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

ON THE STRUCTURE OF A TURBULENT BOUNDARY LAYER PERTURBUED BY A
LARGE-EDDY BREAK-UP DEVICE

Abhishek Tyagi
Department of Aerospace Engineering
Indian Institute of Science
Bengaluru, Karnataka,560012-India
tabhishek@iisc.ac.in

A. Chandan Kumar
Department of Aerospace Engineering
Indian Institute of Science
Bengaluru, Karnataka,560012-India
achandankuma@iisc.ac.in

Sourabh S. Diwan
Department of Aerospace Engineering
Indian Institute of Science
Bengaluru, Karnataka,560012-India
sdiwan@iisc.ac.in

ABSTRACT
Large-Eddy Break-Up (LEBU) devices have been used in
the past as means to reduce the skin-friction drag associated witha turbulent boundary layer (TBL). In this work we report windtunnel measurements on a flat-plate TBL perturbed by a LEBU
located at the edge of the log layer of the oncoming TBL. We
find that the presence of LEBU causes a reduction in the nearwall peak for the streamwise velocity fluctuations, thereby
directly affecting the near-wall turbulence cycle. We show that,apart from breaking up the large-scale eddies, the LEBU
introduces a significant energy at scales 2-3 (and larger) times
the oncoming TBL thickness, through the “rapid shearing” ofturbulent eddies by the new viscous layer generated over the
LEBU surface. This shows that a LEBU can affect the structureof the oncoming TBL in a much more complex manner thanwhat is previously understood. Over a certain distancedownstream of the LEBU, the larger-scale eddies are seen tocause a significant amplitude modulation of smaller-scale
fluctuations. An exercise in amplitude modulation calculation
involving two cut-off wavelengths is also presented. These
results could help us better understand the scale interactions
effected by long structures in a high-Reynolds number TBL.

𝑦𝑦⁄𝛿𝛿𝑐𝑐 = 0.8, where 𝑦𝑦 is the wall-normal distance and 𝛿𝛿𝑐𝑐 is the
99% boundary layer thickness of the canonical TBL at thelocation of the LEBU. They found that the presence of LEBU
breaks down larger-scale structures near the TBL edge andincreases the turbulence intermittency (i.e., the fraction of thetime the velocity signal is turbulent) in that region. Chin et al.
(2017) reported an attenuation of energy over the spanwise+
wavelengths 𝜆𝜆+𝑧𝑧 < 200 and 𝜆𝜆𝑧𝑧 > 500 and an increase in energy+ indicates normalization on
from 200 < 𝜆𝜆+<500(where𝑧𝑧
wall variables) at a streamwise distance of about 50𝛿𝛿𝑐𝑐
downstream of the LEBU. The range 200 < 𝜆𝜆+𝑧𝑧 <500 represents structures that are longer than those present in a
canonical TBL for which the typical spanwise spacing of nearwall streaks is 𝜆𝜆+𝑧𝑧 = 100. The LES study of Chan et al. (2021)
used three different locations ( 𝑦𝑦⁄𝛿𝛿𝑐𝑐 = 0.1, 0.5, 0.8 ) for
positioning the LEBU and explored mechanisms that contributeto the reduction in the wall shear stress. Their results showed thata maximum skin-friction reduction of 30% or higher can berealised for LEBUs located at 𝑦𝑦⁄𝛿𝛿𝑐𝑐 > 0.2. Chan et al. (2022)
investigated the skin friction coefficient in a TBL perturbed bya LEBU and found the LEBU to significantly reduce the skinfriction associated with large scales ( 𝜆𝜆𝑥𝑥 > 3𝛿𝛿 ). The above
numerical studies confirm the primary role of LEBUs as devices
that break up the large-scale eddies. However, the way a LEBU
affects the wide range of scales present in the oncoming TBL is
still not well understood; see Savill and Mumford (1988). A
particularly pertinent question is whether a LEBU can introduce
wavelengths downstream of it which are longer than thosepresent in the oncoming TBL. Carrying out an input-output
analysis of the effect of LEBU on a TBL can help us tackle thisand similar such questions.
In this work, we carry out an experimental investigation on
the scale manipulation in a TBL perturbed by a LEBU located at𝑦𝑦/𝛿𝛿𝑐𝑐 = 0.2, i.e., at the edge of the log layer. We particularly
focus on the region immediately downstream of the LEBU (upto 𝑥𝑥/𝛿𝛿𝑐𝑐 = 3.5; where 𝑥𝑥 is the streamwise coordinate measured
from the location of the LEBU). We find that the LEBU not only
breaks up existing large eddies but also introduces considerable
energy at higher streamwise wavelengths, which can be traced
back to the turbulence energy generated over the LEBU surface
by “rapid-shearing” mechanism. Furthermore, the amplitudemodulation coefficient immediately downstream of LEBU
shows a considerable departure from its behaviour in a canonical
TBL. We also perform a two-scale decomposition of the velocity
signal to calculate the amplitude modulation among different

INTRODUCTION
Manipulating a turbulent boundary layer (TBL) continues
to remain an area of active research for a variety of reasons suchas reducing drag that can be helpful in improving the efficiencyof energy converting devices/machines and in turn saving fuel,and more fundamentally understanding the structure of the TBL.
The Large-Eddy Break-Up (LEBU) devices, in the form of a thin(and short) flat plate or an aerofoil section mounted in the outerregion of a TBL, have been explored in the past for reducing theskin-friction drag over a surface. However, after the towing tankexperiment of Shalin et al. (1988) done at KTH it was realisedthat there was no net drag reduction (and in fact a drag increase)associated with the LEBUs. As a result, the interest in the use of
LEBU as a drag-control device gradually faded; see the recent
review by Alfredsson and Orlu (2018) for a more details.
There has been a renewed interest in LEBUs more recently,
primarily using numerical simulations, towards using LEBUs for
manipulating a “canonical” TBL and investigating the changes
they cause to the TBL structure. For example, Chin et al. (2017)carried out a large eddy simulation (LES) to quantify the change
in the skin friction downstream of a LEBU mounted at1

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
ranges of scales, to enable a better characterization the effect of
LEBU on the scale interactions in a TBL.

streamwise direction as expected. Note that here 𝛿𝛿 represents
the local 99% boundary layer thickness. The r.m.s. intensity ofthe streamwise velocity fluctuations, 𝑢𝑢𝑟𝑟𝑟𝑟𝑟𝑟 ⁄𝑈𝑈∞ , is plotted infigure 2b. One can see an enhancement of 𝑢𝑢𝑟𝑟𝑟𝑟𝑟𝑟 just above theposition of the LEBU, i.e., 𝑦𝑦⁄𝛿𝛿 ≳ 0.2 and a decrease in the 𝑢𝑢𝑟𝑟𝑟𝑟𝑟𝑟
level below the LEBU position, for 𝑦𝑦⁄𝛿𝛿 < 0.2. Figure 2c shows
the velocity-gradient defect of the perturbed TBL with respect tothe canonical TBL. The changes observed in 𝑢𝑢𝑟𝑟𝑟𝑟𝑟𝑟 (figure 2b)
can be attributed to the changes in the mean velocity gradient
due to the presence of LEBU seen in figure 2c. The
increase/decrease in the velocity gradient can result in acorresponding increase/decrease in the local turbulence
production thereby affecting the local 𝑢𝑢𝑟𝑟𝑟𝑟𝑟𝑟 levels. This effect isclearly visible up to 𝑥𝑥 = 1.25𝛿𝛿𝑐𝑐 , explaining the increase anddecrease of r.m.s intensity just above and below the LEBU.

EXPERIMENTAL ARRANGEMENT
The present experiments are conducted in a low-speed opencircuit wind tunnel at the Indian Institute of Science Bengaluru,
which has a test section of size 0.5m x 0.5m x 3m and afreestream turbulence level of less than 0.08%. A flat plate of
2.5m length and 0.5m width mounted inside the test section
forms the measurement surface. A canonical TBL was obtained
at 1m downstream of the leading edge (by tripping the laminarboundary layer), at the free-stream velocity (𝑈𝑈∞ ) of 17.5m/s andwith 𝛿𝛿𝑐𝑐 = 21 mm. The corresponding 𝑅𝑅𝑅𝑅𝜃𝜃 = 𝑈𝑈∞ 𝜃𝜃 ⁄𝜈𝜈 =2600,
where 𝜃𝜃 is the momentum thickness and 𝜈𝜈 is the kinematic
viscosity. The relevant parameters of the canonical TBL arelisted in Table 1. A LEBU in the form of a flat strip of 0.75𝛿𝛿𝑐𝑐
length, 0.015𝛿𝛿𝑐𝑐 thickness and 0.2𝛿𝛿𝑐𝑐 height above the plate ismounted at 1m downstream of plate leading edge (figure 1). The
LEBU height of 0.2𝛿𝛿𝑐𝑐 is chosen so as to investigate the scaleinteraction within the log layer of the TBL. Single-component
hotwire anemometry measurements are carried out using theDantec Streamline CTA and using a 5µm tungsten wire probe.
The velocity signals are sampled at 60 kHz for 30s duration eachmeasurement point using NI data acquisition unit (USB 6363).
The hotwire probe is calibrated against six different speeds using
the King’s law. The hotwire probe is traversed in streamwise andwall normal directions with the help of stepper motors controlled
through a LabVIEW program.

(a)

(b)

(c)

Figure 1. Schematic of the experimental setup (not to scale).
Note that the flat plate is much longer than shown in the figure(total length = 2.5m)
Table 1. Parameters corresponding to the canonical TBL.
Parameters
Boundary layer thickness 𝛿𝛿𝑐𝑐 (𝑚𝑚𝑚𝑚)
Free stream velocity 𝑈𝑈∞ (𝑚𝑚/𝑠𝑠)
Friction velocity 𝑢𝑢𝜏𝜏 (𝑚𝑚/𝑠𝑠)
Reynolds number 𝑅𝑅𝑒𝑒𝜃𝜃
Karman number 𝑅𝑅𝑒𝑒𝜏𝜏 = 𝑢𝑢𝜏𝜏 𝛿𝛿𝑐𝑐 /𝜈𝜈Shape factor H

Values
21
17.5
0.68
2600
893
1.39

Figure 2 Profiles of (a) mean velocity and (b) r.m.s intensity(c) velocity-gradient difference between the perturbued TBL
and the oncoming canonical TBL. Here 𝛿𝛿 is the local
boundary layer thickness and 𝛿𝛿𝑐𝑐 that of canonical TBL
Interestingly the effect of LEBU is felt right down to theinner peak in 𝑢𝑢𝑟𝑟𝑟𝑟𝑟𝑟 located at about 𝑦𝑦⁄𝛿𝛿 ≈ 0.02 . While theposition of the inner peak is not affected by the presence of
LEBU, its magnitude is reduced by about 10-15% (figure 2b).
This reduction cannot be attributed to the local velocity gradient
which is seen to be higher for the perturbed TBL in comparison𝑦𝑦
to the canonical TBL in the region 0.005 < 𝛿𝛿 < 0.05 (figure

RESULTS AND DISCUSSION
Figure 2a shows the evolution of the mean velocity profiles
up to a distance of 3.5 𝛿𝛿𝑐𝑐 downstream of the LEBU. Also
included is the profile of the canonical TBL for comparison. The
velocity defect representing the LEBU wake is apparent in thevelocity profile (figure 2a); the maximum defect decreases in the2

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 20222c), presumably due to the local acceleration caused by thepresence of LEBU. This implies that, in presence of LEBU, thedecrease in Reynolds shear stress in this region must be larger
than the increase in the mean velocity gradient causing theenergy production and therefore the 𝑢𝑢𝑟𝑟𝑟𝑟𝑟𝑟 levels to decrease. The
exact mechanism by which the Reynolds stress near the walldecreases is not clear and is a topic of ongoing investigation.
This exercise shows that by positioning the LEBU closer to thewall (𝑦𝑦⁄𝛿𝛿𝑐𝑐 = 0.2) as done here, it is possible to directly affectthe inner cycle of turbulence.

Figure 3a shows the pre-multiplied spectral energy ofstreamwise velocity fluctuations, 𝜆𝜆𝜆𝜆(𝜆𝜆), as a function of thestreamwise wavelength, 𝜆𝜆 at 𝑦𝑦⁄𝛿𝛿 ≈ 0.21. The wavelength isdetermined from the frequency using the Taylor’s frozen-eddy
hypothesis. Immediately downstream of the LEBU, i.e., at𝑥𝑥⁄𝛿𝛿𝑐𝑐 = 0.05, there is a considerable reduction in the energy for
𝜆𝜆 > 0.2𝛿𝛿 as compared to the oncoming canonical TBL and anenhancement of energy for smaller wavelengths. This represents
the well-understood effect of LEBU in breaking up larger scales
and promoting smaller scales. Interestingly a small distancedownstream, at 𝑥𝑥⁄𝛿𝛿𝑐𝑐 = 0.25, there is a substantial increase in
the spectral energy from 𝜆𝜆 = 0.1𝛿𝛿 to about 20𝛿𝛿 , with adominant peak at 𝜆𝜆 = 2 − 3𝛿𝛿 . Further downstream 𝜆𝜆𝜆𝜆(𝜆𝜆)decreases for all 𝜆𝜆s and at 𝑥𝑥⁄𝛿𝛿𝑐𝑐 = 3.5, it is smaller than that in
the canonical TBL for 𝜆𝜆 > 𝛿𝛿 (figure 3a). From figure 3b we cansee that at 𝑦𝑦⁄𝛿𝛿~0.25 the energy downstream of LEBU isenhanced at all the wavelengths even at 𝑥𝑥⁄𝛿𝛿𝑐𝑐 = 0.05 and again
as with 𝑦𝑦⁄𝛿𝛿~0.21, the spectral energy gradually decreases as wemove further downstream. Figure 3c shows the difference premultiplied spectrogram of the perturbed TBL with respect tocanonical TBL at 𝑥𝑥 ⁄𝛿𝛿𝑐𝑐 = 0.25. Above the LEBU, there is anincrease of spectral energy for nearly all the scales (with thehighest enhancement happening just above the LEBU), whereas
the spectral energy is reduced below the LEBU as compared tothe canonical TBL.

(a)
.

(a)

(b)

(b)
(c)

Figure 4. (a) Mean velocity profile measured over the LEBU
surface compared with the canonical TBL. (b) Spectrogram of premultiplied energy measured over the LEBU surface.
Figure 3 Pre-multiplied spectra of the perturbed TBL
compared with the canonical TBL at (a) 𝑦𝑦/𝛿𝛿 ≈ 0.21 and (b)𝑦𝑦/𝛿𝛿 ≈ 0.25 (c) Difference spectrogram at 𝑥𝑥/𝛿𝛿𝑐𝑐 = 0.25
where the magenta line shows the position of LEBU. The
colour bar shows the difference in the pre-multiplied spectralenergy.
3

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
20 − 30𝛿𝛿 obtained in the experiments of Diwan and Morrison(2017) who subjected a laminar boundary layer to broadband
grid turbulence. They further showed that their results could beinterpreted in terms of the “rapid-distortion theory”. This
provides a support to the present conjecture that the energy
generated within the new layer over the LEBU is due to therapid-shearing mechanism. These newly generated energetic
eddies are swept downstream which is reflected in the premultiplied spectrum in the wake of the LEBU at 𝑥𝑥⁄𝛿𝛿𝑐𝑐 = 0.25,
displaying a prominent peak at 𝜆𝜆 = 3𝛿𝛿 (figure 3a). The elevatedspectral energy for large 𝜆𝜆, in comparison with the canonical
TBL, is also evident in the spectra at 𝑦𝑦⁄𝛿𝛿 ≈ 0.25 up to𝑥𝑥⁄𝛿𝛿𝑐𝑐 = 1.25 (figure 3b). This suggests that a LEBU can affectturbulent fluctuations over a wide range of scales (and not
merely large scales); see also Savill and Mumford (1988).
Figure 5(a) shows the pre-multiplied spectrogram at 𝑥𝑥 =0.25𝛿𝛿𝑐𝑐 downstream of the LEBU. Apart from the elevatedenergies appearing at small wavelengths of the order 𝜆𝜆 = 0.1𝛿𝛿,the spectral energy is primarily focussed at two energy sites –one near the wall at 𝑦𝑦⁄𝛿𝛿 ≈ 0.01 and the other near the LEBU
location at 𝑦𝑦⁄𝛿𝛿 ≈ 0.2. The shape of the spectrogram in figure5(a) resembles that observed in a high-Reynolds number TBL(Hutchins and Marusic 2007) where the spectral energy isfocussed into an inner peak and an outer peak. The scale
separation between these two energy sites in the present
experiment is not as large as that observed for the high-Re TBL,
since our Reynolds numbers are much lower. Nevertheless,perturbing a TBL with the help of a LEBU can be useful inmimicking the spectral structure of the high-Re TBL in a lowReynolds-number wind-tunnel facility to understand the innerouter interaction among different turbulence scales.
Figure 6 (a) presents the amplitude-modulation coefficient,
𝑅𝑅, between the filtered envelope of small scales and the filteredlarge scales as defined by Mathis et al. (2009); a cut-off
wavelength of 𝜆𝜆 = 1.5 𝛿𝛿 is used for this purpose. Note that thestandard practice is to use 𝜆𝜆 = 𝛿𝛿 as the cut-off wavelength fordecoupling of large and small scales in high Reynolds number
TBLs (Mathis et al. 2009). The larger cut-off wavelength usedhere is because the near-wall spectral peak appears around thisvalue of 𝜆𝜆 (figure 5a) in the present experiment, which we would
like to consider as part of the “small scale” range as per the
standard practice. We have confirmed that using 𝜆𝜆 = 1.5 𝛿𝛿 as
the cut-off wavelength produces almost the same result asobtained using a cut-off of 𝜆𝜆 = 𝛿𝛿 (see also Mathis et al. 2009).
It is evident that the presence of LEBU affects the variation of 𝑅𝑅
over the region 0.4 > 𝑦𝑦⁄𝛿𝛿 > 0.02 , beyond which 𝑅𝑅 for the
perturbed TBL is close to that for the canonical TBL (figure 6a).
There is a significant increase in amplitude modulation around𝑦𝑦⁄𝛿𝛿 ≈ 0.2, with 𝑅𝑅 exhibiting large positive values, comparable
to or higher than those seen for the canonical TBL near the wall.
Above the LEBU, there exists a small region of decreased scalecorrelation relative to the canonical TBL. It is clear from figure
6a that larger scales introduced by the LEBU significantly
modulate the smaller scales near its vicinity, thereby altering thestructure of the oncoming TBL.
To better characterize the effect of presence of LEBU on thescale interactions within the TBL, we carry out an exercise of
calculating amplitude modulation coefficients using two cut-off
wavelengths – 𝜆𝜆 = 1.5𝛿𝛿 and 𝜆𝜆 = 0.2𝛿𝛿. This is shown
schematically in figure 5(b). The use of two cut-off wavelengths
results in three different ranges of scales (figure 5b) – (a) R1,
representing scales predominantly induced by LEBU at 𝜆𝜆 >1.5𝛿𝛿, (b) R2, involving the range of scales between 𝜆𝜆 = 1.5𝛿𝛿

(a)

(b)

Figure 5 (a) Pre-multiplied spectrogram at 𝑥𝑥 = 0.25𝛿𝛿𝑐𝑐
downstream of the LEBU. The LEBU is represented by themagenta line. 𝜆𝜆+ is the wavelength scaled on wall variables
using 𝑢𝑢𝜏𝜏 for the canonical TBL. (b) Schemetic of the ranges ofscales (R1, R2 and R3) obtained by setting two cut-off
wavelengths used for calculating the amplitude modulation
coefficient. See the text for more details.
To understand the large amplification of energy observed at𝑥𝑥⁄𝛿𝛿𝑐𝑐 = 0.25, we have carried out velocity measurements “over”
the LEBU (i.e., on the LEBU surface), at the mid-location along
its length. The mean velocity profile compared with thecanonical TBL is shown in figure 4a. As expected, a new viscous
layer is seen to be formed over the LEBU, which is responsible
for breaking up the large eddies. However, there is anotherimportant consequence of the presence of such an “internal”
shear layer within a TBL. The large velocity gradients within
this layer can cause a “rapid shearing” of the turbulent eddies in
the oncoming TBL, giving rise to relatively long streamwise
structures. This is evident from the pre-multiplied spectrogramin figure 4b which shows that a significant energy is generated
in wavelengths 𝜆𝜆 > 𝛿𝛿𝑐𝑐 , with the peak energy at 𝜆𝜆 ≈ 3𝛿𝛿𝑐𝑐 . In fact,
the spectral energies in figure 4b near the LEBU surface arecomparable or higher than those present around 𝑦𝑦/𝛿𝛿 ≈ 0.2 inthe canonical TBL (figure 3a). The wavelength of 3𝛿𝛿𝑐𝑐 represents
a streamwise structure which is about 30 times the thickness of
the internal layer formed over the LEBU (which is ≈ 0.1𝛿𝛿𝑐𝑐 ;figure 4). This is comparable to the streamwise structures of4

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022and 𝜆𝜆 = 0.2𝛿𝛿, and (c) R3, representing scales smaller than 0.2𝛿𝛿that are typically present in the wall layer. These ranges are also
marked on the spectrogram at 𝑥𝑥 = 0.25𝛿𝛿𝑐𝑐 shown in figure 5a.
The modulating effect of R1 on the combined ranges of R2 andR3 has already been shown in figure 6a – which we term as the“conventional” (single cut-off) exercise.
In the following, we compare the amplitude modulation
coefficients obtained by considering different ranges of scaleswith those corresponding to the conventional single cut-off.
First, we list out the features for the modulation of R3 by R2(figure 6b):i. The modulating effect is localized close to the LEBU
𝑦𝑦
location (0.1 < 𝛿𝛿 < 0.25).

(b) R2 on R3

𝑦𝑦ii. The peak positive correlation around 𝛿𝛿 = 0.2 decreases

more rapidly as we move downstream than in figure 6a.
𝑦𝑦iii. The negative correlation from = 0.5 to the edge of the𝛿𝛿boundary layer is reduced drastically. Interestingly thiseffect is observed also for the canonical TBL.
iv. The local minima in R above and below the LEBU are
decreased in magnitude and shifted closer to the LEBU.
Next, we consider the effect of R1 on R2 (figure 6c):𝑥𝑥
i. The peak positive correlation is reduced for 𝛿𝛿 = 0.05(c) R1 on R2

𝑐𝑐

whereas that for other 𝑥𝑥 locations is not much affected.
ii. Overall, the shape and the extent of modulation in wall
normal direction remains similar to the conventional case(figure 6a).
Finally, we describe the modulating effect of scales R1 on scales
R3 (figure 6d):𝑦𝑦i. The peak positive correlation near the LEBU (𝛿𝛿 ≈ 0.2) is𝑥𝑥large for all 𝛿𝛿 > 0.05 compared with that for the case𝑐𝑐

discussed above (figure 6c). It is nearly the same as for theconventional case (figure 6a).
ii. The positive correlation values near the wall are somewhat
increased for the LEBU as well as for the canonical TBL.
iii. The extent of modulation in wall normal direction
compared with that for the canonical TBL is similar to thatobserved for the conventional cut-off (figure 6a).

(a) Conventional(d) R1 on R3

Figure 6 Profiles of the amplitude modulation coefficient for the perturbued TBL compared with those for the canonical TBL. (a)Conventional (single) cut-off case 𝜆𝜆 = 1.5𝛿𝛿, (b) Range 2 on Range 3, (c) Range 1 on Range 2, (d) Range 1 on Range 3. See figure
5 for the definition of the three ranges.
512th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
Chin, C., Orlu, R., Monty, J., Hutchins, N., Ooi, A., andSchlatter, P., 2017, "Simulation of Large Eddy Break-Up Device(LEBU) in moderate Reynolds number turbulent boundary
layer," Flow Turbulence Combust., Vol. 98., pp. 445-460.
Diwan, S.S. and Morrison, JF., 2017, "Spectral Structure andLinear Mechanisms in a Rapidly Distorted Boundary Layer", Int.
J. Heat Fluid Flow, Vol.67, pp. 63-73.
Hutchins, N., and Marusic, I., 2007 "Evidence of very longmeandering features in the logarithmic region of turbulent
boundary layer: ", J. Fluid Mech. Vol. 579, pp. 1-28.
Mathis, R., Hutchins, N., and Marusic, I., 2009 "Large-Scale
Amplitude Modulation of Small-Scale Structures in Turbulent
Boundary Layers: ", J. Fluid Mech. Vol. 628, pp. 311-337.
Savill, A.M. and Mumford, J.C ,1988, "Manipulation of
Turbulent Boundary Layers by Outer -Layer Devices: SkinFriction and Flow Visualization Results", J. Fluid Mech Vol.
191, pp. 389-418.
Shalin, A., Johansson, A.V. & Alfredsson, P.H. 1988, "Thepossibility of drag reduction by outer layer manipulators inturbulent boundary layers", Phys. Fluids, Vol. 31., pp. 28142820.

To summarize the above exercise, we find that the modulating
effect of the large scales in R1 introduced by the LEBU on thesmall scales in R3 (figure 6d) is qualitatively similar to thatobserved with the conventional single cut-off (figure 6a). The
presence of LEBU significantly affects the modulation of small
scales immediately downstream of it, i.e., in its wake region. On
the other hand, the effect of the intermediate scales in R2 on thescales in R3 (figure 6b) is much different from that for theconventional case (figure 6a). In particular, the effect of LEBU
is much more localized and the negative correlation near theedge of the boundary layer is significantly suppressed, which isalso the case for the canonical TBL (figure 6b). The implicationsof these results towards understanding scale interactions within
the TBL perturbed by a LEBU are being explored. We believe
the scale interaction between small scales and “synthetic” large
scales could also help us better understand the amplitude
modulation caused by the “superstructures” in a canonical TBL
at high Reynolds numbers.
CONCLUSION
In this work we have characterized the structure of a TBL
perturbed by a LEBU in its immediate vicinity. We find that the
LEBU not only breaks up the large-scale eddies as understoodconventionally but also introduces significant energy at larger
scales (about 3 𝛿𝛿 ), through the rapid shearing of oncoming
disturbances by the new viscous layer formed over its surface.
The presence of LEBU causes a suppression of the near wall
turbulence peak which is an interesting observation. The
amplitude modulation of small-scale eddies by the larger scales
is significantly altered over a certain region above and below the
LEBU. To better characterize the effect of the presence of LEBU
on the scale interactions within the perturbed TBL, we havecalculated the amplitude modulation coefficient using two cutoff wavenumbers and compared the results with theconventional analysis that uses a single cut-off for thewavenumber. The present work highlights the utility of LEBU
as an effective manipulator of the structure of a canonical TBL.
ACKNOWEDGEMENT
A.T. thanks Mr Satyajit Dey for providing LabVIEW codes forcarrying out the present measurements. S.S.D. acknowledges
financial support from Science and Engineering Research Board(SERB), India through the grant ECR/2018/002417. We thankan anonymous referee for suggesting the amplitude modulation
exercise with two cut-off wavelengths.

REFERENCES
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Chan, I.C., Orlu, R., Schlatter, P., and Chin, R.C 2021, "TheSkin Friction Coefficient of Turbulent Boundary Layer
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