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

HISTORY EFFECTS AND WALL SIMILARITY OF NON-EQUILIBRIUMTURBULENT BOUNDARY LAYERS IN VARYING PRESSURE GRADIENTOVER ROUGH AND SMOOTH SURFACES

Vidya Vishwanathan, Daniel J. Fritsch, K. Todd Lowe, William J. Devenport
Kevin T. Crofton Department of Aerospace
Ocean Engineering
Virginia TechBlacksburg, VA 24060
vidya418@vt.edu, dannyf96@vt.edu, kelowe@vt.edu, devenport@vt.edu

ABSTRACT𝑑𝑼!

The effect of non-equilibrium pressure gradients androughness on the behavior of turbulent boundary layers are investigated. In this experimental study, a family of systematically varying non-equilibrium pressure gradients was generated from the pressure field of a NACA 0012 airfoil over bothsmooth and rough wall surfaces. The rough surface consistedof 2 mm tall, staggered, circular cylindrical elements producing flow conditions that were in the fully rough regime. The
behaviors of the velocity field were measured using a custom
Pitot-probe rake and time-resolved particle image velocimetry (TR-PIV). The results show that the primary effect of theroughness is to increase the magnitude of the outer layer parameters. History effects, due to the changing pressure gradients, are apparent in the integrated boundary layer parameters indicating that rough and smooth wall flows are affectedby both local and historical flow conditions. It is shown thatindirect skin friction methods are sensitive to regression fitsof the mean velocity profiles. Within the uncertainty of theseempirical methods, the effective sandgrain roughness parameter appears to remain constant with streamwise and pressure
gradient flow development, thus supporting the wall-similarity
hypothesis for non-equilibrium rough wall flows.

𝑘"

𝑠

𝑠/2
2𝑠

Figure 1. Staggered, circular cylindrical roughness configuration used in this study; s = 6.93mm, d = 3.14mm, kg = 2mm.
Inset shows features of a cylindrical element.

To understand the concept and behaviors of flows in nonequilibrium, it is useful to first establish what is considered to
be a flow in equilibrium. Equilibrium conditions are idealizedstates in which flow properties are only dependent on local
flow conditions, and the evolution of mean velocity and turbulence quantities with streamwise position can be collapsedby scaling on the basis of self-similarity (Devenport & Lowe(2022)). In a non-equilibrium turbulent flow, the local flow
conditions are now also dependent on the history of conditions that the flow has experienced. In studies of smooth wall
turbulent boundary layers induced by pressure gradients ofchanging signs, Fritsch et al. (2020) and Vishwanathan et al.
(2021) have shown the impact of history effects on the fluctuating pressure and velocity features downstream of the pressure gradient switches. These are evidenced by a streamwise
delayed response of the integrated boundary layer parametersand mean turbulence statistics with respect to the location of
the pressure gradient switch.
For non-equilibrium rough wall flows a key question is thevalidity of the wall-similarity hypothesis, a concept first introduced by Townsend (1980), which suggests that on certain velocity parameter scalings, the boundary layer regions, outsideof the immediate roughness vicinity, collapse to the equivalentconditions in a smooth wall flow. (Jiménez (2004)) refined
the criteria for wall-similarity to specify roughness height (kg )limitations with respect to either the effective sandgrain rough-INTRODUCTION
Turbulent boundary layers are omnipresent in a wide
range of practical applications, such as over an aircraft wingor marine vehicle body. A wide range of studies have established a fundamental understanding of uni-directional pressure
gradient flows (e.g., De Graaff & Eaton (2000); Joshi et al.
(2014)). However, aside from use in controlled laboratory environments, these simple flows are just the building blocks forflows of practical interest. Real flows are susceptible to complex conditions impacted by both roughness and bi-directionalpressure gradients (i.e., pressure gradients that switch sign).
Surfaces in engineering application are usually not considered
to be hydrodynamically smooth either due to macroscopic defects in the surface finish or due to naturally occurring roughness such as dirt, ice, or biofouling. Roughness can contributeto drag, unwanted vibrations, and noise, which can negatively
impact the operation and design of vehicles. However, theseflows are more difficult to model; thus improving the current
array of knowledge for flows in non-equilibrium conditions isa relevant field of interest.

1

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
time. For ease of fabrication, the cylindrical element tips were
tapered by 1o . Given current skin friction estimates computedfrom regression fits of the rough wall law of the wall, theroughness Reynolds number ranges between ks+ = 243 − 488.
Thus, this flow is in the fully rough regime.

ness (ks ) or the boundary layer thickness (δ ). A number ofstudies (i.e., Raupach et al. (1991); Flack et al. (2005); Perry& Joubert (1963); Schultz & Flack (2005))have shown that forroughness sizes less than a certain factor of the boundary layer
thickness (the exact factor varies between authors, but is typically taken as δ /ks ≥ 40) roughness effects remain contained
within the vicinity of the roughness sublayer, thus satisfying
the question of wall-similarity. But enough studies, such asthat by Aubertine & Eaton (2005), suggest that the current criteria for wall similarity is insufficient, and additional parameters relating to the pressure gradient conditions are necessary.
As a majority of these studies have been conducted in equilibrium flow conditions, an evaluation of the wall-similarity
hypothesis in non-equilibrium rough wall flows is needed.
The present work aims to understand the behavior ofhigh Reynolds number wall-bounded turbulence induced under a systematically varying family of pressure gradients anddiscuss its compounding effects with roughness. In particular, investigations of the wall-similarity hypothesis of nonequilibrium rough wall flows are made and traditional analytical methods to determine roughness parameters are scrutinized. This experimental work largely uses the resultsfrom mean and instantaneous velocity fields measured using
time-resolved particle image velocimetry (TR-PIV), a custom
boundary layer rake, and other measures of mean flow conditions.

MECHANISM FOR WALL PRESSURE GRADIENT
A 0.914 m chord NACA 0012 airfoil, swept to both positive and negative angles of attack, generated a systematicallyvarying family of closely two-dimensional pressure gradientson the test section walls. The airfoil quarter chord was positioned at x = 3.45 m and y = 0.925 m with respect to the coordinate origin. Figure 2 shows a top-down schematic, of the test
section configuration. The magnitude of the pressure gradient
was computed using the Clauser pressure gradient parameter
defined as β = (∂ p/∂ x)δ ∗ /τw , where δ ∗ is the displacement
thickness. In this experiment the pressure gradients were mild
(i.e. no relaminarization nor separation), and ranged between−0.8 < β < +0.78. Because of the nominally symmetric airfoil and test section, both of the side walls experience the same
flow families. However, for ease of measurement access, theboundary layer wall of interest considered in this study was the“port” side wall corresponding to the lower wall in Figure 2.
The boundary layer wall experiences both an adverse and favorable pressure gradient. It should be noted that this is not an
airfoil experiment; the airfoil is simply used as a mechanism
to induce the pressure gradients.
Figure 3 shows the distribution of β , on the instrumented
portion of the center streamline on the boundary layer wall ofinterest. A comparison of the rough and smooth wall pressure
gradient distributions is shown in solid and dashed lines, respectively. At positive angles of attack the boundary layer wall
experiences an APG which switches to a FPG at a streamwise
location approximately adjacent to the airfoil quarter-chord.
The opposite phenomena are experienced by the wall when the
airfoil is at negative angles of attack. The β distributions showa systematic set of pressure gradients. Upstream of x = 3.45
m these vary from mildly favorable at negative angle of attack to mildly positive at positive angle of attack, and are very
similar for the smooth wall and rough wall boundary layers.
Downstream of this station, the pressure gradients switch signand the rough and smooth wall flows start to show markedly
different behavior, with significantly greater positive beta excursions for the rough wall.

EXPERIMENTAL FACILITY
All measurements discussed in this paper were conductedin the Virginia Tech Stability Wind Tunnel (VT SWT), which
is a closed-circuit facility. The empty tunnel freestream turbulence levels vary between 0.01% and 0.023% depending on
the flow speed, owing to seven turbulence reducing screens inthe settling chamber. The test section extends 7.32 m and has
a square cross section 1.85 m on edge. The test section sidewalls consist of 0.61 m length modular square aluminum panels that are carefully levelled to produce a continuous boundary layer flow surface. The boundary layer is tripped 3.58 m
upstream of the test section entrance and by the first measurement plane, is close to 51 mm thick in smooth wall and 62 mm
thick in rough wall configurations. These panels are arranged
in a grid pattern that can be removed and replaced with panels with custom instrumentation and wall conditions. The data
discussed in this paper were measured at a Reynolds number
per meter of 2.18 million based on the inflow freestream velocity, which at the time of the rough and smooth wall experimental studies was between U∞ = 33 − 36 m/s.

MEASUREMENT SYSTEMSThe two sidewalls of the test section were equipped with82 static pressure taps each. The taps were carefully flush
mounted to the inner wall/roughness substrate and had a 0.1
mm inner diameter. The mean surface pressure distributions
were measured using an Esterline 9816/98RK pressure scanner with a range of ± 10” H2 O and a 32-channel DTC Initium
scanner with a range of ± 4” H2 O. The reference pressure wasmeasured as the ambient pressure in the control room.
A custom 30-Pitot probe boundary layer rake was used tomeasure the mean velocity profiles at the streamwise locations
indicated by the black stations labeled on Figure 2. The probes
extend 178 mm from the wall, a sufficient length for capturing
the full rough and smooth wall boundary layer thicknesses.
The probe ports were connected to a 20” H2 O pressure range
DTC ESP 32HD pressure scanner. Bernoulli’s equation forstagnation pressure was used to extract the velocity boundary

ROUGHNESS GEOMETRY
A portion of the rough surface used in this study is shownin Figure 1. The surface entails a staggered pattern array ofcircular cylindrical elements that have a roughness height of
kg = 2 mm and diameter of 3.14 mm and are periodic on a
0.61 m x 0.61 m pattern (corresponding to the size of the removable test section panels). As shown in the test schematic in
Figure 2, the rough wall starts at the test section entrance andextends 5.43 m downstream covering the entire port side test
section wall. The elements are spaced s = 6.93 mm apart in thestreamwise direction, and half this distance in the spanwise direction. The roughness elements were fabricated from epoxy
using HDPE molds that were CNC milled with insets in theelement shape. The mold was then overlaid on an aluminum
test section panel and vacuum bag sealed for 24 hours of cure2

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

0.91

𝛼

𝑈!

4m

NACA 0012

𝑦0.925 m3.45 mTrip

Rough Wall

𝑥
5
1.2

m

6
1.8

m

1.85 m7.32 m3.58 m

7m m 8m
2.4 2.62 3.0
5.43 m

9m m 0m
3.6 4.05 4.3

1
4.9

m

Figure 2. Top-down schematic of the test section. Boundary layer wall of interest is the “port” wall, seen here as the lower wall,
which was either in smooth or rough wall configuration. Measurement locations of the boundary layer rake and TR-PIV are indicatedin vertical black and green lines, respectively.

layer profile from the wall. All mean velocity profiles and integrated boundary layer parameters discussed in this paper were
measured using the boundary layer rake.
Time-resolved PIV measurements were made at two
streamwise planes corresponding to the upstream and downstream locations of maximum pressure gradient, occurring approximately at x = 2.62 m and x = 4.05 m. The TR-PIV measurement locations are labeled in green in Figure 2 and indicated by the vertical solid lines in Figure 3. The smoothwall measurements were made in planar 2D, two component
configuration in which 10,000 realizations were recorded indouble-frame mode at a sampling rate of 12.5 kHz. The roughwall measurements were made in a stereoscopic 2D threecomponent configuration, in which 24,839 time realizations
were recorded at a 1 kHz sampling rate. Further information regarding the specifics of the PIV hardware system can befound in Vishwanathan et al. (2021). The camera and lens configurations resulted in spatial resolutions of 2.50 mm for thesmooth wall and 2.25 mm for the rough wall. The conversion
from raw image to velocity field was completed in LaVision’s
DaVis10 and then the data were post-processed for statistics
in MATLAB. All turbulence stress profiles discussed in thispaper were measured using the TR-PIV system.

1.5

1

0.5

0

-0.5

-1

-1.5
0

1

2

3

4

5

6

Figure 3. Streamwise variation of the Clauser pressure gradient parameter, β , as a function of the NACA 0012 angleof attack shown at the boundary layer rake measurement locations. Solid lines are the rough wall, dashed lines are thesmooth wall. Vertical dashed lines indicate locations of the airfoil leading and trailing edge, respectively. Vertical solid lines
indicate the locations of the TR-PIV measurements. Color legend is used for subsequent figures unless otherwise noted.

BOUNDARY LAYER DEVELOPMENT

22

Figure 4 shows the streamwise and pressure gradient dependent progression of the momentum thickness θ for therough and the smooth wall. As expected, the effect of theroughness is to increase the magnitudes of the integrated
boundary layer parameters. Although a similar functional
trend of pressure gradient response is seen in both the smoothand rough wall flows, the slope of the curves appears to be
steeper for the rough wall, indicating that in addition to the absolute thicknesses, the rate of the boundary layer growth is increased due to the pressure drag from the roughness elements.
At positive angles of attack, the naturally occurring flat plateboundary layer thickness is exacerbated due to the presence of
the initial APG flow. This is followed by a decrease in growthrate after the flow has transitioned to the FPG downstream of
the airfoil quarter chord. At negative angles of attack, the flow
is initially accelerated due to the FPG. This is followed by flow
deceleration and an increase in the boundary layer growth rate
due to the transition to APG. The integrated boundary layer parameters for the rough wall also show a crossover downstream

20
18
16
14
12
10
8
6
0

1

2

3

4

5

6

Figure 4. Momentum thickness variation with streamwise
distance and NACA 0012 angle of attack. Solid line is roughwall, dashed line is smooth wall.

3

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
30

1
0.9
0.8

25

0.7
0.6

20
0.5
0.4

15

10 4

10 5

10 6

10 4

10 5

10 6

10 4

10 5

10 6

10 4

10 5

10 6

0.4

10
0.3

5

0.2

0.1

0
10 0

10 1

10 2

10 3

10 4

10 5

0

30
1
0.9

25

0.8
0.7

20

0.6
0.5

15

0.4

10
0.4

0.3

5

0.2

0
10 0

10 1

10 2

10 3

10 4

10 5

0.1

0

Figure 5. Mean velocity profiles normalized on inner coordinates for rough (solid colored lines) and smooth (dashed lines)
configurations at (top) x = 2.62 m and (bottom) x = 4.05 m.
Solid black line is the Spalding curve (Spalding (1961).)

Figure 6. Logarithmic-law diagnostic function used to selectthe logarithmic region for regression fit methods to determine
skin friction from mean velocity profiles; (top) x = 2.62 m and(bottom) x = 4.05 m.

of the pressure gradient transition, a behavior already observedin previous studies of the smooth wall by Fritsch et al. (2020)
and Vishwanathan et al. (2021), a behavior that is attributed toa delayed response to the upstream flow history.

profile shape, a deficit that is larger when the upstream APG
magnitude is higher. The slope of the logarithmic region isdecreased which introduces sensitivities to the mean velocity
regression fits used to indirectly determine skin friction. Although not shown here, Vishwanathan et al. (2021), saw similar velocity deficit trends in the smooth wall mean velocity
profiles as well.

MEAN VELOCITY PROFILES
Figure 5 shows mean velocity profiles for both the roughwall and smooth wall at x = 2.62 m (before the pressure gradient sign change) and at x = 4.05 m (after the pressure gradientsign change). The varying pressure gradient magnitudes cause
the wake strength to increase with progressive streamwise locations. The effect of the roughness is to increase the shear
velocity, thus causing a downward shift of the mean velocity
profiles, which appears as the extra term, ∆U + in the law of thewall for rough wall flows. The rough wall mean velocity profiles in Figure 6 are normalized on outer coordinates. Under
this normalization, the mean velocity deficit due to the impactsof the initially APG (red curves) become apparent, especiallyat the x = 4.05 m station (see bottom set of mean velocity profiles in Figure 6). At this condition, the mean velocity gradientis decreased, and the logarithmic region develops a dip in the

REYNOLDS STRESS PROFILES
Streamwise Reynolds normal stresses for locations before
and after the pressure gradient switch (i.e. x = 2.62 m andx = 4.05 m, respectively) are shown for both the rough andsmooth wall in Figure 7. Conditions at the most adverse, favorable, and nominally zero pressure gradient conditions areplotted (α = +12o , 10o , 0o , respectively). Due to limitations of
the TR-PIV camera field of view with respect to the boundary
layer thickness at x = 4.05 m, the full wall-normal turbulence
stress profile was not captured. At x = 2.62 m, the turbulence412th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
10
2

8

6

1.5

4

1

2

0.5

0

0
0

0.5

1

1.5

1

2

3

4

5

1

2

3

4

5

10
2

8

6

1.5

4

1

2

0.5

0

0
0

0.5

1

1.5

Figure 7. Reynolds streamwise normal turbulence stressplotted on inner-outer coordinates for the rough ( ) and smoothwall (+); (top) x = 2.62 m and (bottom) x = 4.05 m.

Figure 8. Effective sandgrain roughness parameter (ks ) normalized by roughness height (kg ) computed from a regression
fit of the mean velocity profiles. (Top) the selected logarithmic
region is custom to each flow condition, and (bottom) the logarithmic region is taken to be between 8680 < yUe /ν < 21270.

stress magnitudes for the initially APG flow are higher thanwhen the flow is initially in the FPG. This trend reverses after
the pressure gradient sign switch as the flow approaches thestation at x = 4.05 m. In both the rough and smooth wall flows,
the Reynolds normal stress is increased as the flow switchesfrom a FPG to an APG (blue curves), and decreased as theflow switches from an APG to a FPG (red curves). However,a secondary peak becomes more prominent in the red profiles
at x = 4.05 m. It appears that the near-wall turbulence production, which was instigated at the earlier streamwise station,is diffused away from the wall as the flow approaches the station at x = 4.05 m, resulting in the intensified second peak.
This response to the pressure gradient is observed in both therough and smooth wall Reynolds streamwise normal stresses.
Outer-layer similarity appears to be demonstrated in the flow
plane at x = 2.62 m evidenced by a collapse of the smoothand rough wall turbulence stress profiles in the region outsideof the roughness sublayer. It is hypothesized that the wallsimilarity actually extends further into the boundary layer, but
is obscured by an under measurement of the stresses due to therelatively coarse spatial resolution of the TR-PIV cameras.

data have often been used in the literature instead. It is commonly agreed that these methods inherently have their flaws
and result in high uncertainty for the computed shear velocities, uτ (Aubertine et al. (2004)). However, in the absence of
direct measurements and with the acknowledgement of these
uncertainties, these methods can still provide an estimate of
the shear stress in the flow. Their validity in a non-equilibrium
flow environment is yet to be thoroughly evaluated. In thepresent study the regression fit method by Perry & Joubert(1963) is used to estimate skin friction from the mean velocity
profiles. In this method, the law of the wall for rough walls isrearranged in terms of the velocity normalized on the boundary layer edge velocity, Ue , such that the slope and interceptof the curve are functions of the skin friction and roughness
parameter, ∆U + . Then, the effective sandgrain roughness iscomputed from the following relation:∆U + =1ln(ks+ ) − 3.5
κWhere κ is the von Kármán constant and is taken to be 0.41.
Like many mean velocity fit methods, the resulting skinfriction depends on the selection of the logarithmic region,
which relies upon on engineering judgement. In an attempt
to provide quantitative feedback on the selected region used
for the regression fits, the logarithmic law (log-law) diagnostic
function, introduced for the smooth wall by Österlund et al.

WALL-SIMILARITY OF THE ROUGH WALLFLOWAs direct measurements of wall shear stress are not always feasible, particularly with rough wall flows, empiricalmethods, such as mean velocity profiles fits and momentum
integral analyses to determine skin friction from velocity field5

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
ACKNOWLEDGEMENTS(2000), was used. Due to the independence of the roughness
function parameters from wall-normal position, the rough wall
form of log-law diagnostic function remains the same as thatof the smooth wall:

Ξ=

yU∞
ν



The authors would like to thank the Office of Naval Research, Dr. Peter Chang, and Dr. Julie Young for support under
grants N00014-19-1-2109, N00014-18-1-2455, and N001420-1-2821. The authors are also grateful to VT Stability Wind
Tunnel research staff and faculty, AOE Machine Shop, and fellow research students for their support and assistance in theexperimental preparation and testing.

d(U/U∞ )d(yU∞ /ν)Figure 6 shows the log-law diagnostic function for flow
conditions before and after the pressure gradient switch. The
logarithmic region is considered to be within the region of constant Ξ, and provides the basis for selecting the points used in
the mean velocity regression fits. By varying the number oflogarithmic points, it was shown that the resulting skin friction, and by extension the roughness parameter, was sensitive
to the selection of the logarithmic region. In this analysis, thenumber of points in the regression fit was varied and a corresponding ks was recomputed. The number of permutations
for points considered was limited to only include points takenfrom the near-wall to the furthest point with constant Ξ. A 95%
confidence interval using a Student’s t-distribution is plotted as
the error bars on Figure 8. This figure shows a variation of thenormalized ks on the roughness height kg depending on the selected logarithmic region. The location that appears to havea higher sensitivity to this log-region selection is the location
immediately after the flow has switched from APG to FPG,
which can be attributed to the more pronounced mean velocity deficit that reduces its logarithmic shape. However, despite
a lower than expected estimate of the uncertainty, there is no
discernible functional dependence of the local or historical effects on the normalized sandgrain roughness parameter. Thissuggests that the effect of the roughness is contained within
the roughness sublayer and that the non-equilibrium flow features do not impact the roughness function. Thus, within theuncertainty of the empirical method used to determine theskin friction, the ks /kg ratio appears to remain constant withpressure gradient, and the wall-similarity hypothesis for nonequilibrium rough wall flows is supported.

REFERENCES
Aubertine, Carolyn D & Eaton, John K 2005 Turbulence development in a non-equilibrium turbulent boundary layer
with mild adverse pressure gradient. Journal of Fluid Mechanics 532, 345–364.
Aubertine, Carolyn D., Eaton, John K. & Song, Simon 2004
Parameters controlling roughness effects in a separatingboundary layer. International Journal of Heat and Fluid
Flow 25 (3), 444–450.
De Graaff, David B. & Eaton, John K. 2000 Reynolds-number
scaling of the flat-plate turbulent boundary layer. Journal of
Fluid Mechanics 422, 319–346.
Devenport, William J & Lowe, K Todd 2022 Equilibriumand non-equilibrium turbulent boundary layers. Progress in
Aerospace Sciences 131, 100807.
Flack, Karen A., Schultz, Michael P. & Shapiro, Thomas A.
2005 Experimental support for townsend’s reynolds number similarity hypothesis on rough walls. Physics of Fluids
17 (3), 035102.
Fritsch, Danny, Vishwanathan, Vidya, Duetsch-Patel, Julie,
Gargiulo, Aldo, Lowe, Kevin T & Devenport, William J
2020 The pressure signature of high reynolds number
smooth wall turbulent boundary layers in pressure gradientfamily. In AIAA Aviation 2020 Forum, p. 3066.
Jiménez, Javier 2004 Turbulent flows over rough walls. Annual
Review of Fluid Mechanics 36 (1), 173–196.
Joshi, Pranav, Liu, Xiaofeng & Katz, Joseph 2014 Effects offluctuating pressure gradients on boundary layer turbulence.
Journal of Fluid Mechanics 748, 36.
Perry, A. E. & Joubert, P. N. 1963 Rough-wall boundary layers
in adverse pressure gradients. Journal of Fluid Mechanics
17 (2), 193–211.
Raupach, M. R., Antonia, R. A. & Rajagopalan, S. 1991
Rough-wall turbulent boundary layers. Applied Mechanics
Reviews 44 (1), 1–25.
Schultz, M. P. & Flack, K. A. 2005 Outer layer similarity infully rough turbulent boundary layers. Experiments in Fluids 38 (3), 328–340.
Spalding, DB 1961 A single formula for the law of the wall.
Journal of Applied Mechanics 28 (3), 455–458.
Townsend, AAR 1980 The structure of turbulent shear flow.
Cambridge university press.
Vishwanathan, Vidya, Fritsch, Danny, Lowe, Todd K & Devenport, William J 2021 Analysis of coherent structures
over a smooth wall turbulent boundary layer in pressure
gradient using spectral proper orthogonal decomposition. In
AIAA Aviation 2021 Forum, p. 2893.
Österlund, Jens M., Johansson, Arne V., Nagib, Hassan M.
& Hites, Michael H. 2000 A note on the overlap region in
turbulent boundary layers. Physics of Fluids 12 (1), 1–4.

CONCLUSIONS
An experimental study of non-equilibrium turbulent
boundary layers over rough and smooth surfaces was conducted in the Virginia Tech Stability Wind Tunnel. A NACA
0012 airfoil was used as a mechanism to induce a systematically varying family of pressure gradients on the boundary layer walls. Mean and instantaneous measurements ofthe velocity field were made using a boundary layer rake andtime-resolved particle image velocimetry. The trend of the
momentum thickness variation with streamwise development
and non-equilibrium pressure gradient is very similar between
the rough and smooth wall flows. However, the effect of theroughness is to increase the boundary layer magnitude andgrowth rate. Streamwise normal turbulence stresses show anincrease in the outer layer energy after the pressure gradientswitch, presumably due to an outward diffusion of turbulence
produced in the near-wall at an upstream station prior to thepressure gradient sign change. Indirect methods to determine
skin friction, specifically using regression fits of the mean velocity profiles, show high sensitivity of the selected logarithmic region on the computed shear stresses. Despite the inherent uncertainties of such methods, the wall-similarity hypothesis appears to be valid in a rough-wall non-equilibrium flow.

6