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

THE QUIESCENT CORE OF TURBULENT CHANNEL FLOW UNDER THE
INFLUENCE OF INLET TURBULENCE

Masoud Asadi
Department of Energy and Process Engineering
Norwegian University of Science and Technology
Trondheim, Norway
masoud.asadi@ntnu.no

Md Kamruzzaman
Department of Energy and Process Engineering
Norwegian University of Science and Technology
Trondheim, Norway
md.kamruzzaman@ntnu.no

R. Jason Hearst
Department of Energy and Process Engineering
Norwegian University of Science and Technology
Trondheim, Norway
jason.hearst@ntnu.no

ABSTRACT

ulations, examined the structural organization of the QC by
exploring the vortical structures in the flow, stating that thecore boundary is surrounded by a vortex pair with the prograde
vortex to be the main contributor to the mean shear. Later, Jieet al. (2019) examined the effect of the QC on the motion of
spheroidal particles in a channel, finding that the motion of theparticles also tends to be quiescent in the QC. Following theirprevious study, Jie et al. (2021) assessed the distributions ofinertial particles in a turbulent channel flow, stating that particles tend to congregate within the QC.

The quiescent core of turbulent channel flow is examined
under the influence of inlet turbulence using planar particle image velocimetry. Four cases are tested with matched centerline
mean velocities, while the centerline turbulence ranged from
3.7% for the reference case, up to 6.4% for the most turbulent case. A matched friction Reynolds number of Reτ ≈ 770
is found for all cases, which contrasts with similar measurements in a zero-pressure-gradient boundary layer where Reτvaries with freestream turbulence. The added turbulence increases the frequency of core discontinuity inside the channel
and gives rise to new core types. The new cores differ from theconventional ones in their characteristic velocity, while theiroccurrence increases with turbulence intensity. They are associated with a bulk of low- or high-momentum fluid passing
through the measurement domain. Their presence in the channel implies a more turbulent state of the flow inside the coreregion. It is also observed that, under the effect of increased
inlet turbulence intensities, the core boundary moves closer tothe wall, which yields thicker cores.

The sensitivity of zero-pressure-gradient turbulent boundary layers (ZPG-TBL) to the freestream turbulence (FST)
above it has been tested extensively (Sharp et al., 2009; Dogan et al., 2016, 2019; Jooss et al., 2021; Hearst et al., 2021).
FST is known to suppress the wake region of the velocity profile and increase the friction Reynolds number (Reτ ) of ZPGTBLs (Sharp et al., 2009; Dogan et al., 2016). It also affects
ZPG-TBLs by amplifying normal Reynolds stresses as well as
the Reynolds shear stress. Recently, Hearst et al. (2021) investigated UMZs of a ZPG-TBL under the effect of FST, statingthat increased FST pushes the top boundary of the outermost
UMZ towards the wall and increases the velocity jump acrossthis boundary.

INTRODUCTION
The so-called quiescent core (QC) of turbulent channel
flow was first identified by Kwon et al. (2014) as the uniform
momentum zone (UMZ) occupying the central region of thechannel. It was referred to as ‘quiescent’ because the fluctuations of the streamwise velocity remain low throughout thecore. Examining the accumulated probability density function(PDF) of modal velocities (the peaks in the histogram of instantaneous streamwise velocity fields), Kwon et al. (2014)
stated that the core boundaries could be identified using a constant velocity threshold equal to 95 % of centerline mean velocity (the same constant boundary threshold value was foundin later studies by Yang et al. (2016, 2019); Jie et al. (2019,2021)). The QC was always present in the flow fields; however, it became discontinuous in some instances. Kwon et al.
(2014) also observed a sharp jump in the streamwise velocity across the QC boundary which indicated the presence ofa shear layer. Yang et al. (2016), using direct numerical sim-

Most previous internal flow investigations have primarily
focused on Reynolds number effects, e.g., Ng et al. (2011);
Lee & Moser (2015), and recently, a number of studies havebeen conducted to investigate wall motions in turbulent channel flow, e.g., Józsa et al. (2019); however, the effects of inlet
turbulence have not been investigated in great detail for internal flows. Recently, Tuna et al. (2019) explored the evolutionof flow in a duct with an aspect ratio of 2:1 using different
passive grids at the inlet and found that the shear layers met
earlier for increasing centerline turbulence intensity. However,the corners certainly affect the flow in the center of a 2:1 duct
(Vinuesa et al., 2018). Accordingly, to investigate the impactsof added turbulence on the quiescent core of turbulent channel
flow, four different turbulence intensities were produced at the
inlet of a turbulent channel flow, and PIV measurements were
performed in a region far from the inlet.

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12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
Table 1.

Parameters of the test cases.

Case

SymbolColoru′0 /U0 (%)

Uτ (ms−1 )

REF

▶

green

3.7

0.460

A

■

magenta

4.8

0.470

B

•

blue

4.9

0.468

C

♦

red

6.4

0.466

Figure 1. PDFs of the highest (green) and second highest(orange) modal velocities, found in all PIV fields for cases(a) REF, and (b) C. The grey dashed lines mark u = 0.95U0 .
Adapted from Asadi et al. (2022).

EXPERIMENTAL DETAILS
15 Hz using LaVision DaVis 10.1. The same software wasused to process the images using iterative cross-correlation
with a final-pass-window size of 48 pixels × 48 pixels withan overlap of 75 %.

Experiments were conducted in the air channel flow facility at the Norwegian University of Science and Technology. A
centrifugal fan was used to generate the air flow, which blows
air through a series of 4 screens through an expansion. The
flow then passes through a honeycomb before another screen
and then a 48:1 contraction at the end of which is a 600 mm ×
50 mm rectangular duct with an aspect ratio of 12:1. An active
grid is located 125 mm (2.5H, where H = 2h = 50 mm is thechannel height) downstream of the contraction, followed by asandpaper trip another 50 mm (1H) downstream. The active
grid comprises a 12 × 2 array of space-filling 3D-printed PLA
plastic rectangular wings, where each wing is attached to a
stepper motor. Each stepper motor receives prescribed random
rotational direction, velocity, and duration signals. Four test
cases were tested, i.e., the reference case ‘REF’ where the active grid was left in its fully open position, thus acting as an additional flow straightener, together with three different active
sequences referred to as cases ‘A’, ‘B’, and ‘C’, with increasing
centerline turbulence intensity (u′0 /U0 ). The centerline mean
velocity was held constant to within 1% at U0 = 10 m/s, resulting in a Reynolds number of ReH = U0 H/ν = 33,200.
Further details are given in Table 1. The pressure drop along
the channel was measured at 16 pressure taps using a Scanivalve MPS4264 miniature pressure scanner with an accuracyof ±2 % of the full scale. The first tap was located 7.5H downstream of the inlet, and the taps were separated in intervals of
325 mm (6.5H). From the pressure drop measurements, thewall shear stress τ could be estimated, and from it, the friction velocity Uτ . Even though previous studies have observed
an increase in friction velocity for a ZPG-TBL subjected to
FST (Sharp et al., 2009; Dogan et al., 2016), the friction velocity, listed in table 1, is roughly constant for different cases
resulting in an approximately matched friction Reynolds number of Reτ ≈ 770.
Planar particle image velocimetry (PIV) measurements
were performed in the streamwise—wall-normal plane in thecenter of the channel 87H downstream of the inlet. Doubleframe images (5100 image pairs for each test case) were acquired using a LaVision Imager sCMOS camera (5 megapixel) fitted with a Zeiss Milvus 2/100M lens. The final fieldof-view (FOV) was approximately 50 mm × 44 mm, i.e., 2h inheight and 1.75h in length. An industrial smoke machine wasutilized to produce particles with a diameter of approximately
1 µm, which were injected into the flow at the fan entrance.
FOV was illuminated by a Litron Nano PIV laser (Nd-YAG,
532 nm, 200 mJ per pulse). The laser beam was turned intoa thin sheet using LaVision light sheet optics. The lens f number was set to 11, resulting in a particle size of approximately 2-3 pixels, which helped circumvent pixel-locking issues. A LaVision PTU X synchronized the laser and camera,
and the independent samples were recorded at a frequency of

CORE IDENTIFICATION PROCEDURE
The conventional method introduced by Kwon et al.
(2014) is modified here to identify the QC boundary thresholdvalue with less ambiguity. Since the QC is the UMZ with thehighest momentum level in the core, its characteristic velocity corresponds to the highest modal peak in the instantaneous
histogram of the velocity fields. Thus, instead of assessing
the accumulative PDF of all modal velocities detected in thehistograms of instantaneous PIV fields, PDFs of the first andsecond highest modal velocities are assessed here as the characteristic velocities of the two most robust UMZs of the channel. Figure 1(a) shows these PDFs plotted on top of each otherfor case REF. A distinguishable trough is exposed between the
PDFs, whose corresponding value can be picked as the boundary threshold to identify QCs. Accordingly, a constant boundary threshold value of uth = 0.95 U0 is chosen. Although thesame boundary threshold value is found for the added turbulence cases (A, B, and C), the prominence of the trough diminishes for increased inlet turbulence intensities (e.g., see
figure 1(b) for PDFs of case C) due to more spread distributions of the modal peaks. Figure 2 shows three examples of
the identified cores in different fields of case C. Figure 2(a)and 2(b) demonstrate a continuous and a discontinuous core of
the turbulent channel flow, respectively. These two core types
were previously observed by Kwon et al. (2014). It is observed
here that the discontinuous core events increase in frequency
for increased centerline turbulence intensities. In contrast to
the results of Kwon et al. (2014), the present results include
instances in which the QC is not detectable using the opted
constant threshold value, particularly for the highly turbulent
case C (e.g., figure 2(c)). These instances only occur for theadded turbulence cases, and their frequency scales with u′0 /U0 .
In search of finding the core structure for these fields,
in which the conventional QC was not identifiable, the same
PDF analysis was repeated. Figure 3(a) represents the resulting PDFs, where a distinct valley is revealed at uth = 0.85U0 .
Also, the PDFs of both the first and second highest peaks are
displaced towards lower velocity values while showing thesame normal distribution as observed previously in figure 1.
This indicates that the core structure is present in these velocity fields; however, a lower threshold value should be utilized
to identify them. The lower characteristic velocity of thesecores demonstrates a lower momentum level inside the coreregion compared to the conventional QCs (CQC). Therefore,
these new core types are referred to herein as low momentum2

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

.

.

.

Figure 2. Instantaneous streamwise velocity contours from PIV snapshots of Case C. Contour lines of uth = 0.95 U0 are indicatedwith black lines. The thicker lines highlight the QC boundaries. (a) conventional QC, (b) discontinuous QC, and (c) without QC.
Adapted from Asadi et al. (2022).

Figure 3. PDFs of the highest (green) and the second highest (orange) modal velocity, found in the PIV fields of (a) instances without QC, and (b) instances identified by presumed
threshold value, for case C. The grey dashed line marks u =0.85U0 and u = 1.04U0 in (a) and (b), respectively. Adaptedfrom Asadi et al. (2022).

Figure 4. Examples of new core types. (a) an example of avelocity field with a low momentum core (the same field asshown in figure 2(c)), where the core boundaries are marked
by the black contour lines of uth = 0.85U0 . (b) an example
of a velocity field with a high momentum core, where the
new core boundaries are demarcated by the contour lines of
uth = 1.04U0 (black thick lines) and are located within the previously found conventional QC boundaries marked by the contour lines of u = 0.95U (black thin lines). Adapted from Asadi
et al. (2022).

cores (LMC). Furthermore, some of the velocity fields wereidentified in which a new core type is found inside the traditional QC with a higher boundary velocity threshold. To identify these fields, a higher velocity threshold value (1.065U0 )was presumed so that the number of continuous cores identified by this new threshold was close to the number of the previously identified LMCs. Figure 3(b) shows the resulting PDFs
of these newly identified fields, indicating an actual boundary
threshold value of uth = 1.04U0 . This new threshold value canbe utilized to identify the core structure of these fields. In contrast to LMCs, the PDF of the highest modal peak indicates ahigher characteristic velocity for these new cores than that for
CQCs. Thus, these new cores take on higher momentum levels and are referred to herein as high momentum cores (HMC).
Figure 4(b) represents an example of these fields with the actual core demarcated by the contour lines of uth = 1.04U0 ,demonstrating that the newly identified core was previously
hidden within the boundaries of the CQC identified by theconstant threshold value of 0.95U0 . The number of the different core types identified in the PIV fields of the different
test cases is listed in table 2. Like LMCs, HMCs exist only forthe added turbulence cases and occur with the same frequency
as LMCs. The occurrence frequency of the new cores, i.e.,
LMC and HMC, as well as the discontinuous core, increases
with increasing centerline turbulence intensity. Nonetheless,the growth rate of the presence of the new core types is greaterthan that of the discontinuous cores.

CORE STATISTICAL ANALYSIS
Parameters of the core location (yl , yu , and yc denote thecore’s lower boundary, upper boundary, and center location,
respectively, and tc is the core thickness) are illustrated in figure 5. For the statistical analysis of these parameters, the coreboundaries must be single-valued functions of the streamwise
coordinate (x). This is not always the case since the coreboundaries are usually folded back and forth. Kwon et al.
(2014) employed the inner-enveloping method to remedy thisproblem. The same technique is used here, where the closest point to the center of the channel is picked whenever thecore boundary does not have a single value at a specified x.
The examples of inner-enveloped core boundaries are shownin figure 5 as well.
Distributions of the core location parameters are represented in figure 6. Figure 6(a) shows the PDF of the core’s
lower boundary location for the different test cases, where theprobability of the presence of the core boundary in the inner
regions (−0.9 < yl /h < −0.5) is increased by increasing inlet
turbulence intensity. This indicates that increased turbulencepushes the core boundary towards the wall, which is similar
to the observation of Hearst et al. (2021) that in a ZPG-TBL

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

The presence of the various core types in the PIV fields of each test case as a percentage of total fields (5100).

Core type

SymbolNo. of different core types (%) for case

Color

REF

A

B

C

LMC

▲

orange

0

2.3

2.6

11.0

CQC

/

black

97.0

86.6

85.8

68.2

HMC

▼

violet

0

3.2

3.4

11.4

Discontinuous

-

-

3.0

7.9

8.4

9.4

.

the new core states with different characteristic velocities than
CQCs’. The same behavior is also noticed for the zonally averaged streamwise velocity fluctuations outside the core region.
The other averaging method is called conditional averaging. In this method, the wall-normal coordinate (y) is translated to the core lower boundary (yl ), and the streamwise velocity and its fluctuations are averaged across the core boundary (denoted by ⟨⟩). Due to the presence of the new core stateswith different boundary threshold values, the instantaneous
streamwise velocities were offset by the local uth before averaging to make the profiles comparable for different test cases.
Figure 7(c) shows the conditionally averaged streamwise velocity profiles suggesting that the added turbulence does notaffect the behavior of the velocity profile near the boundary of
the core as a sharp jump is observed in the vicinity of the coreboundary for all the test cases. This is typical of UMZs andindicative of the thin shear layer which forms the boundary of
the core (Kwon et al., 2014; Yang et al., 2016). Furthermore,an almost constant velocity is observed inside the core awayfrom the boundary, as was expected for UMZs. Nevertheless,the fitted lines suggest that the added turbulence increases thevelocity jump across the core boundary, which is in line withthe observation made by Hearst et al. (2021) regarding the increased velocity jump across the upper-most UMZ of a ZPGTBL under the influence of FST. This can be explained by recalling the trend observed in figure 6(a), where the core’s lower
boundary is located closer to the wall under the effect of inlet
turbulence. Therefore, under the influence of increased inlet
turbulence, the core is closer to the inner regions with lower
streamwise velocity values, which increases the velocity jumpacross the core boundary. Figure 7(d) demonstrates conditionally averaged streamwise fluctuations. The order of the profiles outside the core boundary scales with u′0 /U0 and indicatesan increasing trend for increased centerline turbulence intensities. Meanwhile, a low turbulence level is observed inside
the core region, approximately equal for the different cases regardless of the added turbulence intensity. This may seem tocontrast with the trends observed in figure 7(b). However, thekey to this implausible paradox lies in the difference between
the two averaging schemes. The zonal-averaging analysis assesses the fluctuations of the streamwise velocity relative tothe zonally averaged velocity in different locations within thechannel, where the emergence of the new cores with different characteristic velocities affects the zonally averaged fluctuations level inside the core region (the results are presented
in the following section). At the same time, the conditionalaveraging scheme assesses the fluctuations of the streamwise
velocity offsetting the velocities by the local boundary threshold value; thereby, the region inside the core appear to be quiescent regardless of the core momentum level.

.

Figure 5. Core location parameters together with enveloped(black solid line) and un-enveloped (black dotted line) coreboundaries. The green dashed line shows the core’s center position. Adapted from Asadi et al. (2022).

subjected to FST, the upper boundary of the outermost UMZ
is moved closer to the wall. Figure 6(a) also indicates that theprobability of the events where the core’s lower boundary ispresent in the near-wall region (yl /h < −0.9) or is thoroughly
dragged above the channel’s centerline (yl /h > 0) is equally
low for all the test cases. Figure 6(b) illustrates the distribution of the core’s center location, where all the PDFs show anormal distribution centered about the channel centerline, as
is expected due to the symmetry of the channel. Figure 6(c)shows the PDFs of core thickness, demonstrating that the increased inlet turbulence intensity yields, on average, thicker
cores.
Two averaging techniques are utilized to assess the impactof the inlet turbulence on the flow characteristics inside andoutside the core region. The first technique zonally averages
the streamwise velocity and its fluctuations (inner normalized)
when the flow is situated inside and outside the core region,
which are denoted by subscripts ‘i’ and ‘o’, respectively (seeKwon et al., 2014, section 4 for details). As shown in figure 7(a), the zonally averaged streamwise velocity takes on
an approximately constant value inside the core region whichscales with U0 . The profiles collapse for all the cases inside
the core region, indicating the same mean velocity inside thecore for different test cases irrespective of the presence of the
new core types. The profiles also match outside the core region. On the other hand, figure 7(b) demonstrates zonally averaged streamwise fluctuation profiles inner normalized by Uτ2 ,indicating an increase in turbulent fluctuations inside the corewith increasing u′0 /U0 . This happens due to the presence of4

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

Figure 6. PDF of (a) the core’s lower boundary location, (b) the core’s center location, and (c) the core thickness, for different test
cases. See table 1 for symbols and colors. Adapted from Asadi et al. (2022).

core types of case C, the zonally averaged profiles are presented in figures 9(a) and 9(b). As shown, the flow takes on
different constant mean velocity levels when located inside
LMCs, CQCs, or HMCs. These constant velocity levels canbe considered as the cores’ characteristic velocities, which are
0.9U0 , 1.0U0 , and 1.1U0 for LMCs, CQCs, and HMCs, respectively, indicating different momentum levels of each core
type. Nonetheless, LMCs and HMCs almost neutralize eachother when cumulatively averaged (figure 7(a)). Figure 9(b)illustrates zonally averaged streamwise fluctuation profiles,
demonstrating an equally low level of fluctuations within the
different cores. As stated in the previous section, the different velocity levels within the cores indicate a generally moreturbulent flow inside the core region for increased inlet turbulence intensities (figure 7(b)). However, when the deviationsof the instantaneous velocity from the zonally averaged velocity are assessed for each core type separately, a low level offluctuations is indicated (figure 9(b)).
Figure 9(c) shows the conditionally averaged streamwise
velocity profiles for the different core types, where the profiles are matched both inside and outside of the core region.
This indicates that the shape of the velocity profile and themagnitude of the relative velocity jump are independent of thecore momentum level. The same concept can be observed infigure 9(d), where a uniformly low level of conditionally averaged streamwise velocity fluctuations is observed inside thecore region, verifying that each core is a localized UMZ andthat the identification process utilized in this study is reliable.

.

Figure 7. Zonally averaged profiles of streamwise (a) velocity and (b) turbulent fluctuations, inside the core (filled symbols) and outside of it (open symbols) for the different test
cases. Conditionally averaged profiles of streamwise (c) velocity and (d) turbulent fluctuations across the core boundary
for the different test cases (the grey dashed line shows the coreboundary). See table 1 for symbols and colors. Adapted from
Asadi et al. (2022).

STATISTICAL ANALYSIS OF NEW CORESIn order to further explore the characteristics of the newly
identified core types, the statistical analysis performed in theprevious section is repeated here for the different continuous
core types. Since case C has the highest number of the newly
identified cores, different continuous core types of this test
case are analyzed here as an example. The discontinuous coresare discarded in the analysis of this section.
Similar to figure 6, figure 8 illustrates the distributions of
core’s location parameters for the different core types of case
C. PDFs of the core’s lower boundary location are shown infigure 8(a), where the lower boundary of LMCs appears to belocated closer to the wall compared with CQCs’. Conversely,
the lower boundary of HMCs generally resides closer to thechannel centerline than that of CQCs. Once more, due to thesymmetry of the channel, a normal distribution, centered at
y/h = 0, is observed for PDFs of the core’s center location
regardless of the core type. Considering the location of thecores’ lower boundary, this implies thicker LMCs and thinner
HMCs on average, as shown in figure 8(c).
Repeating the zonal averaging technique for different

CONCLUSIONS
The inlet turbulence effect on the QC of turbulent channel
flow was investigated using PIV measurements in a region far
from the inlet. Four different inlet turbulence levels were produced using an active grid located at the inlet of the channel.
The centerline mean velocities were matched for the different
test cases. Uτ did not show any correlation with the centerline turbulence intensity as opposed to the previous observations regarding an increase in Uτ of a ZPG-TBL with increasing FST intensities (Sharp et al., 2009; Dogan et al., 2016).
Furthermore, the results indicate that the inlet turbulence significantly impacts the core of turbulent channel flow. It considerably influences the momentum level of the core and generates new core types with lower and higher momentum levels(LMC and HMC, respectively) than that of the conventionalquiescent core (CQC). As a result, different boundary threshold values should be utilized to identify each core type correctly. Inlet turbulence also manipulates the frequency that thecore appears in various types. Thereby, the number of LMCs
and HMCs, as well as the discontinuous cores, increases with5

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

Figure 8. PDF of (a) the core’s lower boundary location, (b) the core’s center location, and (c) the core thickness, for the different
continuous core types of case C. See table 2 for symbols and colors. Adapted from Asadi et al. (2022).

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Figure 9. Zonally averaged profiles of streamwise (a) velocity and (b) turbulent fluctuations, inside the core (filled symbols) and outside of it (open symbols) for the different continuous core types of case C. Conditionally averaged profilesof streamwise (c) velocity and (d) turbulent fluctuations acrossthe core boundary the different continuous core types of caseC (the grey dashed line shows the core boundary). See table 2
for symbols and colors. Adapted from Asadi et al. (2022).

increasing inlet turbulence intensity. The passage of new coretypes with different momentum levels implies a higher turbulence level of the flow situated within the core. Nevertheless,when each core is observed separately, it possesses a uniformcharacteristic velocity and a low turbulence intensity within its
boundaries as an indication of the common nature of the coresas UMZs.
Although the core possesses different momentum levels,
its persistence indicates that it keeps driving the fluid in internal flows, even when the inlet is far from the canonical case.
For more details on this work and greater discussion of
the results, see Asadi et al. (2022).

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