4.1 Intermittency detection

Regarding the transition detection method, an intermittency function $\unicode[STIX]{x1D6FE}$ has been computed to detect turbulence as a function of $Re_{kk}$ . In contrast to methods using integral quantities like $c_{f}$ or $H_{12}$ , intermittency does not require $y$ -profiles and is thus very suitable if measurement times are long. The computation follows the work of Zhang et al. (Reference Zhang, Xu, Pollard and Mi2013) and is demonstrated in figure 4. First, the signal $u^{\prime }$ in figure 4(a) is multiplied by its derivative $\text{d}u^{\prime }/\text{d}t$ to enhance the sensitivity to turbulence. The derivative is determined numerically based on wavelet transforms to smooth noisy experimental data (Luo, Bai & Shao Reference Luo, Bai and Shao2006). The detector function is then averaged into a criterion function every $1/100$ times of the signal length and compared to a threshold value which originates from a reference in laminar flow. The reference signal is multiplied by a constant factor in the range 1–10 to allow manual control of the method. These manual adjustments only become necessary when the set-up changes significantly. It has been found that the results do not change significantly as long as reasonable inputs are given. The intermittency function $\unicode[STIX]{x1D6FE}$ is the percentage of turbulence to the total signal length and can be estimated by summing up the parts of the signal where the criterion function is greater than the threshold value. An intermittency of 0 % or 100 % represents laminar or turbulent flow, respectively, and an intermittency of 50 % is the criterion to define the transition Reynolds number $Re_{kk,tr}$ . This value is considered as the ‘midpoint’ of transition (Halstead et al. Reference Halstead, Wisler, Okiishi, Walker, Hodson and Shin1995; Stotz et al. Reference Stotz, Wakelam, Guendogdu and Niehuis2014) and the same criterion has also been used by Fransson et al. (Reference Fransson, Brandt, Talamelli and Cossu2005). To detect this value for a specific configuration, $Re_{kk}$ was increased by increasing the free-stream velocity in steps of $7.5\times 10^{-4}~\text{m}~\text{s}^{-1}$ and evaluating the signal for each velocity at a fixed downstream station $(x,y,z)=(200,1,0)$ , similarly to Fransson et al. (Reference Fransson, Brandt, Talamelli and Cossu2005). Doing this gives illustrations as shown in figure 4(c) where the transition Reynolds number $Re_{kk,tr}$ is at $\unicode[STIX]{x1D6FE}=0.5$ . The results from this method are confirmed by dye streakline visualizations in a visual check. Further, $y$ -profiles have been measured to confirm the Blasius-flow assumption which is necessary to compute $Re_{kk}$ as a function of $u_{k}$ .

Figure 4.

Intermittency computation: (a) streamwise disturbance signal $u^{\prime }$ , (b) detector function $u^{\prime }\,\text{d}u^{\prime }/\text{d}t$ (yellow online), criterion function (solid black line) and threshold value (dashed line, blue online) and (c) intermittency factor $\unicode[STIX]{x1D6FE}$ .

4.2 Transition in the Fransson et al. (Reference Fransson, Brandt, Talamelli and Cossu2005) experiment

The intermittency method was verified for the Fransson et al. (Reference Fransson, Brandt, Talamelli and Cossu2005) experiment with different roughness heights to see if $Re_{kk}$ is a general quantity which can be compared to the literature independent of dimensional quantities such as $k$ or $U_{e}$ . Three different roughness heights $k=3.5$ , 5 and 10 mm have been installed with constant $x_{k}=57.1$ and $\unicode[STIX]{x1D702}=3$ to match the set-up of Fransson et al. (Reference Fransson, Brandt, Talamelli and Cossu2005). Each experiment was done with both isolated elements and one periodic spanwise array of seven elements of the same type with spacing $\unicode[STIX]{x0394}z=10$ to investigate if arrays in numerical simulations with symmetry conditions or in experiments such as Fransson et al. (Reference Fransson, Brandt, Talamelli and Cossu2005) behave similarly. Moreover, the effect of hysteresis was investigated by determining the transition Reynolds number for both increasing and decreasing free-stream velocities.

The results of this parameter study are summarized in figure 5 and table 1. Figure 5 shows transition Reynolds numbers of three different roughness heights, isolated elements versus arrays and increasing (‘UP’) versus decreasing (‘DN’) free-stream velocities. Figure 5 shows that none of these variations change the transition Reynolds number significantly. In particular the size of the roughness has no significant impact on transition, and for practical purposes $Re_{kk,tr}$ can therefore be considered as a general quantity if other parameters such as $k/\unicode[STIX]{x1D6FF}_{1}$ and $\unicode[STIX]{x1D702}$ are not changed. The differences between ‘UP’ versus ‘DN’ are negligible and are in agreement with Klebanoff et al. (Reference Klebanoff, Cleveland and Tidstrom1992) who investigated quasi-steady oscillating roughness heights and found no noteworthy hysteresis. Interestingly, the greatest difference seems to be in isolated versus array of roughness elements. Arrays are less prone to transition than isolated elements in four out of six cases. The spanwise periodicity of streaks seems slightly stabilizing, but this effect is within the given measurement accuracy and has not been investigated further. It can be concluded that the transition Reynolds number for the Fransson et al. (Reference Fransson, Brandt, Talamelli and Cossu2005) experiment in this work is $Re_{kk,tr}\approx 402$ with an accuracy of $\pm 5\,\%$ independent of the choice of $k$ , $U_{e}$ , isolated element or array. Fransson et al. (Reference Fransson, Brandt, Talamelli and Cossu2005) themselves found $Re_{kk,tr}=422$ , which is only $5\,\%$ higher than our result. The higher Reynolds number is probably due to the smaller turbulence intensity of the MTL wind tunnel at KTH Sweden and also within the given accuracy of the measurement. Unfortunately, the same cannot be said about the agreement with Loiseau et al. (Reference Loiseau, Cherubini, Robinet and Leriche2014), who found a theoretical critical Reynolds number of $Re_{k,c,t}=564$ , equivalent to $Re_{kk,c,t}=489$ . This discrepancy is graphically illustrated by the dashed line in figure 5 and is too high to be explained by measurement error. Apparently, transition does not coincide with global instability for this case. Note that Loiseau et al. (Reference Loiseau, Cherubini, Robinet and Leriche2014) reported good agreement with Fransson et al. (Reference Fransson, Brandt, Talamelli and Cossu2005), which may result from a comparison with $Re_{\unicode[STIX]{x1D6FF}_{1}}=U_{e}\unicode[STIX]{x1D6FF}_{1}/\unicode[STIX]{x1D708}$ instead of $Re_{kk}$ . As already explained in the introduction, we prefer the more established parameter $Re_{kk}$ for such a comparison because it is widely used in the literature and incorporates the effect of ‘blockage’ by the roughness more than any other boundary layer parameter.

Figure 5.

Comparison of transition Reynolds numbers $Re_{kk,tr}$ for different roughness heights $k$ with results from the literature.

Table 1.

Verification study with different roughness heights (first three rows) and comparison with the literature (last two rows). In all cases roughness is isolated with $\unicode[STIX]{x1D702}=3$ and $x_{k}=57.1$ .

4.3 Parameter study

The same comparison has been repeated for the parameter study of Loiseau et al. (Reference Loiseau, Cherubini, Robinet and Leriche2014) with different aspect ratios $\unicode[STIX]{x1D702}=3$ , 2, 1 and 0.85. In contrast to the previous comparison, the streamwise station is now variable to obtain a constant height with respect to the displacement thickness $k/\unicode[STIX]{x1D6FF}_{1}=1.83$ . Experimentally, this requires us to reposition the roughness element many times manually. Such a procedure is practically difficult when experiments are long and not necessarily required if the boundary layer grows relatively slowly with $x$ . Similarly to the well-known parallel-flow assumption in theory, the experimental parameter study has been adapted in order for the experimental circumstances to retain the required level of automation. First, a fixed station $x_{k}$ has been determined at which theory predicts the Reynolds number to be critical. Then, only the free-stream velocity has been changed. The fixed station $x_{k}$ at which the roughness was placed in the experiment is provided in table 2. To distinguish $\unicode[STIX]{x1D702}=3$ of the parameter study from the Fransson et al. (Reference Fransson, Brandt, Talamelli and Cossu2005) experiment, the latter case is marked by ‘(F)’ in case of confusion.

Comparing the transition Reynolds numbers determined as shown in figure 6 with the critical Reynolds numbers from theory confirms that there is again a discrepancy, as in the Fransson et al. (Reference Fransson, Brandt, Talamelli and Cossu2005) experiment. The relative deviation (dev.) between $Re_{k,tr}$ and $Re_{k,c,t}$ is given in table 2 and is computed with the formula dev. $=2\times (Re_{k,tr}-Re_{k,c,t})/(Re_{k,tr}+Re_{k,c,t})\times 100$ . Particularly for large aspect ratios, the relative error is large and reduces with smaller aspect ratio. A possible explanation for this phenomenon is related to the smaller receptivity to free-stream turbulence. More importantly, there is an obvious mismatch between theory and experiments for all cases in this parameter study despite the good agreement between the experimental mean flow and theoretical base flow (see § 3). Therefore, global instability may not be the decisive mechanism for transition at moderate Reynolds numbers and globally critical Reynolds numbers can hardly be compared to transition Reynolds numbers from experiments, contrary to what has been attempted by Loiseau et al. (Reference Loiseau, Cherubini, Robinet and Leriche2014). This attempt has also been done by the present authors in a visual attempt to find transition in Puckert et al. (Reference Puckert, Subasi, Rist and Gunes2015) but without the accuracy of a quantitative measurement technique. The relevance of global instability in roughness-induced transition must be different and the next section aims at shedding light on this apparent discrepancy.

Table 2.

Transitional and critical Reynolds numbers with deviations from theory (Loiseau et al. Reference Loiseau, Cherubini, Robinet and Leriche2014).

Figure 6.

Intermittency of different aspect ratios $\unicode[STIX]{x1D702}$ . $Re_{k,tr}$ is provided in table 2. Probe position $(x,y,z)=(200,1,0)$ with 100 s measurement time for each Reynolds number.

6.1 Amplifier

A low subcritical Reynolds number of $Re_{k}=430$ was chosen in this experiment to reduce the influence of uncontrolled background noise. The horizontal vibrating wire has been installed at $(x,y)=(-7,0.9)$ upstream of the roughness element to introduce controlled disturbances with a forcing frequency of $\unicode[STIX]{x1D714}=0.73$ (2 Hz), close to the expected frequency of the stable global mode $\unicode[STIX]{x1D714}_{t}=0.8$ at $Re_{k}=550$ : see Loiseau et al. (Reference Loiseau, Cherubini, Robinet and Leriche2014). This frequency is damped in an undisturbed Blasius boundary layer, but convective amplification may happen in the presence of roughness. Fine mechanical adjustment of the forcing generator’s eccentric wheels has been done to increase the wire oscillation amplitude linearly from 0 to 0.2 mm in steps of 0.025 mm. Figure 11(a) shows 5 s excerpts of the time signals measured at $(x,y,z)=(12,1,0)$ for increasing wire oscillation amplitudes. The $x$ -position is chosen far enough from the recirculation zone and also far enough from possible transition. From their envelopes it is obvious that the oscillation amplitudes are well controllable by the amplitude of the forcing wire. A more quantitative impression is given in figure 11(b), which shows the fluctuation r.m.s. as a function of wire amplitude for both undisturbed flow and roughness-disturbed flow. In the undisturbed flow, the fluctuation increases linearly with increasing forcing amplitude. This is exactly what is expected from a convective instability that evolves as a wave-like disturbance in the linear regime of the flow: $u_{rms}^{\prime }/U_{e}\sim A_{wire}$ where the control parameter is the wire oscillation amplitude $A_{wire}$ . The same is true for the roughness-disturbed flow, but linear dependency is only valid up to ${\sim}3.5\,\%$ of $U_{e}$ . A flow is typically considered linear up to $1\,\%$ fluctuation amplitude. However, in practical applications the nonlinear terms can often be neglected even for higher fluctuation amplitudes. The linear relation between forcing amplitude and response amplitude proves that the roughness acts as an amplifier of convective disturbances in the subcritical regime and it can be assumed that the amplification rate is a function of Reynolds number, which has been fixed in this experiment. Here, the controlled disturbances have been amplified by a factor of approximately 12 by the roughness. When the oscillating wire amplitude is further increased and the disturbance amplitude grows beyond $3.5\,\%$ of $U_{e}$ , nonlinear saturation sets in and the disturbance amplitude increases similarly to a square-root function. Depending on the stability of the downstream boundary layer, this disturbance may develop into turbulence. Variations of frequency lead to similar observations but with different amplification factors.

Figure 11.

Forced roughness for $(\unicode[STIX]{x1D702},Re_{k})=(3,430)$ with horizontal wire amplitude $A_{wire}$ being the control parameter. (a) Time signals with increasing $A_{wire}$ every 5 s, (b) r.m.s. of streamwise fluctuation velocities.

6.2 Wavemaker

At higher Reynolds numbers, the flow dynamics may change from amplifier to wavemaker due to an unstable self-sustained global mode. If the global instability is purely hydrodynamic without a far-field feedback loop, it necessarily requires a region of local absolute instability within the WKBJ (Wentzel–Kramers–Brillouin–Jeffreys) approximation as shown by Chomaz et al. (Reference Chomaz, Huerre and Redekopp1991) and Monkewitz et al. (Reference Monkewitz, Huerre and Chomaz1993) for general conditions. The region of local absolute instability nurtures a globally unstable mode by shedding upstream and downstream travelling waves, in contrast to local convective instabilities which shed only downstream travelling waves. The temporal evolution of disturbances is investigated here by introducing a wavepacket to the same geometric set-up as previously, but this time the vibrating wire is activated only for the first 6 s and remains off for the remaining 44 s at each measurement point. The probe has been placed at $(y,z)=(1,0)$ and four different streamwise stations at $x=10$ , 20, 30, 40. The time signals have been recorded five times and ensemble-averaged to reduce random influences. The excitation frequency has been chosen constant at 3 Hz, which is still close to the most receptive frequency expected in the vicinity of the critical Reynolds number, as in the previous section. The higher frequency is due to the higher Reynolds numbers in this experiment. Repeating the acquisition of ensemble-averaged time signals for different Reynolds numbers gives the contour plots of figure 12, where greyscale shows the normalized disturbance magnitudes of ensemble-averaged time signals at different Reynolds numbers. Disturbances in figure 12(a) have peak magnitudes at approximately $t=2$  s and 8 s due to transient effects when the wire is switched on and off. The time difference from $t=0$  s to 2 s is the time required by the wavepacket to travel from its source to the probe location for the case $x=10$ in figure 12(a). At more downstream probe stations, the front and trailing edges of the wavepackets appear at later times, as can be seen in figure 12(a–d), because the wavepackets need to travel over longer distances from their source to the probe. In contrast, the wavepacket front and trailing edges appear earlier when increasing the Reynolds number due to higher convection velocities. Remarkably, the wavepacket trailing edge becomes slower in all plots when the Reynolds number is increased. A similar phenomenon is reported in experiments on rotating disc flows by Lingwood (Reference Lingwood1996) and has been explained by the rise of an absolute instability. The hydrodynamic feedback of upstream and downstream travelling waves is similar here and can be explained by a global instability which is most likely based on a sufficiently large region of absolute instability. The threshold at which this happens has already been detected and the graphs of figure 12 show interesting features at the experimental critical Reynolds number $Re_{k,c,e}=556$ . In figure 12(b) the light grey disturbance magnitudes approach this value asymptotically, in (c) there is even a strip of low disturbance magnitude below $Re_{k,c,e}=556$ and in (d) this strip becomes thicker, separating the sub- from the supercritical regime most obviously. A precise detection of a threshold is difficult with figure 12, because convective instabilities partially overshadow the changeover to global instability. With this experiment, however, it is shown that the wavepacket trailing edge velocity becomes slower with increasing Reynolds number and is eventually zero or negative. This confirms the existence of a global instability in the dark regions at high Reynolds numbers and convective instability at low Reynolds numbers.

Figure 12.

Ensemble-averaged disturbance evolution versus $Re_{k}$ at (a) $x=10$ , (b) $x=20$ , (c) $x=30$ and (d) $x=40$ .

The coexistence of both convective and global instabilities is schematically drawn in figure 13. In the subcritical regime, convective instabilities (CI) prevail and background noise can be amplified to large amplitudes due to the influence of the roughness. The supercritical regime begins at $Re_{k,c,e}$ with a region of global instability (GI). The dashed line symbolizes the evolution of wavepacket leading and trailing edges.

Figure 13.

Schematic of instability regions derived from figure 12.

6.3 Varicose versus sinuous mode

It is known from both early and more recent experimental literature that hairpin vortex shedding begins when the Reynolds number is high enough. Hairpin vortices are in general symmetric (varicose) with respect to the streamwise centreline whereas other famous examples of vortex shedding such as the von Kármán street behind 2-D cylinders are antisymmetric (sinuous). In the work of Loiseau et al. (Reference Loiseau, Cherubini, Robinet and Leriche2014), the first unstable global mode is of varicose nature if the roughness aspect ratio is large ( ${\geqslant}2$ ) but sinuous if the aspect ratio is small (1 or below). The agreement for large aspect ratios is good as already shown by Puckert et al. (Reference Puckert, Subasi, Rist and Gunes2015); however, to the authors’ knowledge there is no reported experimental observation of sinuous von Kármán-type vortex shedding behind 3-D roughness elements embedded into a boundary layer. This apparent disagreement with the work of Loiseau et al. (Reference Loiseau, Cherubini, Robinet and Leriche2014) is investigated here by means of PIV.

PIV snapshots in the $xz$ -plane at the height of the roughness are shown in figures 14 and 15. Greyscale represents the magnitude of the instantaneous in-plane velocity, showing the unsteady streaky wake of the roughness element with the roughness being highlighted light grey for clarity. In the case of a large aspect ratio $\unicode[STIX]{x1D702}=3$ (F) (see figure 14), the disturbance symmetry is clearly symmetric with respect to the spanwise centreline. Here, the Reynolds number $Re_{k}=700$ is supercritical and thus supports the observation of a leading unstable varicose mode from global LST. However, the symmetric unsteadiness can also be seen for lower Reynolds numbers in the subcritical regime due to amplification of background noise (Puckert & Rist Reference Puckert, Rist, Dillmann, Heller, Krämer, Radespiel and Wagner2016; Bucci et al. Reference Bucci, Puckert, Andriano, Loiseau, Cherubini, Robinet and Rist2018). Therefore, global and convective instability cannot be clearly distinguished based on mode symmetry for this kind of configuration.

Figure 14.

PIV snapshot of the $xz$ -plane with $\unicode[STIX]{x1D702}=3$ , $x_{k}=57.1$ and $Re_{k}=700$ .

Figure 15.

PIV snapshots of the $xz$ -plane with $\unicode[STIX]{x1D702}=1$ , $x_{k}=166.4$ for (a) $Re_{k}=990$ , (b)  $Re_{k}=1130$ and (c) $Re_{k}=1230$ .

Interestingly, this is different for small aspect ratios. Figure 15 shows three snapshots for $\unicode[STIX]{x1D702}=1$ at increasing Reynolds numbers. On the one hand, the leading disturbance in figure 15 is clearly symmetric for $Re_{k}=990$ (figure 15 a), but on the other hand it becomes antisymmetric for $Re_{k}=1230$ (figure 15 c). At an intermediate Reynolds number $Re_{k}=1140$ (figure 15 b) the unsteadiness can be understood as a mixture between symmetric and weakly antisymmetric disturbances. Supplementary movie 1, available at https://doi.org/10.1017/jfm.2018.211, demonstrates this changeover even more descriptively. In this experiment, the water channel velocity has been continuously increased to increase the Reynolds number. The free-stream velocity has been measured simultaneously to the PIV measurements with a hot-film probe and with this information, the instantaneous Reynolds number can be provided. The movie shows clearly how the patches of velocity excess and deficit alternate symmetrically in the subcritical regime and antisymmetrically in the supercritical regime. Obviously there must be a changeover in the competition between varicose and sinuous modes when the Reynolds number is increased. Moreover, this changeover occurs close to the theoretical critical Reynolds number $Re_{k,c,e}=1040$ and it can be deduced that this observation is due to the unstable global sinuous mode found by Loiseau et al. (Reference Loiseau, Cherubini, Robinet and Leriche2014) for thin aspect ratios. To our knowledge, there has not been any experimental observation of a sinuous disturbance behind isolated roughness elements before, probably due to the strong influence of convective hairpin shedding. At subcritical Reynolds numbers the varicose disturbance dominates because the sinuous global mode is stable. Note that in a physical flow, the two modes coexist and interact nonlinearly with each other. As a result, the sinuous mode can remain hidden in visual observations.

This is demonstrated in figure 16. The pictures show dye streakline visualizations with potassium permanganate around and on top of the roughness with $\unicode[STIX]{x1D702}=1$ for two different Reynolds numbers. Hairpin vortices can be seen downstream of the roughness in both the subcritical (figure 16 a) and supercritical regimes (figure 16 b) . Apparently, the varicose hairpin shedding is still active in the supercritical regime despite the globally unstable sinuous mode. Although the basic mechanism of the convective varicose disturbance is different from the global sinuous mode, both disturbances grow to nonlinear saturation at high Reynolds numbers. When the critical Reynolds number is exceeded, the roughness is both amplifier and wavemaker. As a result, there is competition between globally unstable modes from the intrinsic system dynamics and highly amplified external noise. Strong convective growth can outweigh the temporal growth of global modes, and the sinuous oscillation predicted by Loiseau et al. (Reference Loiseau, Cherubini, Robinet and Leriche2014) may thus only dominate in extremely low turbulence environments. When looking closely at the legs of the hairpin vortices in figure 16(b), one can see antisymmetric wiggling submerged in the overall varicose shedding. Similar visualizations have been done for many different roughness elements of various shapes, some of them available in Puckert et al. (Reference Puckert, Subasi, Rist and Gunes2015), and in none of these cases could a clear von Kármán-type vortex shedding be observed. Instead, the shedding seems rather influenced by different modes.

Figure 16.

Potassium permanganate visualization of $\unicode[STIX]{x1D702}=1$ with (a) $Re_{k}=820$ and (b)  $Re_{k}=1080$ .

The remaining question is whether the stable sinuous mode in the subcritical regime can also be forced similarly to the varicose mode. This is demonstrated in an experiment with symmetric and antisymmetric disturbance sources to force both varicose and sinuous modes. The Reynolds numbers for this experiment are in the subcritical regime and forcing frequencies were chosen according to expected maximum amplification in theory. Either the horizontal or vertical disturbance generator is installed at a time and the goal of this experiment is to demonstrate the sensitivity of the subcritical flow to both varicose and sinuous modes. The roughness with $\unicode[STIX]{x1D702}=1$ is again placed at $x_{k}=57.1$ and both Reynolds numbers and forcing amplitudes are carefully adjusted to obtain detectable disturbances. The signal-to-noise ratio needs to be as high as possible, but too large Reynolds numbers or forcing amplitudes can lead to uncontrolled vortex shedding which can disturb phase-locked hot-film measurements. It turned out that antisymmetric forcing needs to be much stronger than symmetric forcing due to shear sheltering at the edge of the boundary layer (Hernon, Walsh & McEligot Reference Hernon, Walsh and McEligot2007). Higher excitation amplitudes are thus required.

Figure 17.

Varicose forcing with $f_{f}=0.7~\text{Hz}$ ( $\unicode[STIX]{x1D714}=0.68$ ) at $Re_{k}=620$ , $\unicode[STIX]{x1D702}=1$ .

Figure 18.

Sinuous forcing with $f_{f}=0.65~\text{Hz}$ ( $\unicode[STIX]{x1D714}=0.56$ ) at $Re_{k}=694$ , $\unicode[STIX]{x1D702}=1$ .

Figures 17 and 18 show the phase-locked measurements in $xz$ -slices for the symmetric and antisymmetric forcing, respectively. The spatial resolutions in the $x$ and $z$ directions are $0.5$ and $0.25$ , respectively, and the measurement time was 30 s at each position, adding up to a total measurement time of 14 h. Figures 17 and 18 show remarkably well that both sinuous and varicose modes can be forced if parameters are chosen correctly. For the varicose mode this was expected; however, forcing of the sinuous mode is a relatively new technique (see Shin et al. Reference Shin, Rist and Krämer2015). With this method it could be demonstrated that von Kármán-type instabilities grow when the respective forcing is strong enough. Sinuous modes can thus also develop convectively, similarly to the varicose disturbances which account for hairpin vortex shedding. Although theoretical data of these cases are not at hand, there is qualitative agreement with global mode shapes in Loiseau et al. (Reference Loiseau, Cherubini, Robinet and Leriche2014). Both forced convective instabilities can (quasi-)resonate (Bucci et al. Reference Bucci, Puckert, Andriano, Loiseau, Cherubini, Robinet and Rist2018) in the roughness wake. The reason for the hairpin vortex shedding in most experimental facilities is therefore due to (i) rather varicose background noise and (ii) higher growth rates of the varicose mode behind the roughness. Nevertheless, the predicted sinuous mode can also be found experimentally with the right environmental conditions.