only the first harmonic ($m(0,2$), figure 13Ic–IVc) show a considerable amplification at the step location.

In addition to changes in disturbance amplitude, the strong amplification of the primary disturbance mode $m(0,1)$ near the FFS edge results in a significant mean flow distortion and saturation of the CF vortices. This mean flow distortion is evident in the change of the shape of the mode which leads to the development of two clearly distinguishable local maxima, as shown in figure 13(IVb). In a smooth wing CFI development, the appearance of this second upper lobe signals a typical nonlinear development of stationary CFI which results in a strong mean flow distortion and the onset of secondary instability modes (Haynes & Reed Reference Haynes and Reed2000; White & Saric Reference White and Saric2005). Nevertheless, in this case, breakdown of the CF vortices only occurs for the case $C_3$ at $x_t/c_x \approx 0.27$ and $D_3$ at $x_t/c_x \approx 0.22$ as indicated on figure 3(a).

Based on the partial reconstruction (i.e. $\sum ^{5}_n m(0,n)$), the amplitudes of the disturbance profile $\langle \hat {w}_{R}\rangle _z$ lower ($A_{L}$) and upper ($A_{U}$) lobes are presented in figure 14(Ia–Ib). The results for the FFS cases indicate that the amplitude of the lower lobe ($A_{L}$) intensifies rapidly upstream of the step and reaches a maximum value just downstream of the step edge. Hereinafter, as the amplitude of the upper lobe increases ($A_{U}$) (i.e. stronger mean flow distortion), there is a steep decay in $A_{L}$ which leads to values below the clean baseline case (black line in figure 14a). Once this minimum is reached a second region of growth is observed for the cases $A_3$ and $B_3$, which do not undergo laminar breakdown in the region $0.18 \leqslant x/c_x \leqslant 0.25$ as indicated by the IR thermal maps on figure 5(Ib–Ic).

Figure 14. Steady disturbance profile amplitudes: (Ia) lower lobe amplitude ($A_L$); (Ib) upper lobe amplitude ($A_U$); (IIa) primary CFI mode ($m(0,1$)) maximum amplitude; (IIa) first harmonic ($m(0,2$)) maximum amplitude; (IIb) IR-B PSD extracted at $\lambda _z = 7.5\ \mathrm {\mu }\textrm {m}$; (IIIb) primary CFI mode ($m(0,1$)) standard deviation along the span direction of the wall-normal gradient at $y/\delta ^{*}_{w,r} = 0.68$.

The overall amplification trend is in good agreement with the detailed experimental work presented by Eppink & Casper (Reference Eppink and Casper2019) and Eppink (Reference Eppink2020b), where a similar amplification–decay–amplification pattern has been observed on the $\langle \hat {u}\rangle _z$ perturbation peak amplitude. Moreover, the results presented in figure 14 in Eppink (Reference Eppink2020b) indicate that the slope of the second region of growth becomes steeper with increasing step height.

Evidence of this amplification–decay–amplification pattern was previously presented in the spectra of the IR thermal maps (figure 5) for the small ($A_3$) and moderate ($B_3$) cases. As noted before, for cases $C_3$ and $D_3$, the second amplification maxima in the IR maps are instead related to the laminar–turbulent transition front. Therefore, the analysis of this pattern is restricted to the cases $A_3$ and $B_3$ for which the boundary layer flow remains in a laminar condition for the entire measurement region. To further probe the correlation between the growth of the CF vortices and the pattern observed in the spectral analysis of IR-A thermal maps, the power content ($P$) pertaining to the primary forced mode ($\lambda _z/\lambda _{z,D} = 1$) is shown in figure 14(IIb). At each streamwise location $P$ is normalised with the value corresponding to the most upstream ($x/c_x = 0.176$) location ($P_0$). In addition, figure 14(IIIb) presents the standard deviation along the span direction of the velocity gradient in $y$ ($\partial {\overline {w_{R}}}/\partial {y}$) at $y/\delta ^{*}_{w,r} = 0.68$ above the wall. The results presented in figure 14(IIb,IIIb) show a striking correlation, reconciling the amplification–decay–amplification pattern in the spectra of the IR thermal maps to local changes in the surface heat transfer properties due to variations in wall shear (i.e. changes in $\partial {\overline {w_{R}}}/\partial {y}$) related to the amplification of the CFI by the step.

Figure 14(IIIa) suggests a similar amplification trend for the harmonic ($m(0,2$)) past the step location, displaying a similar amplification–decay–amplification pattern. These results are in agreement with previous observations (Eppink Reference Eppink2020b; Rius-Vidales & Kotsonis Reference Rius-Vidales and Kotsonis2020) and support the spatial analysis of the IR measurements in figure 5, which showed an amplification of the first harmonic at the step location for all the FFS cases. However, it is striking to note the relatively ‘delayed’ amplification of this first harmonic compared with the primary mode. For each FFS case, the peak of $m(0,2)$ occurs downstream of the corresponding peak of $m(0,1)$. This behaviour further suggests a (partially) indirect influence of the higher harmonics by the FFS. More specifically, the primary CFI increases in amplitude due to interaction with the FFS, inherently forcing nonlinear amplification of higher harmonics as well as of mean flow distortion. In addition, future fully three-dimensional measurements in this region are deemed necessary to characterise a possible deformation of the recirculation region downstream of the FFS location.

Eppink (Reference Eppink2020b) proposed that the first region of growth is linearly caused by a destabilisation of the stationary CFI modes due to the strong inflectional profiles caused by the adverse pressure gradient near the step. In turn, the second region is attributed to a nonlinear development due to the modulation of the recirculation region downstream of the FFS edge, which resulted in streamwise oriented vortices which amplify the harmonics of the primary mode. The behaviours observed by Eppink (Reference Eppink2020b) and the ones explained in this work, highlight the sensitivity and complexity of the FFS–CFI interaction.

Based on the findings presented so far, the steady interaction of the CF vortices with the FFS can be summarised as follows. As the CF vortices travel towards the FFS they experience an adverse pressure gradient which results in an outboard spanwise motion (figures 5IVc and 9d), a decrease in the wall-tangent velocity components (figure 6Ib) and an increase in the amplitude of the spanwise ($w$) disturbance profile (figure 13IIa) when compared with the clean configuration. In addition, at the step a portion of the wall-tangent velocity component converts into a strong vertical ($v$) velocity component due to the upward deflection (figure 7IIa–IIe). This vertical component is very localised and appears to reach a maximum on the inner side of the upwelling region of the CF vortices. Downstream of the step, there is a further amplification of the spanwise ($w$) disturbance profile (figure 14Ia at $x/c_x \approx 0.205$) and a sudden inboard spanwise motion (i.e. favourable pressure gradient). This strong amplification drives a further increase of mean flow distortion and rise of nonlinear interactions (figures 9 and 14). This leads to a saturation of the primary CF vortices (figure 14Ia at $x/c_x \approx 0.21$), and subsequent increase in harmonic amplitude. Farther downstream, the stationary CFI decay and the CF vortices experience an outboard spanwise motion (i.e. adverse pressure gradient). Finally, a second region of growth enhanced by the nominal favourable pressure distribution of the wing develops for the smaller FFS cases.

One of the most significant outcomes of the aforementioned observations is the apparent mismatch between the transition location behaviour evaluated using the IR imaging maps (figure 3) and the amplitude growth of the stationary CFI as evaluated in figure 14. In fact, for all cases of FFS investigated in this work, the partial reconstructed ($\sum ^{5}_n m(0,n$)) amplitude at the downstream end of the PIV domain is lower than the clean case. This is certainly expected for the two highest step case ($C_3$ and $D_3$), as the imminent breakdown of the vortices downstream of the step effectively breaks the spanwise modulation, ‘smoothening out’ the apparent amplitude. However, for the two smaller step cases ($A_3$ and $B_3$), the laminar boundary layer survives the passage over the step and emerges apparently stabilised in the downstream vicinity of the step. Naturally this effect is localised, as the CF vortices start growing again, as evident in figure 14(Ia) as well as from the appearance of the second maxima in the thermal maps spectra (figure 5IIb,IIc). In addition, figure 6 confirms the spanwise averaged flow recovery to the clean case at $x/c_x \approx 0.24$. In combination, it becomes apparent that the drastic effects of the FFS on the transition location cannot be traced solely to the evolution of stationary instabilities, highlighting the importance of temporal fluctuations. Henceforth, the following discussion focuses on the effect of the FFS on the unsteady disturbances.

4.4. Impact of the FFS on the unsteady disturbances

The analysis of temporal velocity fluctuations in specific regions within the CF vortices provides important information regarding steady and unsteady instability development and eventual laminar breakdown. Within the highly distorted boundary layer subject to primary stationary CFI, several regions of coherent fluctuations have been identified, typically corresponding to either primary travelling modes or secondary high-frequency instabilities of Kelvin–Helmholtz type. The first region of fluctuations has been classified as a type-I mode (Wassermann & Kloker Reference Wassermann and Kloker2002, Reference Wassermann and Kloker2003) or $z$-mode (Malik et al. Reference Malik, Li, Choudhari and Chang1999). This region coincides with the local minimum of the spanwise gradient located at the outer side of the upwelling region of the CF vortices (area $B$ in figure 15IIIa). The second region of fluctuations has been classified as type-II mode (Wassermann & Kloker Reference Wassermann and Kloker2002, Reference Wassermann and Kloker2003) or $y$-mode (Malik et al. Reference Malik, Li, Choudhari and Chang1999). This region coincides with higher levels of the wall-normal gradient and manifests near the top of the CF vortices (area $C$ in figure 15Ia). Finally, the third region of fluctuations known as type-III mode (Wassermann & Kloker Reference Wassermann and Kloker2002; Bonfigli & Kloker Reference Bonfigli and Kloker2007) has been observed near the wall on the inner side of the upwelling region and coincides with the local maxima of the spanwise gradient (area $A$ in figure 15IIIa).

Figure 15. Contours of time-averaged velocity gradients and spanwise velocity (grey line 10 levels from 0 to 1) $z^*$ positive direction outboard, spatially filtered between $\sum ^{5}_n m(0,n)$: (a) clean; (b) $A_3$; (c) $C_3$; (d) $D_3$. (Here $\delta ^{*}_{w,r} = 514\ \mathrm {\mu }\textrm {m}$ and $\lambda _{z,D} = 7.5\ \mathrm {\mu }\textrm {m}$). Areas $A$ and $B$ are defined in figure 16.

The origin of the velocity fluctuations in the region pertaining to type III has been traced to the interaction between travelling and stationary CFI modes (Wassermann & Kloker Reference Wassermann and Kloker2002, Reference Wassermann and Kloker2003; White & Saric Reference White and Saric2005; Serpieri & Kotsonis Reference Serpieri and Kotsonis2016). The type III instability can be considered as a primary CF instability with non-zero frequency. Nevertheless, in the environment of enhanced stationary CFI modes relevant to the present study, type III instability is identified through the ‘footprint’ of the nonlinear interaction between stationary and travelling modes.

Conversely, the velocity fluctuations in the regions pertaining to type-I and type-II differ entirely in nature from the type-III, as they have been associated with secondary instabilities which emerge on the strong velocity shears as the CF vortices reach saturation. These high frequency, rapidly amplifying instabilities are extremely sensitive to small changes in the developing shears and lead to the breakdown of the CF vortices and transition to turbulent flow (Wassermann & Kloker Reference Wassermann and Kloker2002; White & Saric Reference White and Saric2005; Serpieri & Kotsonis Reference Serpieri and Kotsonis2016). Previous studies on the mechanisms of these instabilities have shown the appearance of a secondary set of finger vortices which develop along the shear layer on the outer side of the upwelling region (Wassermann & Kloker Reference Wassermann and Kloker2002; Serpieri & Kotsonis Reference Serpieri and Kotsonis2016).

Due to the inherent relation between unsteady secondary instabilities and mean velocity gradients, the latter are first inspected. The interaction of the stationary CFI with the FFS results in a topological modification of the structure of the CF vortices which further manifests as alterations in the vertical and spanwise velocity gradients presented in figure 15. As already shown, downstream of the FFS edge ($x/c_x = 0.204$, figure 9IIb–IIc) the sudden and abrupt increase in $\bar {w}_z$ leads to a substantial decrease in the boundary layer momentum thickness ($\delta ^{*}_w$, figure 6c) when compared with the clean configuration. This transfer of high-momentum fluid towards the wall increases the vertical gradient ($\partial \bar {w}_{R} / \partial y$) near the wall in the downwelling region of the CF vortices as shown in figure 15(IIb–IId). In addition, a localised region of negative vertical gradient ($\partial \bar {w}_{R} / \partial y$) is found at the centre of the upwelling region near the wall for the moderate ($C_3$) and high ($D_3$) steps. While the inclusion of the steps produces notable effects on the vertical gradient near the wall, the effect is largely minimal at the cusp of the stationary CFI (area $C$), where type-II secondary instability is expected to grow. This behaviour reconciles with the observations in § 4.2 where the major deflection and shearing motion experienced by the stationary CF vortices was identified to be largely oriented in the spanwise direction.

The strong changes in amplitude as well as spanwise shearing motion of the stationary CF vortices past the step edge, results in noticeable changes in the spanwise velocity gradients, which are predominantly located at the outer and inner sections of the upwelling regions. In contrast to the vertical gradient, changes in the spanwise gradient are global and affect both positive (i.e. inner, area $A$ in figure 15IIIa) and negative (i.e. outer, area $B$ in figure 15IIIa) gradients. Particularly the outer spanwise gradients have been typically associated with the growth of type-I secondary instability. In all monitored FFS cases, the step induces higher gradient levels than in the clean configuration near the step (figure 15IVa–IVd). This influence is already evident slightly upstream of the step as shown in figure 15(IIIa–IIId).

While the intensification of the spanwise gradient is consistently observed for all cases at the vicinity of the step, the downstream development of $\partial \bar {w}_{R} / \partial z$ is highly dependent on the step height. In the case of the highest FFS ($D_3$), the interaction of the stationary CFI with the step leads to an abrupt amplification, saturation and breakdown of the CF vortex structure as shown in figure 15(Vd). The interaction of the stationary CFI with the moderate step case ($C_3$) follows a similar trend as the CF vortices experience a strong amplification near the step followed by saturation. This leads to a loss in spanwise coherence and decrease in the intensity of the spanwise gradients (figure 15IVc–VIc) prior to laminar breakdown, which occurs at $x/c_x \approx 0.27$ (figure 3a).

In contrast, for the small FFS cases $A_3$ and $B_3$ (not shown in figure 15) the CF vortices do not experience breakdown in this streamwise region. Yet, the spanwise gradient experiences a significant decay farther downstream of the step. Particularly for the shallowest case $A_3$, the spanwise gradient at $x/c_x$ = 0.239 (figure 15VIb) is in fact rendered lower than the corresponding clean case at the same streamwise location. This is a direct consequence of the stabilisation and decrease in amplitude of the stationary CFI, as identified in figure 14.

The significant changes on both vertical and spanwise velocity gradients due to the step can further be associated with the development and growth of unsteady shear layer instabilities, widely acknowledged to play an important role in the breakdown of CFI-dominated flows. Figure 16 presents a set of contour plots of spanwise temporal velocity fluctuations ($\sigma {w}_R$) at selected streamwise locations upstream and downstream of the FFS location. Time-resolved hot-wire anemometry (known as HWA) measurements, on the same configuration as the present clean case and similar flow conditions by Serpieri & Kotsonis (Reference Serpieri and Kotsonis2016, Reference Serpieri and Kotsonis2018), identified type-I/type-II instabilities in the frequency range between 3.5 and 8 kHz and type-III modes in the range between 350 and 550 Hz, albeit for a lower DRE amplitude. Considering the low repetition-rate of PIV acquisitions employed in the present study (i.e. 15 Hz), spectral analysis and frequency filtering are not applicable. Nevertheless, the long sampling time (i.e. 80 s) ensures that the fluctuating velocity field represents an ensemble of both low- and high-frequency disturbances, which can be considered temporally uncorrelated. Furthermore, these instabilities are strongly localised within the structure of the stationary CFI, allowing direct evaluation of the development of each type.

Figure 16. Contours of spanwise temporal velocity fluctuations and spanwise velocity (grey line 10 levels from 0 to 1), $z^*$ positive direction outboard spatially filtered between $\sum ^{5}_n m(0,n)$: (a) clean; (b) $A_3$; (c) $C_3$; (d) $D_3$. (Here $\delta ^{*}_{w,r} = 514\ \mathrm {\mu }\textrm {m}$ and $\lambda _{z,D} = 7.5\ \mathrm {\mu }\textrm {m}$). Extraction areas $A$ and $B$ are defined as isolines of 85 % of the local maximum amplitude of unsteady fluctuations on the inner and outer side of the upwelling region.

The results for the clean baseline case in figure 16(Ia–VIa), show a local maximum of fluctuations at the location corresponding to a type-III mode ($A$ in figure 16Ia). Monitoring a downstream location (figure 16Va) indicates a decaying interaction between weak travelling CF modes and the forced stationary CF vortices, as the magnitude of the fluctuations in this region decrease. To better illustrate this decaying behaviour, figure 17 presents average values of spanwise velocity gradient and temporal fluctuation amplitude extracted within areas $A$ and $B$ indicated in figures 15 and 16. The two extraction areas are defined for each plane and step case as isolines of 85 % of the local maximum amplitude of unsteady fluctuations on the inner and outer side of the upwelling region. Naturally, values corresponding to area $A$ refer to positive spanwise gradients and type-III dominated fluctuations, while values corresponding to area $B$ refer to negative gradients and type-I dominated fluctuations.

Figure 17. Streamwise evolution of averaged extracted values in areas $A$ and $B$ (defined in figures 15 and 16): (a) positive (area $A$) and negative (area $B$) averaged spanwise velocity gradients; (b) averaged velocity fluctuations in area $A$; (c) averaged velocity fluctuations in area $B$.

Figure 17(b) confirms the decay in the temporal velocity fluctuations ($\sigma {w_R}$) in region $A$ corresponding to type-III instabilities in the clean baseline case (black line) in the range of $x/c_x > 0.2$. The addition of small ($A_3$) to moderate ($C_3$) steps result in a further reduction of velocity fluctuations ($\sigma {w_R}$) in this region. Evidently, the addition of the FFS leads to a reduction in the interaction between travelling and stationary CF modes. Furthermore, it is striking to note that this stabilising effect is already active upstream of the FFS (compare figure 16Ia–Id). This behaviour strongly suggests a change in stability characteristics of the incoming boundary layer. Considering the findings described in figure 14, for the same streamwise range ($0.18< x/c_x<0.2$), the primary stationary CFI appears to destabilise and increase in amplitude. The concurrent dampening of type-III modes can then be associated with a combination of (possibly conflicting) linear effects (i.e. change of the stability of the mean boundary layer due to the FFS modification) and nonlinear interaction between stationary and travelling modes. The exact identification of the relative significance of these two effects requires a combination of parameter variations in high-resolution experiments as well as accurate numerical simulations in the near-step region.

Considering the development of secondary instabilities, detailed experimental studies (White & Saric Reference White and Saric2005; Serpieri & Kotsonis Reference Serpieri and Kotsonis2016) have shown that as the stationary vortices saturate, the strong mean flow distortion results in the development of streamwise and spanwise velocity shears. These give rise to high-frequency inviscid instabilities of Kelvin–Helmholtz type. In the present study, the primary CFI arrives at the FFS location at a relatively high and constant amplitude of approximately 13 % of the local free stream (figure 14), signalling saturation levels. Consequently, a noticeable increase in the velocity fluctuations in the region corresponding to the type-I mode (area $B$ in figure 16Ia) is registered. The clean baseline case in figure 17(c) shows an increase in the velocity fluctuations ($\sigma {w_R}$) in this region. Moreover, the addition of an FFS appears to affect the development of these fluctuations considerably. The results in figure 17(c) show an increase in velocity fluctuations ($\sigma {w_R}$) with respect to the clean configuration in the region associated with the type-I secondary instability. This is consistent for all step cases in the region directly downstream of the FFS location ($x/c_x \approx 0.21$). For the highest step height ($D_3$) this increase correlates well with the breakdown of the CF vortices presented in figure 16(IVd). For the moderate step height ($C_3$), the velocity fluctuations ($\sigma {w_R}$) in the region associated with the type-I mode increase even further for $x/c_x > 0.22$ with respect to the clean configuration as shown in figure 16(Vc and VIc). This amplification of the secondary instability correlates well with the anticipation of the laminar–turbulent transition, presented in figure 3 for the respective cases.

In contrast, for the smaller FFS cases ($A_3$ and $B_3$) the velocity fluctuations ($\sigma {w_R}$) associated with the type-I mode decrease downstream of the FFS location ($x/c_x > 0.22$) to a level lower than the corresponding level in the clean baseline configuration, compare figure 16(VIa–VIb). Moreover, the reduction in $\sigma {w_R}$ presented in figure 17(c) correlates well with a decrease in the spanwise gradients in region B as shown in figure 17(a). High-resolution and time-resolved measurements are required to identify the spectral content and further confirm the origin of the observed velocity fluctuations. In addition, such future dedicated studies will indicate the connection, if any, to the vortex-shedding mechanisms proposed by Eppink (Reference Eppink2020b). The unsteady behaviour reconciles sufficiently with the overall delay of transition presented in § 3.1 for the small FFS ($A_3$) and provides a first-order insight into the possible transition delay mechanisms pivoting on the reduction of the spanwise gradients and the stabilisation of the type-I secondary instability.