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

ON THE STABILITY AND TRANSITION TO TURBULENCE OF THE FLOWOVER A WIND-TURBINE AIRFOIL UNDER VARYING FREE-STREAM
TURBULENCE INTENSITY

Thales C. L. Fava1
fava@kth.se

Brandon A. Lobo2
brandon.a.lobo@fh-kiel.de

Ardeshir Hanifi1
hanifi@kth.se

Alois P. Schaffarczyk2
alois.schaffarczyk@fh-kiel.deMichael Breuer3
breuer@hsu-hh.de

Dan Henningson1
henning@mech.kth.se

1 Department of Engineering Mechanics, KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden
2 Mechanical Engineering Department, Kiel University of Applied Sciences, D-24149 Kiel, Germany
3 Department of Fluid Mechanics, Helmut-Schmidt-University Hamburg, D-22043 Hamburg, Germany

ABSTRACT

to transition processes with an initial growth not describedby the exponential amplification of the main modes of the
Orr-Sommerfeld/Squire equations. This often results instreamwise-elongated structures called streaks, regions of highor low streamwise velocity compared to the mean flow. Bothsinusoidal and varicose modes have been identified, and theirmechanism is well documented (Asai et al., 2002).
Recent measurements on a wind turbine (Schaffarczyk
et al., 2017) in the free atmosphere found that transition via
TS instabilities was unlikely and that Mack’s correlation (fromwind tunnel studies) for the amplification factor was not directly applicable. Özçakmak et al. (2020) showed experimentally and numerically that bypass transition occurs under high
FST, while natural transition by TS waves happens otherwise.
The present work aims at identifying and characterizing
the flow instabilities triggering transition over a section of awind turbine blade of the type LM45.3p (20 % thickness) inthe presence of inflow turbulence at varying T I. This analysis is done using wall-resolved large-eddy simulations (LES)
and linear stability analysis. Three test cases are consideredwith T I = 0, 1.4, and 2.8 %. Turbulence is generated withthe synthetic turbulence inflow generator proposed by Klein
et al. (2003) and injected within the domain (Breuer, 2018).
Isotropic turbulence is generated with an integral length scale
L/c = 0.118 and a time scale T = L/u∞ extracted from the experimental work of Hain et al. (2009) and also used by Breuer(2018). All cases have a constant angle of attack of 4◦ and achord Reynolds number Rec = u∞ c/ν = 105 . The generationand injection of the inflow turbulence into the LES domain
and corresponding results and conclusions are found in Loboet al. (2022). All units are non-dimensionalized by the inflow
velocity (u∞ ) and chord length (c).

The present work investigates the laminar-turbulent transition of the flow around a typical section of a wind turbine
blade under different levels of isotropic inflow turbulence ata Reynolds number of Rec = 105 . Wall-resolved large-eddy
simulations are performed under different turbulence intensities (T I) up to T I = 2.8 %. The results are analyzed with tools
based on the linear stability and optimal-perturbation theory.
At T I = 0%, transition to turbulence via the breakdown ofKelvin-Helmholtz (KH) rolls formed over the laminar separation bubble (LSB) is seen. These modes start to grow upstream of the LSB as an inflectional instability. At T I = 1.4 %rolls are also seen; but, instabilities formed by the interaction between streaks and the LSB also contribute to transition. The streaks are estimated to have a spanwise wavenumber around β = 100 ( β δ ∗ = 0.19 at 20 % chord; δ ∗ is the displacement thickness) and a frequency in the range f = 5 − 8( f δ ∗ /ue = (1.4 − 2.3) × 10−2 at 40 % chord; ue is the boundary layer edge velocity), close to that of the shear-layer instability. In the T I = 2.8 % case, the flow is heavily influenced
by the presence of streaks, which stabilize the flow concerning
inflectional/KH instabilities, but, at the same time, undergoes
varicose-type instabilities and breakdown to turbulence.

INTRODUCTION AND METHODOLOGY
For the design of wind turbine blades with increased energy output and lifespan and reduced noise emissions, it isparamount that the transition mechanisms under free-stream
turbulence (FST) with varying turbulence intensities (T I) andlength scales are better understood. Different transition scenarios are known to occur within the boundary layer depending on the scale and intensity of the FST. For low
T I, typically T I < 0.5 − 1 %, transition usually takes placethrough two-dimensional Tollmien-Schlichting (TS) instabilities (Reshotko, 1976). The TS instability may arise in flows
with no pressure gradient through a viscous mechanism. In thepresence of an adverse pressure gradient, the velocity profiles
may become inflectional, allowing an inviscid instability.
At higher T I, bypass transition occurs. This refers

RESULTS
Flow Characterization
Table 1 summarizes certain parameters of the different
flow cases such as the locations of the leading and trailingedges of the laminar separation bubble (LSB) (xb1 and xb2 ), thelocation and the value of the LSB maximum height (xymax and1

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
ymax /δ ∗ , δ ∗ being the local displacement thickness). Also included are the positions downstream of which adverse pressure
gradient (APG) and inflectional velocity profiles occur (xa andxi ). The start of transition is given by the x location where theReynolds stresses normalized by the free-stream velocity reachthe threshold −u′ v′ /u2∞ = 0.001 (xtr1 ) (Yuan et al., 2005).
Table 1: Characteristics of the LSB and transition.
TI

xb1

xb2

xymax

0.0 %

0.50

0.74

0.62

1.4 %

0.51

0.76

2.8 %

0.52

0.75

ymax

/δ ∗

xa

xi

xtr1

0.51

0.33

0.38

0.50

0.64

0.48

0.34

0.34

0.44

0.63

0.38

0.34

0.39

0.39

(a) T I = 0 %As indicated in Table 1, at a T I of 0 %, a LSB is formed in
the region x = 0.50 − 0.74, with a maximum height of 0.51 δ ∗at x = 0.62, as a result of the adverse pressure gradient (APG)
that acts for x > 0.33. With an increase in T I to 1.4 %,the LSB is slightly displaced downstream with its height reduced to 0.48 δ ∗ , which is connected to the entrainment of
fluid into the LSB by the vortices formed close to its trailingedge (Burgmann & Schröder, 2008) and to the enhancementin the near-wall momentum by the non-linear interaction between streaks and streamwise vortices (Karp & Hack, 2020).
However, the amplitude of the streaks is not high enough totrigger bypass transition. Moreover, the beginning of amplification moves 6 % upstream to xtr1 = 0.44 A further increase in
T I to 2.8 % promotes an additional reduction in the size of the
LSB, with its maximum height dropping to 0.38 δ ∗ (25 % reduction compared to T I = 0 %). Furthermore, transition starts
earlier (xtr1 = 0.39), which coincides with xi , indicating thatthe growth is likely due to an inflectional instability.
To gain insight into the structures responsible for transition, the contours of streamwise velocity perturbations (u′ ) on
the suction side are plotted in Fig. 1 for arbitrary snapshots.
Considering the T I = 0 % case shown in Fig. 1a, the formation of spanwise-uniform wavefronts (spanwise wavenumber
β = 0) is seen starting at x = 0.38, which is the same location where the flow becomes inflectional. Therefore, they are
possibly related to an inflectional instability. These structures
agree with Squire’s theorem stating that two-dimensional disturbances are the first to become unstable in a parallel flow,which is observed despite the non-parallelism of the current
flow. The presence of an inflection point for x ≥ 0.38 also
fulfills Rayleigh’s necessary condition for shear-flow instability. The frequency of these waves can be estimated from thetemporal auto-correlation of the normal velocity perturbations(Rvv ) for a point inside the boundary layer by defining the period of these waves as half the distance to the first minimumof Rvv . Figure 2a shows a plot of these frequencies along thechord. It is possible to infer that the frequency of the dominant flow structures upstream of the LSB (x = 0.4 and 0.5),
which are spanwise wavefronts, is f = 9.6. Furthermore, asharp rise is noticed already at x = 0.25, i.e., before the appearance of the inflection point and the corresponding spanwiserolls at x = 0.38. Stability analyses with the Orr-Sommerfeld
and parabolized stability equations (PSE) showed no unstablemode upstream of the inflection point, ruling out viscous instabilities as the cause of this rise in frequency. However, theelliptical nature of the pressure equation allows disturbances
to be felt upstream, which may be the reason behind the increase in amplitude for frequencies that are stable upstream of
the inflectional region. Additionally, spanwise rolls appear at(b) T I = 1.4 %(c) T I = 2.8 %Figure 1: Contours of streamwise velocity perturbations(u′ ) (arbitrary snapshot (T = 9.4)). Slices are taken at awall-normal height equal to the displacement thickness
at 20 % chord.

(a) Frequency ( f ) for T I = 0 % and T I = 1.4 %.

(b) Spanwise wavenumber (β ) scaled by the chord and displacement thickness (β δ ∗ ) for T I = 1.4 %. Blue area shows transition.
Figure 2: Frequency and spanwise wavenumber fromauto-correlations of normal and streamwise velocity perturbations, respectively, at y = 0.5δ ∗ .

2

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
x = 0.54, with higher amplitude and larger streamwise wavelength than the modes growing upstream of separation. It is
worth noting that these structures appear shortly after the inception of the LSB, and they have been attributed to the roll-upof the shear layer due to a KH instability as noticed in numerical (Jones et al., 2010) and experimental studies (Burgmann &Schröder, 2008). The frequency of these rolls can be estimatedas seen in Fig. 2a, which yields f = 7.8 for x = 0.6, slightly
lower than the frequency of the waves upstream of the separation bubble. The KH rolls begin to break down around 70 %chord. Reattachment at x = 0.74 promotes fully turbulent flow.
Similar structures as those observed in the case with noinflow turbulence are also identified for the T I = 1.4 % case(see Fig. 1b). Spanwise-uniform wavefronts are observed at
x = 0.34, which matches the position where the APG and, correspondingly, the inflection starts to act. The frequency ofthese waves is estimated from Rvv presented in Fig. 2a thatyields f = 10.4, 10.9, and 13.2 for x = 0.3, 0.4, and 0.5, respectively. The increase in frequency seen at x = 0.5 coincides with the location where streaks interact with the separated shear layer. It is known that streaks faster than the mean
flow interact with the instantaneous separation bubble and shift
separation downstream, whereas streaks slower than the mean
flow shift the separation bubble upstream (Lobo et al., 2022).
A corresponding rise in frequency is also found in the amplitude spectrum discussed later. Larger 2D rolls of the KH kindare observed as early as x = 0.52 (time-dependent). This isimmediately downstream of the leading edge of the separation
bubble located at x = 0.51. The frequency of these rolls canbe estimated as f = 9.3 at x = 0.6 and f = 7.7 at x = 0.65, asimilar frequency as in the case with T I = 0 %. The spanwise
wavenumber (β ) of the streaks, which are seen to originate
near the leading edge of the airfoil, can be estimated from thespatial auto-correlation in the spanwise direction of the streamwise velocity perturbations inside the boundary layer (Ruu ).
The results are displayed in Fig. 2b, which shows the timeaveraged and instantaneous values of β and β δ ∗ . The timeaveraged value β tends to remain constant close to β = 25
(corresponding to waves spanning the whole span) until it displays a sharp rise at the x-position of the breakdown of the KH
rolls, probably due to the generation of structures with smaller
wavelengths. However, the instantaneous β –distribution indicates the presence of structures with β = 115.2 at x = 0.10
and β = 98.7 at x = 0.15 and 0.20, which correspond to thestreaks seen in Fig. 1b. Their absence in the time-averaged
β –distribution may be linked to a temporal scarcity of thesestructures at relatively low T I levels.
The results for the T I = 2.8 % case are presented inFig. 1c. Streaks that start to develop close to the leading edgeof the airfoil seem to dominate the flow over the spanwiseuniform disturbances associated with modal growth. However,
it is still possible to observe reminiscences of the 2D wavefronts and rolls in the region x = 0.55 − 0.62, which is inside
the LSB. Unfortunately, data were collected only at specificflow locations for this case, preventing the inclusion of autocorrelation analyses in time and spanwise direction.

(a) T I = 0 %(b) T I = 1.4 %(c) T I = 2.8 %Figure 3: Amplitude spectral density of streamwise ve-locity perturbations. Dashed lines indicate that the station presents turbulent regions.
related to a strong APG. The 2D waves evolving upstream of
the LSB present λx = 5.5 × 10−3 at x = 0.46 (spanwise rollseen in Fig. 1a) and f = 9.6 (see Fig. 2a), which lies within
the range observed in the PSD and yields a phase speed cs =0.053 while the RMS of the fluctuating streamwise velocity
component at this location has a speed urms = 0.049 This phasespeed is lower than that of TS waves, generally found in theinterval cs = 0.3 − 0.4. Once again, a growth is noticed in
the PSD at x = 0.3 occurring in the same range of frequencies
observed at x = 0.4 and 0.5. This is attributed to the ellipticalnature of the pressure equation. The phase speed of the rolls inthe separated shear layer can also be estimated from λx = 0.05
retrieved from Fig. 1a and f = 7.8 (Fig. 2a), which gives cs =0.40. This is in the range reported by Dovgal et al. (1994)
and Yarusevych et al. (2008) for KH instabilities developing
over an LSB on an airfoil. Thus, it is possible to associate therolls evolving over the LSB to the shear layer roll-up due to a
KH instability. The spectrum for x ≥ 0.6 presents a broadband
characteristics typical for turbulent flow.
The spectrum of the T I = 1.4 % (Fig. 3b) reveals an amplitude rise in the range f = 3.6 − 20.0 for x = 0.4 and 0.5.
Moreover, the wavefronts evolving upstream of the LSB atx = 0.3 to 0.5 have frequencies of f = 10.4 − 13.2 (Fig. 2a),Flow Stability and Transition
The amplitude spectral density of the streamwise velocity
perturbations at nine locations along the chord are presented inFig. 3. For T I = 0 % (Fig. 3a), there is a significant increase in
the perturbation amplitude at x = 0.3 (Reδ ∗ = 193) to x = 0.5(Reδ ∗ = 435) in the range f = 3.6 − 20.0, with a maximum
around f = 7.8 at x = 0.4 and 0.5. The fact that the frequency
increases with x in the current case until x = 0.5 is possibly312th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022

(a) T I = 0 %.

(a) T I = 0 %.

140

120

100
80
60

(b) T I = 1.4 %.

(b) T I = 1.4 %.

140
120

100

80

60
40

(c) T I = 2.8 %.

(c) T I = 2.8 %.

Figure 4: Contours of N factor from PSE analysis for
β = 0. The black lines are isolines of the real part of thestreamwise wavenumber α, and the red line represents
the coordinates of the maximum N factor.

Figure 5: N factor versus x of the modes constituting theenvelope of amplification for β = 0.
cant amplification around f = 15.8 and 30.5. This is too highfor the growth of streaks, as discussed later in the optimalperturbation analysis, but it corresponds to the location of theappearance of the varicose mode that is formed by the interaction of the high and low-speed streaks. These frequencies
are in the range of those indicated by Asai et al. (2002) (after
a proper nondimensionalization) for varicose modes on a flat
plate. Moreover, flow visualizations indicate the presence of avaricose mode at x = 0.4, where it is possible to see the breakdown of a streak in Fig. 1c. Snapshots showing this instability
in more detail can be found in Lobo et al. (2022).
To identify the modes responsible for the flow instability,
PSE analysis is used to compute the evolution of the N factor
with x as a function of f . Only β = 0 modes were considered,as they are the most unstable ones for parallel shear flows,
and the structures observed in the simulations at T I = 0 %are spanwise-uniform. Notice that streaks cannot be computedwith the PSE as they have the streamwise wavenumber (α)
equal to zero. The results are shown in Fig. 4, where the blacklines are isocontours of α. For T I = 0 % (Fig. 4a), the unstableregion spans the range f = 5.4 − 21.1 and the maximum amplification occurs around f = 12.6, 11.3, and 9.8 for x = 0.4,
0.5, and 0.6, respectively. However, the maximum amplification tends to the frequency f = 7.8 as x increases, the samewith a corresponding amplitude growth in the spectrum. Thisis particularly visible at x = 0.5, with the first region of highamplitude around f = 7.8 and the second around f = 13.2.
The KH rolls are associated with f = 7.8 as discussed for thecase with T I = 0 %. However, x = 0.5 is upstream of the location of the separation bubble and this upstream peak is once
again attributed to the elliptical nature of the pressure equation. As discussed earlier, the peak at f = 13.2 corresponds tothe interaction of the streaks with the separation bubble.
The results for T I = 2.8 %, displayed in Fig. 3c, indicate
an amplitude growth in the range f = 12 − 24 for x = 0.2 and0.3. This is the location where the overlap of a high- and lowspeed streak first takes place (see Fig. 1c) and is described indetail in Lobo et al. (2022). This seems to possess a similarfrequency as that described earlier for T I = 1.4 % on the interaction of high-speed streaks and the separation region (negative mean velocity). It is possible that these interactions, which
are both an overlap of a relatively high-velocity region withthat of a low-velocity region (compared to the mean flow),possess a similar frequency. At x = 0.4, an increase in amplitude can be seen in the range f = 7.3 − 47.6, with a signifi-

412th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022

Figure 6: Normal profiles of the absolute value of streamwise (u′ ) and normal (v′ ) velocity perturbations for f = 7.4 andβ = 0. The wall-normal coordinate is normalized by the local displacement thickness.
Considering the T I = 1.4 % case, the f = 7.4 mode is again
the first one to present a rise in amplitude upstream of the region with inflectional velocity profiles. However, unlike theT I = 0 % case, there is further amplification after a local maximum inside the separation bubble at x = 0.66, where the KH
rolls start to break down. If only the region x ≤ 0.66 is considered, one notices that the modes display a lower amplification compared to the T I = 0 % case, which indicates that thestreaks and disturbances entering the boundary layer dampen
the inflectional and KH instabilities, probably by reducing theinflectional character of the flow and the LSB, as shown in Table 1. An even better agreement between the growth rates from
PSE and LSE is obtained for this case. This is particularly true
for the f = 10.6 mode, but also for the f = 7.4 and 8.5 ones.
Finally, the T I = 2.8 % case, for which only PSE results areavailable, indicates that the frequency of f = 7.4 still displays
the maximum growth and growth rate. Nevertheless, due tothe increase of momentum mixing close to the wall by the incoming perturbations and streaks, which renders the flow lessunstable, the growth displayed for this case is lower.

frequency obtained from the PSD for x = 0.4 and 0.5. Thisfurther indicates that the peaks observed in the spectrum at
f = 7.8 for x = 0.4 and 0.5 result from a propagation of these
disturbances as discussed earlier and, therefore, cannot be predicted in the PSE computations.. There is also a drop in α(rise in λx ), observed in the inflectional and KH instabilities as
they evolve in x. Figure 4b shows the results for T I = 1.4%.
The instability region is quite similar to that of the T I = 0 %case, but it displays slightly lower growth rates. This could
be on account of the streaks, as discussed earlier. Besides, amore accentuated drop in f and α of the most amplified wave,
i.e., the inflectional instabilities developing upstream of the
LSB, present higher f and α, whereas the KH instability inthe LSB presents lower values of these parameters comparedto the T I = 0 % case. The highest growth occurs at f = 7.8 as
x increases, which agrees with the frequency of the amplitude
peak in the PSD for x = 0.4 and 0.5. . For a further increasein the turbulence intensity to T I = 2.8 %, as shown in Fig. 4c,
the N factor is substantially reduced due to the mean-flow distortion promoted by streaks, particularly the transport of momentum to the near-wall region and reduction of the size of the
LSB. The maximum amplification takes place at f = 7.2, andthe value of α for maximum amplification also decreases inrelation to the lower T I cases. This issue indicates that modal
instabilities with longer wavelengths are more amplified underhigher T I values. Moreover, no particular amplitude rise at
this frequency could be noticed in the spectrum, which showsthat the main instability mechanism changes from modal tonon-modal from T I = 1.4 % to 2.8 %.

Figure 6 displays the shape of the absolute value of
streamwise (u′ ) and normal (v′ ) velocity perturbations from
LES (after FFT) and PSE for T I = 0 %. Only a mode close
to the most amplified frequency is shown. At x = 0.35, i.e.,
upstream of the region of inflectional velocity profiles (xi =0.38), u′ from the PSE has a shape close to that of a TS wave,
while the one obtained from the LES does not indicate a phase
inversion in the inviscid region (y/δ ∗ = 3.0). However, there isgood agreement between both far from this region. The perturbation reaches a maximum amplitude at y/δ ∗ = 1.02, close to
the boundary layer edge. Notice that the PSE indicates that thismode is stable, making the presence of a viscous instability unlikely. Further downstream at x = 0.45, which is already in theinflectional flow region, u′ presents three peaks. A near-wallpeak appears in the LES results, probably associated with theinflection point in the velocity profiles. The other two peaks
are located at the boundary layer edge and y/δ ∗ = 3.0, similar
to what was observed at x = 0.35. However, the outer-mostpeak is much more pronounced at x = 0.45. Analogous modes
were observed inside recirculating flow regions (Dovgal et al.,1994). This structure is observed upstream of the LSB, withthe leading edge at x = 0.50. This supports the claim that the
inflectional instabilities upstream of separation gradually turninto shear-layer modes, such as KH ones, inside the LSB (Diwan & Ramesh, 2009). At x = 0.55, the double-peak structure
characteristic of a KH mode is observed for u′ , which matches
the appearance of rolls in the simulations. Nevertheless, theouter-most peak is much more pronounced in the LES results
than in the PSE ones. There is a close agreement between the
LES and PSE profiles of v′ for all x stations.

Figure 5 shows the N factor from the PSE and LES (afterFFT) as a function of x of the modes that constitute the envelope of amplification. Since the PSE is a linear method, one
can move its N-factor curves in the vertical direction. This isdone to match the slopes of the LES results, which represent
the amplification rates. For the T I = 0 % case, the first mode tostart amplification is at f = 7.4, which occurs upstream of theregion of inflection. However, the PSE analysis does not predict any unstable mode in this region, which is expected basedon our earlier discussions regarding the origin of these modes
at upstream locations. Moreover, for f = 7.4 and 8.5 the slopeof the N factor curves becomes steeper around x = 0.5, where
the LSB is formed, indicating higher amplification in the separated region compared with the area with inflectional velocity
profiles upstream of the bubble (x = 0.38 − 0.50). The amplification downstream of separation agrees with the analysis that
this mode is associated with the KH instability. Close agreement between the amplification rates of the PSE and LES is obtained for f = 7.4, 8.5, and 10.6 in the range x = 0.45 − 0.56,
particularly for the latter frequency. Further downstream, theagreement reduces because the amplitude of the rolls is highenough to trigger non-linear effects. The modes with f = 13.8
and 14.9, obtained from the PSE, display lower growth rates
than those from the LES, which could not be explained so far.

Optimal perturbation analysis (Andersson et al., 1999)
was performed to gain further insight into non-modal instabilities, particularly into the growth of streaks (α = 0 struc-5

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
Notice that their frequency is close to that of the inflectional
instabilities present in the flow, making their direct interaction
possible. Finally, transition in the T I = 2.8 % case is heavily influenced by streaks. Despite rendering the flow morestable with respect to inflectional instabilities, enhancing thenear-wall momentum and reducing the LSB, these streaks arestrong enough to undergo secondary instabilities, particularlyof the varicose type, and thus break down to turbulence.

Figure 7: Growth rate of streaks as a function of the op-

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tures) in the cases with non-zero inflow turbulence. The mean
flow of the T I = 0 % case was employed as the basic flow
for the computations. The analysis was performed for several
frequencies ( f ), spanwise wavenumbers (β ), and optimization
locations (x f ), i.e., locations where the amplification reaches
a maximum. The flow visualization of the T I = 1.4 % case(Fig. 1b) displayed streaks forming at about x = 0.02 and extending downstream. They initially grow quite rapidly up toaround 10 % chord and then continue to grow but at a lower
growth rate as was observed by following a streak moving
downstream. Furthermore, from Fig. 2b and corresponding
to the time instant seen in Fig. 1b, the streaks evidently possess 75 < β < 125. Corresponding to this range of spanwise
wavenumbers, the growth rate at different frequencies was investigated. It was found that the growth rate in the range
f = 5 − 8 matches the observations from the LES. As seenin Fig. 7, at f = 5, a growth rate greater than G = 1 is seenfor β ≥ 75 while only β in the range of 75 to 125 follows the
trajectory of a very high growth rate up to around 10 % chord
followed by a reduced growth rate up to 40 % chord. At f = 8,
this trend is observed for β between 100 and 150. A further
increase in f results in streak decay (G < 1) for the β values
obtained from the LES, at some downstream position, which
was not seen in the simulation. Therefore, it can be concluded
that the streaks formed at T I = 1.4 % with β between 75 and125 lie within the frequency range of f = 5 to 8. High frequency data was not collected for the T I = 2.8 % case, but bycomparing the PSD plots (Fig. 3), a similar frequency range
experiences an increase in amplitude while the streaks from
Fig. 1c seem to have a similar region of growth up to x = 0.1,
indicating a similar range of β and f also for this case.

CONCLUSIONS
Wall-resolved large-eddy simulations of an airfoil under
three turbulence intensity values are performed, and the results are analyzed in the light of linear stability analysis andoptimal-perturbation theory. It is shown for T I = 0 % thattransition is dominated by the inflectional instabilities that start
to develop upstream of the LSB and gradually turn into KH
modes in the separation bubble. These modes appear as rolls
over the LSB, with a phase speed cs = 0.40, agreeing withthe values found in the literature for a KH instability, and they
break down to turbulence close to the reattachment location.
The T I = 1.4 % case presents contributions from both inflectional and streak instabilities, which are noticed by the concurrent shedding of KH rolls from the LSB and the secondary
instability formed by the interaction between streaks and theLSB. These streaks possess a dimensionless frequency in therange f = 5 − 8 and a spanwise wavenumber around β = 100.

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