2.1.1. Swept wing model

The diagram of the experimental set-up in figure 1(b) shows two different coordinate systems. On the first system ($X,Y,Z$), the streamwise $X$-coordinate is parallel to the wind tunnel floor and the velocity components are given, respectively, by $U,V$ and $W$. In contrast, for the second system ($x,y,z$) the streamwise $x$-coordinate is normal to the leading edge of the swept wing. Note that both systems’ origins coincide with the leading edge at the wing midspan.

The M3J model is equipped with a total of 92 streamwise oriented (i.e. along $X$-coordinate) static pressure taps equally divided on the upper (outboard) and lower (inboard) side of the model as depicted on the diagram in figure 1(b). Note that all the measurements are conducted on the ‘pressure side’ of the model. Figure 1(a) shows the static pressure measured by the taps using a multichannel pressure scanner. The pressure distributions at $Re_{c_X} = 2.17 \times 10^6$ and $\alpha = 3^\circ$ on the outboard and inboard side of the model indicate a predominantly favourable pressure gradient (i.e. pressure minima $X/c_X \approx 0.65$). Moreover, in agreement with Serpieri & Kotsonis (Reference Serpieri and Kotsonis2016), the validity of the infinite swept wing assumption used in the boundary-layer and stability calculations is confirmed due to the nearly identical pressure distributions on the inboard and outboard side of the wing.

From the measured pressure distribution for a clean reference case (i.e. without FFS), a numerical solution of the steady and incompressible 2.5D (i.e. spanwise invariant) laminar boundary layer is calculated along the $x$-coordinate. In addition, the stability of this boundary layer is determined using the Orr–Sommerfeld equation in its spatial theory formulation (see Arnal & Casalis Reference Arnal and Casalis2000) assuming a zero spanwise growth rate due to the infinite swept wing condition.

2.1.2. Experimental simulation of surface irregularities

Following the strategy presented by Perraud & Seraudie (Reference Perraud and Seraudie2000), Holmes et al. (Reference Holmes, Obara, Martin and Domack1985) and Rius-Vidales & Kotsonis (Reference Rius-Vidales and Kotsonis2020, Reference Rius-Vidales and Kotsonis2021), the FFS surface irregularity is simulated on the existing swept wing model using a thin flexible surface add-on. Thus, polyethylene terephthalate foils were cut to size with a CNC DCS 2500 Gerber machine and installed on the swept wing as indicated in figure 1(b). This study only considers FFS surface irregularities with a sharp edge (i.e. no ramp or chamfer).

During the experiments, the FFS height of each configuration was quantified in situ by traversing a Micro-Epsilon 2950-25 laser profilometer (reference resolution of $2\,\mathrm {\mu }{\rm m}$) along a spanwise segment of 200 mm. Table 1 presents the FFS streamwise location ($x_{h}/c_x$) and its average step height ($\bar {h}$) and standard deviation ($\sigma _{h}$) along the measured spanwise segment. In addition, from the aforementioned boundary-layer and stability calculations the displacement thickness ($\delta ^*_h$) and the estimated vortex core height ($y_c$, according to the definition by Tufts et al. Reference Tufts, Reed, Crawford, Duncan and Saric2017) for the forcing mode $\lambda _{z,D}$ are determined at the step location.

Table 1. Geometrical parameters of tested configurations. For all cases nominal DREs settings are $\lambda _{z,D} = 8\,{\rm mm}$, $d_D = 2\,{\rm mm}$, $k_{D} = 200\,{\rm \mu} {\rm m}$, $x_{D}/c_x = 0.02$.

2.1.3. Forcing of stationary CFI modes

Following previous work by Rius-Vidales & Kotsonis (Reference Rius-Vidales and Kotsonis2020, Reference Rius-Vidales and Kotsonis2021) a late-growth (i.e. with respect to the most amplified mode at the step location) is forced to study its interaction with the FFS surface irregularity. This forcing condition is compatible with the one used by Eppink (Reference Eppink2020b) albeit at a significantly higher initial amplitude. At the nominal conditions of this study, the aforementioned linear stability analysis indicates that a stationary CFI mode with a spanwise wavelength ($\lambda _z$) close to 8 mm is a late-growth CF mode ($N \approx 3.6$) with respect to the most unstable mode ($N \approx 3.9$) at the step location and is highly unstable at and downstream of the step location.

Henceforth, for all the configurations presented in table 1, stationary CF modes are conditioned using discrete roughness elements (DREs) spaced at $\lambda _{z,D} = 8\,{\rm mm}$. The DREs result in a narrowing of the evolving perturbations wavelength band and conditioning of the amplitude of the stationary CF modes, which destabilise the boundary-layer flow. Consequently, their use minimises potential non-uniformities in amplitude and wavelength of the CF vortices imposed by the model's micro surface roughness which can compromise the reproducibility and statistical relevance of the experiments. Therefore, DREs have proven to be an essential tool for the fundamental understanding of the development of CFI (e.g. Reibert et al. Reference Reibert, Saric, Carrillo and Chapman1996; Saric, Carrillo & Reibert Reference Saric, Carrillo and Reibert1998; White & Saric Reference White and Saric2005; Serpieri & Kotsonis Reference Serpieri and Kotsonis2016). Despite the simplifications imposed by the DREs, the fundamental interaction dynamics unveiled in these controlled cases are valuable for the understanding of cases without them.

It must be noted here that the use of DREs inherently implies the existence of intentional three-dimensional surface irregularities near the leading edge of the model. However, the term ‘surface irregularity’ in this work is strictly reserved for the FFS, as DREs are used only as a conditioning device and are invariantly present in all cases.

In line with Rius-Vidales & Kotsonis (Reference Rius-Vidales and Kotsonis2020, Reference Rius-Vidales and Kotsonis2021) and Zoppini, Ragni & Kotsonis (Reference Zoppini, Ragni and Kotsonis2021), the DREs are manufactured in-house from an adhesive vinyl film using a CNC laser cutting system. In all the cases, the DREs are installed upstream of the neutral point of the forced mode. The amplitude of the DREs was chosen based on the instability regime of interest. More specifically, the present study describes the unsteady interaction of CF vortices and the step geometry. For a stationary CFI-dominated flow, it is well established that unsteady fluctuations form as secondary instabilities after saturation of the primary stationary CF vortices (e.g. White & Saric Reference White and Saric2005). As such, in the present study, the DREs nominal height was set relatively high ($k_D = 200\,{\mathrm {\mu }}{\rm m}$) in order to anticipate the growth and saturation of the primary CF disturbance. This further facilitates the development of the secondary instability in both the clean and step cases while allowing for a common HWA traversing range among all tested cases.

2.2.1. Infrared thermography

The Reynolds analogy provides an effective relationship between the wall shear stress and surface heat transfer in fluids. Considering the rapid increase in skin-friction associated with the laminar–turbulent transition, IR thermography has proven to be a robust and efficient method for detecting the boundary-layer transition location in experimental studies on swept wings (e.g. Zuccher & Saric Reference Zuccher and Saric2008; Crawford et al. Reference Crawford, Duncan, West and Saric2015b; Rius-Vidales & Kotsonis Reference Rius-Vidales and Kotsonis2020).

In the present work, IR thermography measurements are conducted on the pressure side of the model using two Optris PI640 IR cameras ($640\,{\rm px} \times 480\,{\rm px}$, uncooled focal plane array, $7.5\text {--}13\,{\mathrm {\mu }}{\rm m}$ spectral range, NETID 75 mK). The diagram on figure 1(b) shows the cameras’ measurement region (IR-A, yellow; IR-B, blue). The first camera IR-A is equipped with a telephoto lens ($f = 41.5\,{\rm mm}$) to capture the near step region ($226 \times 175 \,{\rm mm}$ centred at $X/c_X = 0.27$ and $Z/b = 0.02$). The second camera IR-B is equipped with a wide-angle lens ($f = 10.5\,{\rm mm}$) to capture a larger extent of the model surface ($760 \times 300 \,{\rm mm}$ centred at $X/c_X = 0.23$ and $Z/b = 0.04$). During the measurements seven halogen lamps ($1 \times 1000\,{\rm W}$ and $6 \times 400\,{\rm W}$) are positioned outside the wind tunnel test-section and used to actively heat up the model. In this active modality the lower temperatures correspond to the turbulent part while higher temperatures indicate the laminar part of the boundary-layer flow.

The extraction of the transition location from the thermal maps of camera IR-B involves using a custom-designed recognition algorithm. For each configuration tested (see table 1) a physical space transformation and distortion correction was applied to a time-averaged thermal map calculated from 50 IR images acquired at a sampling rate of 3.5 Hz. Subsequently, a differential IR thermography technique (Raffel & Merz Reference Raffel and Merz2014) is applied following the procedure established by Rius-Vidales & Kotsonis (Reference Rius-Vidales and Kotsonis2020), which considers successive measurements at increasing Reynolds numbers. The transition location is identified through a linear fit on the gradient of the binarized differential IR thermography image. Note that the confidence bands of this linear fit indicate the uniformity of the transition front (i.e. jagged or smooth), which can provide an essential insight into the dominant transition-inducing mechanism. More specifically, due to their localised nature, stationary CF vortices tend to transition in a well-defined, jagged pattern of localised wedges, while travelling disturbances essentially ‘blur’ the transition front reducing the spanwise variance of the transition location.

In addition to the global transition location, the thermal maps of camera IR-A provide a qualitative representation of the CF vortices’ thermal footprint, from which the spatial organisation of coherent structures in the boundary layer as they interact with the FFS can be extracted. To this end, a spatial spectral analysis is performed on thermal intensity profiles extracted along the spanwise $z$-direction. Based on the selected camera configuration (i.e. camera location and lens) the smallest wavelength resolved according to the Nyquist limit is 0.84 mm.

2.2.2. Hot-wire anemometry

Recent studies from the authors (e.g. Rius-Vidales & Kotsonis Reference Rius-Vidales and Kotsonis2021) as well as by Eppink (Reference Eppink2020b) utilised several variations of particle image velocimetry (PIV) for a detailed reconstruction and analysis of pertinent CFI features in the vicinity of surface irregularities. A common outcome in these studies is the importance of the unsteady fluctuations in the incoming boundary layer and their relation to the surface irregularity's effect on transition. Despite a wealth of spatially correlated information extracted from optical velocimetry techniques, accurate measurement of amplitude and spectra of minute velocity fluctuations, especially in the vicinity of walls, is at best challenging. Hence, the PIV applicability towards evaluation of unsteady boundary-layer instabilities and their interaction with the FFS is limited by the sampling rate and the random and bias errors stemming from wall reflections, camera noise and laser light illumination. To this goal, the present work uses HWA as a well-established, accurate and time-resolved technique, albeit providing single-point measurements.

The boundary-layer flow measurements are conducted using a HWA probe (single wire BL probe, Dantec Dynamics 55P15) operated by a TSI IFA-300 constant temperature bridge. A custom analogue–digital (24bit) acquisition system registers and converts the HWA voltage signal to the corresponding flow velocity based on in situ calibration and correction for variations in atmospheric pressure and flow temperature (Hultmark & Smits Reference Hultmark and Smits2010). The LTT wind tunnel facility is furnished with an automated traversing system capable of translating the HWA probe (figure 1b) along the $X, Y$ and $Z$ directions with a resolution of $2.5\,{\mathrm {\mu }}{\rm m}$ in each axis. The probe is mounted on a counterbalanced steel sting of approximately 2.5 m long. Despite the heavy construction of the sting, inevitable mechanical vibrations affecting the measurements within the characteristic resonance frequencies are detected, as will be discussed in § 5.2.1. For the entirety of measurements, the wire of the HWA probe is mounted vertically (i.e. aligned to the $Z$ axis) and orthogonal to the $X$-coordinate direction as illustrated on the diagram in figure 1(c).

A series of wall-normal boundary-layer scans were conducted along the $z$-direction to form $y_{t}$–$z$ measurement planes at different streamwise locations ($0.20 \leqslant x/c_x \leqslant 0.28$) to characterise the streamwise development of the CFI. It must be mentioned here that due to the curvature of the M3J wing, successive planes are not parallel to each other, rather normal ($y_t$) to the local tangent at the wall. Nonetheless, due to the large chord ($c_X=1.27$ m) and limited measurement domain (${<}10\,\%$ chord), the difference in wall-tangent angle is only $1.2^\circ$ between the most upstream and most downstream measurement planes. Each plane consists of 60 boundary-layer profiles equispaced in the $z$ direction. Each profile is constructed with 40 measurement points along the wall-normal direction $y_{t}$. At each measurement point, the hot-wire signal was acquired at a sampling rate of $f_{s} = 51.2\,{\rm kHz}$ for a total measurement time of two seconds. The final resolution along the $z$-coordinate is fixed at $\Delta z = 533\,{\mathrm {\mu }}{\rm m}$ while the resolution along the wall-normal direction differs per streamwise location ($60\,{\mathrm {\mu }}{\rm m} \leqslant \Delta y_t \leqslant 90\,{\mathrm {\mu }}{\rm m}$) to account for the growth in the boundary layer. For each $X/c_X$ station, the measurement planes’ starting position along the span ($z^{*}$) has been adjusted to track the evolution of three full CF vortices. Furthermore, when performing boundary-layer HWA measurements it becomes important to consider that the measurement points near the wall are being affected by spurious heat transfer to the wall, thus leading to the so-called ‘tail’. Hence, it is customary to commence the measurements at a given position away from the wall and later retrieve the wall location through an extrapolation of the velocity profile (see Saric Reference Saric2007). In this work, the starting position for each measurement plane is identified as the wall-normal distance for which the registered velocity reaches around $20\,\%$ of the local freestream velocity. In addition, a Taylor–Hobson microalignment telescope was used to monitor the starting distance from the wall. Finally, during post-processing the location of the wall is determined by performing a linear regression on the velocity profiles.

2.2.3. Amplitude growth metrics

The impact of the FFS on the stability characteristics of the CF vortices is assessed by calculating the steady and unsteady disturbance profiles from the HWA measurements acquired as indicated in § 2.2.2. Following White & Saric (Reference White and Saric2005) and Downs & White (Reference Downs and White2013) the experimental steady disturbance profile is calculated for each HWA $y_t$–$z$ measurement plane as the spanwise root-mean-square of the time-average perturbation as given by (2.1). In this work the maximum ($A_{M} = \max (\langle \hat {q}(y_t)\rangle _z)$) of these profiles along the $y_t$-coordinate is non-dimensionalized with the local external velocity ($\bar {Q}_e$) and used to monitor streamwise changes in the stationary CF vortices;

(2.1)\begin{equation} \langle\hat{q}(y_t)\rangle_z = \sqrt{\frac{1}{n}\sum_{j=1}^{n}(\bar{Q}(y_t,z_j) - \bar{Q}_z(y_t))^2}. \end{equation}

In the typical decomposition used in linear stability analysis, the velocity perturbation ($u'$) can be calculated by subtracting a basic state or baseflow from the measured velocity component. In the present experiment, $\hat {q} \ne q'$, since $\bar {Q}_z(y_t)$ (used in (2.1)) corresponds to the spanwise time-average distorted flow and not to a baseflow. Nonetheless, for the experimental study of CFI, this metric has been commonly used (e.g. White & Saric Reference White and Saric2005; Downs & White Reference Downs and White2013; Serpieri & Kotsonis Reference Serpieri and Kotsonis2016).

For the study of the secondary instability, the methodology follows the one employed in White & Saric (Reference White and Saric2005), Downs & White (Reference Downs and White2013) and Serpieri & Kotsonis (Reference Serpieri and Kotsonis2016). For each $y_t$–$z$ measurement plane, a wall-normal profile is calculated by numerically integrating the temporal standard deviation ($\sigma _{Q}$) along the $z$-coordinate (i.e. spanwise direction) for every $y_t$ position. Then, the resulting profiles are integrated along the $y$-coordinate to obtain the amplitude $a$ as indicated in (2.2). This metric is used to monitor the streamwise development of unsteady disturbances;

(2.2)\begin{equation} a = \frac{1}{\overline{Q_e}}\frac{1}{y_t^m}\frac{1}{z^m}\int_{0}^{y_t^m}\int_{0}^{z^m}\sigma_{Q}(y_t,z) \,{\rm d}z \,{\rm d}y_t. \end{equation}

5.2.1. Unsteady disturbances on the inner side of the CF vortices ($P_3$ $\bullet$)

Figure 9, shows the spectral analysis of probe $P_3$ (i.e. $\bullet$ in figure 8Ia–IVd on the inner side of the upwelling region) for the measurement planes between $0.253 \leqslant x/c_x \leqslant 0.270$. In addition, to monitor the spectral content in the freestream flow, an extra probe is located at the exterior of the boundary layer for the clean configuration. As anticipated, the power spectrum in the freestream is relatively flat except for two features of interest. The first one is a pair of low-frequency peaks ($f \approx 170$ and 370 Hz), which correspond to unavoidable mechanical vibrations in the supporting arm of the hot-wire probe appearing at all measurement locations. Similar to Eppink & Wlezien (Reference Eppink and Wlezien2011), these probe vibrations lead to a qualitative match of the filtered velocity fluctuations (i.e. bandpass filter around the low-frequency peaks) and the topology of the time-average wall-normal velocity gradient. The second feature of interest is the high-frequency (${>}10^4\,{\rm Hz}$) hump inherent to the HWA bridge.

Figure 9. Spectral analysis at the inner side of the upwelling region, probe $P_3$ ($\bullet$ in figure 8) at measurement planes downstream of the step location: (Ia) $x/c_x = 0.253$; (Ib) $x/c_x = 0.256$; (IIa) $x/c_x = 0.260$; and (IIb) $x/c_x = 0.270$. Shaded grey and blue regions indicate different frequency bands.

Instead, inside the boundary layer at $x/c_x = 0.253$ (figure 9Ia) the spectral analysis for the clean configuration reveals the dominance of low frequency velocity fluctuations between $450\,{\rm Hz} \leqslant f \leqslant 3\,{\rm kHz}$, herein this frequency band is referred to as $B_L$ as indicated in figure 9. Although the increase of temporal velocity fluctuations at this location is in agreement with Serpieri & Kotsonis (Reference Serpieri and Kotsonis2016, Reference Serpieri and Kotsonis2018) and Rius-Vidales & Kotsonis (Reference Rius-Vidales and Kotsonis2021), contours of the temporal velocity fluctuations filtered at the bandpass $B_L$ (figure 10Ia–IVa) show a relatively weaker development of type III modes. This is largely expected since the velocity fluctuations typically associated with the type III mode are in fact the result of the interaction between travelling and stationary CF modes. The latter is considerably stronger in the present study due to the larger amplitude associated with the DREs used at the leading edge.

Figure 10. Bandpass filtered ($B_{L},450\,{\rm Hz} \leqslant f \leqslant 3 \,{\rm kHz}$) contours of temporal velocity fluctuations (dashed lines indicate the limit between the inner/outer side used for the calculation of $a^*$) and time-average velocity (grey solid lines 10 levels $\bar {Q}/\overline {Q_e}$ from 0 to 1 same contours as in figure 5): (a) clean, (b) A; (c) B; (d) C ($\delta ^*_Q = 620\,{\mathrm {\mu }}{\rm m}$ and $\lambda _{z,D} = 8\,{\rm mm}$).

When considering a critical FFS case (A and B, in table 1) an increase in the temporal velocity fluctuations with respect to the clean configuration occurs mainly inside the low-frequency band $B_L$ as shown in figure 9. Even though the shape of the power spectrum remains similar to the clean configuration, the deviations from it in this frequency band become considerable by $x/c_x = 0.270$ (figure 9IIb).

In contrast, the shape of the power spectrum for the supercritical FFS case (case C in table 1) differs considerably from the clean baseline. More specifically, downstream of the FFS at $x/c_x = 0.253$ and $0.256$ (figure 9Ia,Ib) the temporal velocity fluctuations at the low frequency band $B_L$ appear in two distinct regions $B_{L1}$ ($450\,{\rm Hz} \leqslant f \leqslant 1050 \,{\rm Hz}$) and $B_{L2}$ ($1700\,{\rm Hz} \leqslant f \leqslant 2300 \,{\rm Hz}$). In addition, high-frequency fluctuations appear ($B_H, 3.5 \,{\rm kHz} \leqslant f \leqslant 9\,{\rm kHz}$) as a prelude to the flattening of the power spectrum (i.e. turbulent flow) by $x/c_x = 0.260$ as shown in figure 9(IIa).

5.2.2. Unsteady disturbances on the outer side and cusp of the CF vortices ($P_1$ $\blacksquare$ and $P_2$ $\blacktriangle$)

Figures 11 and 12, present the spectral analysis for the probes $P_1$ (i.e. $\blacksquare$ in figure 8 on the outer side of the upwelling region) and $P_2$ (i.e. $\blacktriangle$ in figure 8 on the top part of the CF vortices) for the measurement planes between $0.253 \leqslant x/c_x \leqslant 0.270$. In the clean configuration, the power spectrum for probe $P_1$ and $P_2$ (figures 11 and 12, respectively) indicates temporal velocity fluctuations at the high-frequency band $B_H$. The high-frequency content in the power spectrum at the location of these probes is in agreement with previous studies at similar conditions (e.g. Serpieri & Kotsonis Reference Serpieri and Kotsonis2016, Reference Serpieri and Kotsonis2018), which identified velocity fluctuations corresponding to a type I secondary instability mode between 3.5–6 kHz, and a type II mode between 7–8 kHz. In addition, the IR measurements in figure 2(Ia) confirm that shortly downstream of the last HWA measurement plane, a localized breakdown (i.e. turbulent wedges) of the boundary-layer occurs as expected from the rapid development of these secondary instability modes in this case without FFS.

Figure 11. Spectral analysis for probe on the outer side of the upwelling region $P_1$ ($\blacksquare$ in figure 8) at measurement planes downstream of the step location: (Ia) $x/c_x = 0.253$; (Ib) $x/c_x = 0.256$; (IIa) $x/c_x = 0.260$; and (IIb) $x/c_x = 0.270$. Shaded grey regions indicate different frequency bands.

Figure 12. Spectral analysis for probe on the cusp of the CF vortex $P_2$ ($\blacktriangle$ in figure 8) at measurement planes downstream of the step location: (Ia) $x/c_x = 0.253$; (Ib) $x/c_x = 0.256$; (IIa) $x/c_x = 0.260$; and (IIb) $x/c_x = 0.270$. Shaded grey regions indicate different frequency bands.

Consequently, the bandpass filtered contours of $\sigma _{Q_f}$ at the frequency band $B_{H}$ (figure 13Ia–IVa) show temporal velocity fluctuations spatially located on the outer side of the upwelling region as well as top part of the CF vortices overlapping with the minimum spanwise gradients and positive wall-normal gradients shown in figure 7. This topology of temporal velocity fluctuations is typical of type I and type II modes (Serpieri & Kotsonis Reference Serpieri and Kotsonis2016).

Figure 13. Bandpass filtered ($B_{H},3.5\,{\rm kHz} \leqslant f \leqslant 9 \,{\rm kHz}$) contours of temporal velocity fluctuations (dashed lines indicate the limit between the inner/outer side used for the calculation of $a^*$) and time-average velocity (grey solid lines 10 levels $\bar {Q}/\overline {Q_e}$ from 0 to 1 same contours as in figure 5): (a) clean; (b) A; (c) B; (d) C ($\delta ^*_Q = 620\,{\mathrm {\mu }}{\rm m}$; and $\lambda _{z,D} = 8\,{\rm mm}$).

Previous numerical and experimental studies (e.g. Bonfigli & Kloker Reference Bonfigli and Kloker2007; Serpieri & Kotsonis Reference Serpieri and Kotsonis2016, Reference Serpieri and Kotsonis2018) in clean (i.e. without surface irregularities) stationary CFI cases showed that type I secondary instabilities of Kelvin–Helmholtz type develop in the shear layer of the primary CFI. Therefore, the frequency of these secondary instabilities varies as they convect to higher- and lower-velocity regions in the distorted boundary layer. This behaviour manifests on the bandpass filtered velocity fluctuations at the frequency band $B_L$ (figure 10Ia–IVa), which indicate that temporal velocity fluctuations are also located on the outer side of the upwelling region at a location closer to the wall than the ones observed for the higher frequency band $B_H$.

For the critical FFS cases (A and B), the spatial organization of the bandpass filtered contours of $\sigma _{Q_f}$ at the low $B_L$ (figure 10Ib–IVc) and high $B_H$ (figure 13Ib–IVc) frequency bands closely matches the development of the secondary instabilities (type I and type II modes) observed in the clean configuration. A mild amplification of these fluctuations is observed as a function of step height, which is attributed to the strengthening of the stationary CF vortices and subsequent intensification of the spanwise and wall-normal shears, which drive these secondary instabilities. In contrast, in the supercritical FFS case C (figures 10Id–IVd and 13Id–IVd) the spatial distribution of the temporal velocity fluctuations strongly differ from the clean case. More specifically, downstream of the FFS (i.e. $x/c_x = 0.256$), the maximum temporal velocity fluctuations occur at the upwelling region's inner side coinciding with the location of a possible recirculation region as identified by Eppink (Reference Eppink2020b). Henceforth, the nature of these fluctuations will be further investigated.

5.2.3. Unsteady disturbances in the supercritical FFS

The spectral analysis (figure 9Ib) at the location of probe $P_3$ (i.e. $\bullet$ in figure 8Id–IVd) downstream of the FFS ($x/c_x = 0.256$) shows the occurrence of temporal velocity fluctuations at two distinct sub-bands $B_{L1}$ and $B_{L2}$. To further investigate the origin of these unsteady disturbances, the temporal velocity fluctuations for the clean and FFS cases at this streamwise position are filtered in these frequency bands and presented in figure 14.

Figure 14. Bandpass filtered $B_{L1}$(I) ($450\,{\rm Hz} \leqslant f \leqslant 1050\,{\rm Hz}$) and $B_{L2}$(II) ($1700\,{\rm Hz} \leqslant f \leqslant 2300 \,{\rm Hz}$) contours of temporal velocity fluctuations (solid contour lines indicate the positive and dashed ones negative spanwise (I) and wall-normal (II) velocity gradients, the contours corresponds to values in figure 7): (a) clean; (b) A; (c) B; (d) C ($\delta ^*_Q = 620\,{\mathrm {\mu }}{\rm m}$ and $\lambda _{z,D} = 8\,{\rm mm}$).

The spatial organization of the temporal velocity fluctuations presented in figure 14 reveals a striking difference between the supercritical FFS (case C, figure 14Id,IId) and the rest of the cases. In particular, for the clean and critical FFS cases (figure 14Ia–IIc), the maximum temporal velocity fluctuations are spatially located on the outer side of the upwelling region. In contrast, for the supercritical FFS the maximum fluctuations are located on the inner side of the upwelling region. More importantly, for the band $B_{L1}$ figure 14(Id) the maximum temporal velocity fluctuations in the supercritical FFS coincide with the second positive spanwise gradient maxima near the wall ($D_1$ in figure 14Id) while the one in the frequency band $B_{L2}$ overlaps with the region of strong positive wall-normal gradient ($D_2$ in figure 14IId) identified as region (D) in figure 7(IId).

As mentioned earlier, Eppink (Reference Eppink2020b) proposes that the strong positive wall-normal gradient in this region is related to the shear layer, which develops on the top of the recirculation region downstream of the FFS. Interestingly, Eppink (Reference Eppink2020b) identified two distinct frequency bands at which the fluctuations in this region occur and reports that their range closely matches the one expected from flapping ($0.12 U_e/L \leqslant f_F \leqslant 0.2U_e/L$, with $L$ being the mean reattachment length) and shedding ($0.6 U_e/L \leqslant f_S \leqslant 0.7 U_e/L$) frequencies of separated shear layers in two-dimensional boundary layers. The qualitative agreement of the wall-normal gradients (region D on figure 7IId) in this work with the ones reported in Eppink (Reference Eppink2020a, figure 7) indicate the possibility that a strong modulated recirculation region develops downstream of the highest FFS (case C).

Considering that the shedding of the recirculation region may occur at the peak frequency in band $B_{L2}$ (i.e. $f_S \approx 2000\,{\rm Hz}$ in figure 9Ib), a rough estimation of the mean reattachment length ($7.4\,{\rm mm} \leqslant L_E \leqslant 8.6 \,{\rm mm}$) and possible flapping frequency range ($343\,{\rm Hz} \leqslant f_F \leqslant 667 \,{\rm Hz}$) is obtained for the highest FFS case based on the shedding and flapping criteria used in Eppink (Reference Eppink2020b). Although the assumptions in this method are rather crude, the estimated flapping frequency range falls partially within the low-frequency band ($B_{L1}$, figure 9Ia–Ib) at which the power spectrum of the supercritical FFS (case C) strongly differs from the clean baseline one. Moreover, at this low-frequency band $B_{L1}$ (figure 14Id) the maximum velocity fluctuations are also located on the inner side of the upwelling region (i.e. where flow recirculation is expected) and extend towards the wall.

Therefore, the evidence in this work points to a possible connection between the flapping/shedding mechanism described by Eppink (Reference Eppink2020b) and the unsteady disturbances on the inner side of the upwelling region for the supercritical FFS (case C). Nevertheless, the origin of the inner side fluctuations remains unclear, and particularly its relation to the mean flow deformation imparted by the step on the flow. As noted by Eppink (Reference Eppink2020b) a possible recirculation region downstream of the FFS edge is not uniquely dependent on the step height but is also influenced by the amplitude of the CF vortices. Similarly, a second mechanism possibly providing the necessary velocity shears for these fluctuations could potentially be the appearance and development of near-wall Görtler vortices, due to the concave shape of the streamlines as the flow passes the step, similar to the observations presented in Marxen et al. (Reference Marxen, Lang, Rist, Levin and Henningson2009) in a pressure-induced laminar separation bubble. To conclusively determine the stationary and unsteady flow structure in the vicinity of the FFS, fully three-dimensional velocity measurements or numerical simulations are required.

Finally, when comparing the spectral analysis results on the inner (figure 9) and outer (figure 11) side of the upwelling region for this supercritical FFS (case C), it is clear that the power spectrum flattens first on the inner side. These results indicate that the laminar–turbulent transition for this case might not initiate on the outer side of the upwelling region as expected from the typical development of the type I secondary instability. This behaviour will be further assessed in § 6.