12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022

THE NEAR-WAKE OF DISCRETE ROUGHNESS ELEMENTS ON SWEPTWINGS: TOMOGRAPHIC PTV MEASUREMENTS

Giulia Zoppini
Theodoros Michelis
AWEP Department-Aerodynamics AWEP Department-Aerodynamics
Delft University of Technology
Delft University of Technology
The Netherlands, 2629HS
The Netherlands, 2629HS
g.zoppini@tudelft.nl
t.michelis@tudelft.nl

Daniele Ragni
Marios Kotsonis
AWEP Department-Wind Energy-Aeroacoustics AWEP Department-Aerodynamics
Delft University of Technology
Delft University of Technology
The Netherlands, 2629HS
The Netherlands, 2629HS
d.ragni@tudelft.nl
m.kotsonis@tudelft.nl

ABSTRACTstudies dedicated to stationary CFI adopting this technique,only few numerical simulations focussed on the investigationof the near-element flow features and the receptivity process(Brynjell-Rahkola et al., 2015; Kurz & Kloker, 2016). This
relates to the limited experimental access to the small regionof interest, as well as to the numerous parameters involved in
the relation between the external disturbances and CFI onset.
The numerical simulations conducted by BrynjellRahkola et al. (2015) and Kurz & Kloker (2016), identified
the development of a horseshoe vortex system around and aftof the element, in analogy with 2D-BL flows (Baker, 1979). A
low-speed streak develops in the elements’ wake, surroundedby two adjacent high-speed streaks. The presence of the crossflow velocity component in the baseflow, introduces a significant asymmetry in the flow features, leading to a flow fielddominated by the crossflow direction of rotation. Accordingly, all the structures co-rotating with the crossflow are sustained in their downstream evolution, while the counter rotating structures are dampened. The discussed DNS studies, provide significant insights regarding the near-DRE flow topology
and the instabilities development, however they still lack a fullcharacterization of the receptivity process relating the external
forcing to the CFI onset. Additionally, numerous experimental and numerical works investigating roughness elements in
2D-BL flows, identified transient mechanisms as fundamental for the near-wake development (White et al., 2005; Breuer& Kuraishi, 1994; Cherubini et al., 2013). Therefore, the initial growth of transient near-wake instabilities is a fundamental
part of the receptivity process, eventually setting the onset amplitudes for the modal CFI.
The present work provides the first experimental investigation of the near-DRE flow field, aiming at further clarifying the receptivity process and the flow features dominating
the CFI onset. The measurements are conducted through specialized high-magnification tomographic particle tracking velocimetry (PTV), acquiring 3D velocity fields in the element
vicinity, while modifying the DRE height. The collected experimental data, provide a characterization of the near-element
flow topology, identifying the dominant flow structures andtheir organization. The structures downstream evolution isThis work presents the first reported experimental characterization of the flow field in the direct vicinity of discreteroughness elements (DRE), in a swept wing boundary layer.
High magnification tomographic Particle Tracking Velocimetry (3D-PTV) measurements are used to acquire time-averaged
velocity and standard deviation fields in a 3D volume directly
aft of the DRE elements. The collected data detail the nearelement flow topology, providing information on the developing wake and emerging flow structures, their organization andamplitude evolution. A transient growth behaviour is identified in the element wake, while onset and growth of crossflow
instabilities is observed further downstream. As such, the nearelement flow is confirmed to be a fundamental part of the receptivity process, contributing in setting the initial amplitudes
for the crossflow instability evolution.

INTRODUCTION
Laminar to turbulent transition of swept wing boundary layers (BL) in low freestream turbulence environments, isdominated by the development of stationary crossflow instabilities (CFI, Bippes, 1999; Wassermann & Kloker, 2002; Saric
et al., 2003; Serpieri & Kotsonis, 2016). One of the most challenging and least described phases of the CFI development,is receptivity (Mack, 1984), defined as the process throughwhich the external disturbances (mainly freestream turbulenceand surface roughness) enter the boundary layer leading to theonset of instabilities. Previous investigations, proved that thestationary CFI are mostly affected by surface roughness (Saric
et al., 2003; Downs & White, 2013). This sensitivity is typically profited towards obtaining a more uniform flow fielddominated by a monochromatic crossflow mode. Specifically,
discrete roughness elements (DRE) can be arranged in a periodic array along the wing span with a fixed element spacing corresponding to the desired mode wavelength (Reibert
et al., 1996; Saric et al., 1998; Serpieri & Kotsonis, 2016).
The use of DREs to condition experimental or numerical CFI
configurations is well established, albeit governed by a littleunderstood receptivity process. However, of the numerous

112th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022
(Wieneke, 2012) to identify the particle trajectories in the acquired 3D volume. Binning and conversion to a Cartesian gridof the obtained particle tracks, are performed through an inhouse developed Matlab routine. The final vector spacing isapproximately 0.25mm in the xz plane, and 0.04mm along y.
Time-averaged (u, v, w) and standard deviation (u0 , v0 , w0 )velocity fields are obtained for all three velocity components
in the x,y,z domain. For the sake of brevity, the main data processing techniques adopted in this work, are briefly describedhereafter as only applied to u. The treatment of v and w follow
a similar procedure. The wall-normal BL evolution (ub ) is estimated by averaging the u velocity signal along z for each fixed
xy location acquired (i.e. ub ). The freestream velocity u∞ isestimated as the average of ub for y > δ99 . The disturbance velocity field (ud ) can be computed as ud = u(x, y, z) − ub (x, y).
An estimation of the wall-normal evolution of the perturbations in the boundary layer is then obtained by computing huiz ,i.e. the root mean square (rms) of the ud velocity signal along z
for each fixed x,y-location (Reibert et al., 1996; Tempelmann
et al., 2012). Furthermore, a spatial Fourier analysis is performed on the spanwise velocity signal at each x,y-location(FFTz (u)), in order to characterize the development of thedominant crossflow mode and its harmonics. Finally, the total
perturbation amplitude as well as the individual Fourier modes
amplitudes are estimated by respectively integrating the huiz
profile or the corresponding Fourier shape function along y,following the integral amplitude definition by Downs & White(2013); Reibert et al. (1996). This provides an estimation of
the modes growth and evolution along the airfoil chord, alongwith information on the CFI onset amplitude.

analysed estimating the instabilities amplitudes and spectral
composition, allowing for the identification of transient mechanisms occurring in the element near-wake.

METHODOLOGYWind Tunnel, Swept Wing Model and DREs
The presented measurements are performed on an inhouse designed swept wing model (M3J), with constant chord
c=1273mm and sweep angle 45◦ (Serpieri, 2018). The wingmodel features a favourable pressure gradient up to x/c=0.63,
thus allowing investigation of primary and secondary CFI and
BL transition (Serpieri & Kotsonis, 2016).
The measurements are performed in the low speed low
turbulence wind tunnel, an atmospheric closed return tunnel at
the TU Delft, featuring low freestream turbulence level in thetest section flow (Serpieri, 2018). The flow fields are acquired
at a fixed angle of attack (α=-3.36◦ ) and freestream Reynolds
number (Rec =2.17 × 106 ). The reference system used in thisinvestigation (x,y,z and corresponding velocities u,v,w) has its
x and z axes orthogonal and aligned to the leading edge, respectively.
Following Reibert et al. (1996), DRE arrays are applied on the wing in order to focus the developing CFI ona single monochromatic mode. The forced mode is chosen to coincide with the most critical wavelength λ1 =8mm
for the present conditions, as indicated by previous investigations and linear stability simulations (LST, Malik et al.,
1999; Serpieri, 2018). The array elements have a cylindrical shape with nominal diameter d'2mm. To gain better access to the experimental domain of interest, DREs are applied
at a fixed chord location of x/c=0.15 (Zoppini et al., 2022).
Three different element heights are considered throughout thiswork, k1 =0.1mm, k2 =0.2mm and k3 =0.3mm, corresponding
to roughness Reynolds numbers of Rek1 =25, Rek2 =90 andk×|u(k)|, Gregory & Walker, 1956).
Rek3 =190 (Rek =ν

RESULTS DISCUSSION
The investigation of the time-averaged velocity fields, allows for the direct characterization of the near-element flow
topology and of the stationary perturbations. Figure 1 shows
the ud (figures (a-c)), and u0 contours (figures (d-f)) for a BL
forced with Rek3 . Both the xz and yz planes reported in figures 1(a-c), indicate that a low-speed streak develops aft ofeach cylindrical element, in correspondence to the element’s
wake. The low-speed wake is accompanied by two high speed
streaks developing on its sides. The latter correspond well tothe horseshoe vortex legs wrapping around and extending aftof the elements, which induce a momentum redistribution process leading to the streak formation (Kurz & Kloker, 2016;
Baker, 1979). In between the elements, the flow maintains
a laminar behaviour, as the introduced perturbations are relatively weak in amplitude. This is confirmed by the velocity
contours in the yz plane extracted at x1 =0.154c (figure 1(b)),
which show that the developing streaks structures only affectthe near-wall BL region (i.e. up to y'0.5δ99 ), without introducing the boundary layer velocity modulation typical of CFI.
The developing flow topology closely resembles the nearwake flow features incurred by isolated roughness elements
in 2D or 3D-BL (e.g. Brynjell-Rahkola et al., 2015; Kurz &Kloker, 2016; Baker, 1979; Loiseau et al., 2014). The maindifference between the flow features pertaining to the two BL
is linked to the overall flow asymmetry introduced by the presence of the crossflow velocity component in the baseflow. Thisis clearly visible in the presented results, as the high speed
streaks developing on the two sides of the wake, undergo adifferent growth and evolution process. In particular, in figure 1(a) the outboard high-speed streak (full line) is decaying being substituted by an outer low-speed streak (dash-dotline); while the inboard high-speed streak (dashed line) per-Tomographic PTV
The instantaneous velocity distribution is measured
through a tomographic velocimetry configuration (Elsinga
et al., 2006) in a 3D domain centred at x/c=0.165 and extending for 35×3.5×35mm along x,y,z. The three directions are
non-dimensionalized by the chord, δ 99 (i.e. the δ99 of the laminar boundary layer at x/c=0.15) and λ1 respectively.
The light source is a Quantel Evergreen Nd:YAG dual
cavity laser (200 mJ pulse energy), optically accessing the test
section through a plexiglass window. Through suitable optics,
the laser beam is shaped in a 4mm thick sheet parallel to thewing surface in the area of interest. The flow is imaged through4 sCMOS LaVision Imager cameras equipped with a 2X teleconverter, a 200mm lens and a lens-tilt mechanism to comply
with the Scheimpflug condition. This optical arrangement results in a 400mm focal length for each camera, with f# =11 inorder to keep the particles in focus throughout the entire volume depth. The cameras are installed on the outer side of thetest section with a tomographic aperture of approximately 45◦ .
The model surface is at '1m distance, resulting in a resolutionof 67px/mm. Flow seeding is obtained by dispersing 0.5µm
droplets of a water-glycol mixture in the wind tunnel.
For each considered case, 4000 image pairs are acquired
at a frequency of 15Hz. The time interval between paired images is 8µs, corresponding to a freestream particle displacement of almost 10 pixels. Each image pair is processed in
LaVision DaVis 10 through a 2-pulse shake-the-box algorithm

212th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022

1

1

0

0

-1

-1

-2

-2

0.15 0.155 0.16 0.165 0.17 0.175

0.15 0.155 0.16 0.165 0.17 0.175

1

1

0

-2

-1

0

1

1
0

0

1

-2

-1

0

1

-2

-1

0

1

0

0

0.05

0.1

0

0.05

0.1

1

1
-2

-1

0

1

0

0

Figure 1. Contours of (a-c) ud and (d-f) u0 for Rek3 =192 forcing. Time-averaged ud fields (a, d) in the xz plane at y=0.17δ 99 ; (b, e)
in the yz plane at x1 =0.154c (vertical dashed line in (a)), and (c, f) at x2 =0.176c (vertical dash-dot line). (h, i) Velocity disturbance
profiles huiz at x1 and x2 for all three velocity components.

sists in the flow, with lowered amplitudes, up to the end of theacquired domain. As a result, the far-wake flow evolution isdominated by a simple high- and low-speed region alternation,
given by the downstream development of the inboard highspeed streak and the outer low-speed streak respectively. Thisis confirmed by the velocity contours collected in the downstream yz plane (x2 =0.176c, figure 1(c)), showing that the disturbances are affecting the whole boundary layer wall-normal
extent, thus modulating the baseflow. The spanwise modulation of the BL velocity and momentum visible in figure 1(c),is a typical feature of CFI development (Bippes, 1999; Saric
et al., 2003) . Nonetheless, the identified flow features describe a BL only weakly affected by CFI, as the acquired flow
domain is only representative for the CFI initial growth stages
mostly unaffected by non-linearities. Finally, all the observed
streak structures appear to be developing at an angle of almost
6◦ with respect to the freestream direction. This value is comparable to the angle predicted by LST as well as to the angle measured between the developing crossflow vortices andthe freestream velocity in the same set-up at more downstream
chord locations (Serpieri & Kotsonis, 2016).

again in agreement with studies dedicated to isolated roughness elements, suggesting that the developing near-wake instabilities are strongly related to the shear layers characterizing
the near-wake flow region (figure 1(e), Brynjell-Rahkola et al.,2015; Klebanoff et al., 1992). Overall, the fluctuations level
reduces as the flow evolves downstream and localizes in correspondence of the inboard high-speed streak. This is accompanied by the growth of the instability structures size along
the y direction (figures 1(h-i)), which is also connected to thenatural thickening of the BL.
To further characterize the observed flow features, a spatial Fourier analysis of the span-wise ud velocity signal is performed. Figure 2(a) shows the spectra development in the x-λz∗
plane extracted at y/δ =0.17. The forced λ1 mode is clearlypresent in the flow field corresponding to a significant spectralenergy peak. However, in the near-wake region (i.e. at x1 ),the λ1 mode development is accompanied by strong harmonics
content. This effect can be associated to the pseudo-pulse behaviour of the DRE wake, which contains all spatial frequencies due to its highly localised form. The observed modes,
however, are not necessarily instability modes, as it is the finite diameter of the DRE that is responsible for the observed
energy distribution. In particular, up to 51% of the total perturbation spectral energy is contained by the dominant mode
and its first four harmonics, confirming these modes absorb the
majority of the flow energy. At the most downstream locationconsidered (x2 =0.176c), the spectra peaks reach overall lower

The u0 contours (figures 1(d-f)) reflect the stationary
streak organization and development described above. Morespecifically, in the element vicinity, stronger velocity fluctuations are localized in correspondence of the low-speed streak,slightly shifting towards the region between the outboard highand low-speed streaks as moving downstream. This is once3

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022

2

2

2

1

1

0

0

2

2

1

1

0.04
1
0.02
0

0

2
0.04
1
0.02
0

0
0.155 0.16 0.165 0.17 0.175

0

0.02

0
0

0.5

1

1.5

2

0
0

0.05 0.1

0 0.025 0.05

0.04

Figure 2. Spanwise Fourier analysis of ud for forcing at (a-d) Rek3 and (e-h) Rek2 . (a, e) Spectra in the x-λz plane. (b, f) Spectra
extracted at fixed x and y with x1 =0.154c; x2 =0.176c; y1 =0.17δ 99 ; y2 =0.6δ 99 . (c, g) huiz profile and λ1 shape function at x1 and (d, h)
at x2 . LST λ1 shape function (gray - - profile), element height (horizontal full line).

amplitude values, and the λ1 mode is now evidently dominating the flow evolution only accompanied by weak λ2 and λ3
harmonics (figure 2(b)). This aspect can be further investigatedby comparing the λ1 mode shape functions extracted from theFourier analysis with the huiz profile for the two considered
chord locations, as shown in figure 2(c). At x1 , the two profiles show a comparable shape, however their maximum amplitude significantly differs. This can be related to the high energy contained in the harmonic modes, which contribute to thenear-wake flow perturbations development. On the other hand,
at x2 where the λ1 mode dominates the flow development, thecorresponding shape functions satisfactorily describe the total
flow perturbation. The spectra reported as dash-dot lines in∗figure 2(b) are extracted at a higher wall-distance (y/δ =0.6).
At this y location, the near-wake spectra extracted at x1 showsno relevant modal content. This is in agreement with figure
1(c, d), as the upper half of the boundary layer is still mostly
unaffected by flow perturbations in this flow region. Instead, at
x2 , the spectra extracted at the two wall-normal locations (figure 1(b)) display comparable features, with the dominant peakcorresponding to mode λ1 accompanied by weaker harmonics. A similar analysis is reported for the Rek2 case (figures2(d-f)), showing comparable flow characteristics, despite theoverall smaller amplitudes and spectral energy of the developing instabilities.

tonically decaying as evolving downstream. Comparable behaviour is expected for the Rek1 forcing case, however is it hindered by the overall weaker instabilities. Thus, this case is disregarded in the following analysis. A relative streak amplitude
metric is as well computed, following the definition given byAndersson et al. (2001), i.e. AAnd =0.5*(max(ud ) - min(ud )).
The resulting amplitude trends are reported in figure 3(b), andconfirm that mild instability growth occurs in the near-wake,
followed by an amplitude decay. Additionally, none of theconsidered cases reaches an amplitude value higher than thecritical threshold identified by Andersson et al. (2001) for thelaminar structure breakdown (i.e. AAnd =0.2u∞ ).
The observed initial instability growth is further investigated by analysing the integral total perturbation amplitude
and the individual Fourier modes amplitude, estimated following the definition given by Downs & White (2013). The resulting trends are reported in figure 4 for Rek3 and Rek2 , showing comparable flow features. Apart from the initial amplitudedecay, the total perturbation amplitude shows little chordwise
variations within the acquired domain. Nonetheless, the modal
amplitude associated to λ1 significantly decays immediately
aft of the element. The λ1 mode recovers amplitude values
comparable to the total perturbation further downstream (i.e.
downstream of x/c=0.165), indicating that it dominates the BL
evolution in this flow region. The second harmonic λ2 follows a comparable trend, retaining lower amplitude values up
to the domain end. However, the higher harmonics (λ3 -λ6 ) allshow a mild amplitude growth in the element vicinity, sustaining the total perturbation amplitude. These modes all decay
shortly downstream, leaving a boundary layer dominated by
the primary stationary mode. The spectral energy distribution
among individual Fourier modes closely resembles the observations by White et al. (2005), and suggests that a transientmechanism (possibly transient growth, Schmid & Henningson, 2001) driven by the stationary mode harmonics dominates

From the ud and u0 analysis of figure 1, an initial growthphase can be identified for both the high- and low-speed
streaks amplitudes in the near-wake region. More specifically, figure 3(a) quantifies the chordwise evolution of thehigh-/low-speed streak amplitudes (Astr ) computed as maximum/minimum value of the ud velocity field respectively. The
amplitude trends extracted for Rek2 and Rek3 forcing, show
a mild growth of the high-speed structures in the near-wakeregion, followed by an amplitude decay shortly downstream.
The low-speed structures absolute amplitude is instead mono-412th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022
0.3

0.5

0.2
0
0.1
-0.5

0
0.152 0.154 0.156 0.158 0.16 0.162 0.164

0.152 0.154 0.156 0.158 0.16 0.162 0.164

Figure 3. Amplitude analysis for varying Rek (i.e. DRE amplitude). (a) Streak amplitude Astr for high-speed (full line) and low-speed(-. lines) streaks; (b) Andersson amplitudes AAnd and amplitude limit for laminar streak breakdown (-. line) (Andersson et al., 2001).

10-1

10-1

10-2

10-2

10-3

10-3
0.15

0.155

0.16

0.165

Total

Figure 4.

0.17

0.175

1

2

0.15
3

0.155

0.16

0.165

4

5

6

0.17

0.175

Aint for the total disturbance field and for the λ1 − λ6 Fourier harmonics for forcing cases (a) Rek3 and (b) Rek2 .

the near-wake flow evolution. Despite its short chordwise extent, a non-modal growth mechanism can lead to rapid initial
growth of the near-wake instabilities, enhancing their downstream development. Eventually, such transient process contributes to setting the onset conditions for the CFI (Breuer &Kuraishi, 1994; Lucas, 2014), becoming a fundamental step in
receptivity.
Based on the previous considerations, the onset of modal
CFI would occur downstream of the transient process identified in the near-wake flow region. Following this hypothesis,
the CFI onset amplitude A0 can be estimated as the amplitudeachieved by the λ1 mode at x/c'0.164 (i.e. '9.5d downstreamof the elements). Figure 5(a) shows the total perturbation
amplitude Aint reaches a minimum value around x/c'0.164,
modally growing further downstream. In fact, the primary stationary mode contains almost 80% of the total perturbationenergy at this chord location, dominating the BL evolution.
Accordingly, the A0 estimation delivers a representative value
for the CFI onset amplitude corresponding to A0 '0.024u∞
for Rek3 , A0 '0.012u∞ for Rek2 . Using the extracted A0
value, an effective N-factor (Saric et al., 2019) can be computed from experimental data as Neff =log(Aint /A0 ), describing
the CFI modal evolution downstream of x/c=0.164. The resulting growth curves are reported in figure 5(b) compared tothe effective N-factor extracted for the λ1 mode from the LST(NLST Serpieri, 2018). The experimental growth trends andthe numerical solution show a satisfactory match, confirming
the exponential (i.e. modal) growth process followed by the
instabilities downstream of x/c=0.164.

through high-magnification tomographic PTV. The flow field
is forced by applying critically spaced DRE arrays at x/c=0.15
for various forcing amplitudes. Time-averaged and standard
deviation velocity fields are acquired in a 3D volume locatedimmediately downstream of the DRE.
The near-element stationary flow topology is dominatedby a low-speed streak located in correspondence of the element wake, while two high-speed streaks develop on its sides.
The presence of the crossflow velocity component in the baseflow induces a 6◦ misalignment between the freestream velocity vector and the developing streaks. Additionally, the flow
field evolution is dominated by the crossflow-direction of rotation, resulting in an asymmetric downstream development of
the identified flow structures. These effects lead to the formation of high- and low-speed regions alternating along the
span in the downstream portion of the acquired domain. Their
presence results in the modulation of the BL velocity and momentum, typically associated to the presence of CFI. However,
the CFI onset occurs at a finite distance from the DRE location, suggesting that the development of the individual element
wake is fundamental to set the flow conditions for the modal
instabilities onset. This consideration is confirmed by the amplitude analysis, which indicates the presence of a transientmechanism dominating the near-wake evolution. In particular,
the individual Fourier modes behaviour, shows that the primary mode and its second harmonics both decay in the element
vicinity, while the higher harmonics initially grow sustaining
the total perturbation amplitude. Further analysis is needed to
fully characterize the observed transient mechanism. Nonetheless, by comparing the evolution of the total perturbation amplitude and of the individual λ1 mode, a direct estimation of
the CFI onset amplitude (A0 ) is performed. The comparisonof experimental and numerical growth rates based on A0 , confirms the exponential nature of the instabilities growth process

CONCLUSION
The near-element flow of roughness elements applied ina swept wing boundary layer, is experimentally investigated5

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022

10-1

100

10-2

0.15

10-2

0.155

0.16

0.165

0.17

0.175

0.164 0.166 0.168 0.17 0.172 0.174 0.176

Figure 5. Experimental (a) Aint and (b) Neff estimation for the λ1 mode (symbols, 1 out of 5) and for the total perturbation amplitude(dashed line). NLST estimation for the λ1 mode (solid lines).
Lucas, J.M. 2014 Spatial optimal perturbations for transient
growth analysis in three-dimensional boundary layers. PhD
thesis.
Mack, L.M. 1984 Boundary-layer linear stability theory. Tech.
Rep.. California Inst of Tech Pasadena Jet Propulsion Lab.
Malik, M.R., Li, F., Choudari, M.M. & Chang, C.L. 1999
Secondary instability of crossflow vortices and swept-wingboundary-layer transition. Journal of Fluid Mechanics 399,
85–115.
Reibert, M., Saric, W.S., Carrillo, Jr.R. & Chapman, K. 1996
Experiments in nonlinear saturation of stationary crossflow
vortices in a swept-wing boundary layer. In 34th Aerospace
Sciences Meeting and Exhibit. American Institute of Aeronautics and Astronautics.
Saric, W.S., Carrillo, R. & Reibert, M. 1998 Leading-edge
roughness as a transition control mechanism.
Saric, W.S., Reed, H.L. & White, E.B. 2003 Stability and transition of three dimensional boundary layers. Annual Review
of Fluid Mechanics 35 (1), 413–440.
Saric, W.S., West, D.E., Tufts, M.W. & Reed, H.L. 2019 Experiments on discrete roughness element technology forswept-wing laminar flow control. AIAA Journal 57 (2),641–654.
Schmid, P.J. & Henningson, D.S. 2001 Applied mathematicalsciences.
Serpieri, J. 2018 Cross-flow instability. PhD thesis.
Serpieri, J. & Kotsonis, M. 2016 Three-dimensional organisation of primary and secondary crossflow instability. Journalof Fluid Mechanics 799, 200–245.
Tempelmann, D., Schrader, L.U., Hanifi, A., Brandt, L. &Henningson, D.S. 2012 Swept wing boundary-layer receptivity to localized surface roughness. Journal of Fluid Mechanics 711, 516–544.
Wassermann, P. & Kloker, M. 2002 Mechanisms and passive
control of crossflow-vortex-induced transition in a threedimensional boundary layer. Journal of Fluid Mechanics
456, 49–84.
White, Edward B., Rice, Justin M. & Ergin, F. Gökhan 2005
Receptivity of stationary transient disturbances to surface
roughness. Physics of Fluids 17 (6), 064109.
Wieneke, Bernhard 2012 Iterative reconstruction of volumetricparticle distribution. Measurement Science and Technology
24 (2).
Zoppini, G., Westerbeek, S., Ragni, D. & Kotsonis, M. 2022
Receptivity of crossflow instability to discrete roughness
amplitude and location. Journal of Fluid Mechanics 939.

further downstream. Therefore, the transient instabilities identified in the element near-wake are confirmed to be a fundamental part of the receptivity process, contributing in setting
the initial amplitudes for the modal CFI onset and downstream
evolution.

REFERENCES
Andersson, P., Brandt, L., Bottaro, A. & Henningson, D.s.
2001 On the breakdown of boundary layer streaks. Journalof Fluid Mechanics 428, 29–60.
Baker, CJ 1979 The laminar horseshoe vortex. Journal of fluid
mechanics 95 (2), 347–367.
Bippes, H. 1999 Basic experiments on transition in threedimensional boundary layers dominated by crossflow instability. Progress in Aerospace Sciences (35), 363–412.
Breuer, Kenneth S. & Kuraishi, Takeo 1994 Transient growthin two- and three-dimensional boundary layers. Physics of
Fluids 6 (6), 1983–1993.
Brynjell-Rahkola, M., Schlatter, P., Hanifi, A. & Henningson,
D.S. 2015 Global stability analysis of a roughness wake ina falkner-skan-cooke boundary layer. Procedia IUTAM 14,
192–200.
Cherubini, Stefania, de Tullio, Marco, de Palma, Pietro & Pascazio, Giuseppe 2013 Transient growth in the flow past athree-dimensional smooth roughness element .
Downs, R.S. & White, E.B. 2013 Free-stream turbulence
and the development of cross-flow disturbances. Journal of
Fluid Mechanics 735, 347–380.
Elsinga, G. E., Scarano, F., Wieneke, B. & van Oudheusden,
B. W. 2006 Tomographic particle image velocimetry. Experiments in Fluids 41 (6), 933–947.
Gregory, N.T. & Walker, W.S. 1956 The effect on transitionof isolated surface excrescences in the boundary layer. HM
Stationery Office.
Klebanoff, P. S., Cleveland, W. G. & Tidstrom, K. D. 1992
On the evolution of a turbulent boundary layer induced by athree-dimensional roughness element. Journal of Fluid Mechanics 237, 101–187.
Kurz, H.B.E. & Kloker, M.J. 2016 Mechanisms of flow
tripping by discrete roughness elements in a swept-wingboundary layer. Journal of Fluid Mechanics 796, 158–194.
Loiseau, J.C., Robinet, J.C., Cherubini, S. & Leriche, E. 2014
Investigation of the roughness-induced transition: global
stability analyses and direct numerical simulations. Journalof Fluid Mechanics 760, 175–211.

6