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

FLOW PAST SUDDEN STEP-CHANGE IN SURFACE TOPOGRAPHYFROM STREAMWISE RIDGES TO SMOOTH WALL

Takfarinas Medjnoun
Aerodynamics and Flight Mechanics
University of Southampton
Southampton SO16 7QF, UK
t.medjnoun@soton.ac.uk

Bharathram Ganapathisubramani
Aerodynamics and Flight Mechanics
University of Southampton
Southampton SO16 7QF, UK
g.bharath@soton.ac.uk

INTRODUCTION

that when a turbulent boundary layer experiences roughness
discontinuities, a new internal layer begins growing farther
downstream (Garratt, 1990). While within the old “outer”
layer the mean and turbulent flow remains characteristic of
the upstream boundary condition, an equilibrium layer grows
which adjusts to the new surface condition (Hanson & Ganapathisubramani, 2016). On the other hand, turbulent boundary layers with secondary flows are shown to reach a selfpreserved form after a given distance downstream, with only
a weak growth rate (Hwang & Lee, 2018). This observation
leads to the main question: to what extent secondary flows canpersist past a heterogeneous-to-homogeneous step-change? To
examine this question, we specifically designed an experimental study to investigate the streamwise development of theselarge-scale secondary motions along with their impact on thefrictional drag. The consequences on the internal boundary
layer, turbulent properties as well as the validity of the classical scaling laws will further be discussed.

Within the last two decades, the recent advances in wallbounded turbulence have considerably extended our understanding of rough-wall flow physics (Chung et al., 2021), buthave additionally shed more light on the challenges in predicting the drag, essentially, due to the complex nature of therough-wall and turbulent flow interactions. A fortiori, predicting drag becomes even harder when considering spanwise
heterogeneous rough-wall surfaces (Medjnoun et al., 2018).
These surfaces have come under scrutiny to investigate themechanisms behind the manifestation of the resulting largescale secondary motions/currents, which entail a highly threedimensional flow with alternating high- and low-momentum
pathways (Mejia-Alvarez & Christensen, 2013). These havenow been fairly-well explored across a wide range of surface conditions such as in rough-wall channels (Willingham
et al., 2014; Anderson et al., 2015; Chung et al., 2018; Castro et al., 2021; Schäfer et al., 2022), open-channels and riverflows (Nezu et al., 1993; Wang & Cheng, 2006; Zampiron
et al., 2021), pipes and Taylor-Couette flows (Chan et al.,2018; Bakhuis et al., 2020) but also in boundary layers (Nugroho et al., 2013; Barros & Christensen, 2014; Medjnoun
et al., 2020; Wangsawijaya et al., 2020; Xu et al., 2020). The
emergence of these secondary flows is shown to be tied to the
spanwise characteristic wavelength of the surface but can also
be influenced by other factors such as; the geometry, the amplitude, directionality and perhaps above all, the type of heterogeneity; ridge-type, strip-type or mixed-heterogeneity (Medjnoun et al., 2020, 2021). In addition to the large-scale modification in the mean and turbulent flow structures, recent studies
have shown these secondary flows can substantially affect theheat transfer properties of the flow (Stroh et al., 2020; Bon &Meyers, 2022).
Despite the current vast body of work on secondary flows,
the development of these structures past a heterogeneous-tohomogeneous step-change remains unexplored. In fact, to ourknowledge, all of the existing literature on step-changes exclusively consider flows growing over homogeneous surfaces undergoing either smooth-to-rough or rough-to-smooth changes(Antonia & Luxton, 1971, 1972). These studies have shown

EXPERIMENTAL METHODS
Surface heterogeneity
The measurement campaign has been performed in
an open-circuit suction wind tunnel at the University ofSouthampton (see Medjnoun et al. (2020) for details). The
surface heterogeneity was modelled using a smooth ridge ofa rectangular shape, made of clear perspex. These ridges extended from the test section inlet over a length of 40δ (δ being the spanwise-averaged boundary layer thickness measured
2.8m downstream the inlet), before we imposed a step-change
to a smooth wall, where we define the streamwise origin (seefigure 1). The nominal heights and spanwise spacings wereh = 6 mm and S = 80 mm, chosen to match 0.1 and 1 times δ ,respectively, to maximize potential secondary flows.

Oil-film interferometry
The frictional drag is directly measured through the interferometry technique. Oil droplets with widths less than 0.1δ(to obtain spanwise-independent measures) are deposited at1

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022
The quantifications of the changes in the wall shear stressare presented in figure 3, showing the variations caused by the
spanwise topographical variation at different streamwise locations. The spanwise distribution of the friction velocity (Uτ ) is
illustrated in figure 3(a) and is shown to vary periodically withweak (negative for x < 3h) magnitudes being recorded past theridge and their vicinities while the valley remains relatively
constant across the span. The streamwise development is captured by the colour tone and varies from darkest near the step
to lightest farther away, with an overall magnitude of Uτ at thevalley symmetry plane being relatively unchanged. This indicates that this part of the flow remains resilient to the presenceof a streamwise step-change, as opposed to the flow past theridge.
The changes between the spanwise peak and valley symmetry planes are further examined and compared with the
spanwise-averaged skin-friction coefficient ⟨C f ⟩, as seen in
figure 3(b). The results show that in the valley, the skin friction
remains unaffected by the streamwise step-change and stays
constant (within the uncertainty of the measurement) throughout the distance herein explored. However, past the ridge, theskin friction is shown to undergo a sharp increase which issimilar to that observed in rough-to-smooth wall step-changes.
This is shown to occur for x < 0.6δ which is followed by aweakening in skin friction between 0.6 < x < 1.5δ . Past a certain distance (x > 1.5δ ), the skin friction start recovering again
with a relatively weak growth rate. The spanwise-averaged
friction is illustrated in black and clearly shows the overall skinfriction to only marginally grow in the streamwise direction
indicating perhaps very minor changes in the near-wall flow
behaviour, as opposed to the classical rough-to-smooth flows.
To highlight the difference with the latter flows, two cases
from the experimental study of Hanson & Ganapathisubramani (2016) who examined the effect of homogeneous roughto-smooth transition of a mesh- and grit-type roughness arepresented in figure 3(c) The current results indicate that ⟨C f ⟩undergoes strong changes near the step (x < 0.5δ ), in contrast
with the homogeneous cases which recover slowly. Despite
the upstream flow being heterogeneous in the spanwise direction, the near-wall flow shows a faster recovery towards
a new “streamwise-equilibrium” state than a homogeneouscase. However, this pseudo-equilibrium state (shown by theinvariance of the drag) is different from the classical homogeneous rough-to-smooth cases. Considering that large-scalesecondary motions have been previously observed in the outerregion, the way the outer flow interacts with the near-wall region is likely to be play an important role.

various spanwise locations. The droplets are then illuminatedusing a sodium lamp with a wavelength of 589 nm. A 16 MP
camera with a 200 mm lens set at an angle of 25o from thevertical is used and fitted to a Scheimpflug adapter to satisfy
the Scheimpflug condition. A calibration target positioned at
the wall in the (x, z)-plane is used to calibrate the camera, resulting in a FOV of around 0.6S × 1.2S in the (x, z)-plane, allowing a simultaneous capture of the development of different
spanwise interferograms. 100 images per streamwise location
at a nominal speed of U∞ = 20 m/s are acquired for 10 minutes in any given run. This process is repeated several times atvarious streamwise locations to cover the variation of the skinfriction in the non-equilibrium region, and reconstruct a mapof the skin friction with an extent of 8S × 1.2S in the (x, z)plane.

Particle image velocimetry
The flow is diagnosed in the cross-plane (y, z) using
stereoscopic PIV measurements at four different streamwise
stations. The flow is traced by vaporised glycerol-water particles, then illuminated with a laser light sheet sourced by a
two-pulse laser operating at 250 mJ. An optical system for the
beam focus/expansion of the light sheet is used to obtain a constant thickness in the measurement plane. The particle images
are recorded by 16 MP cameras fitted with 200 mm lenses andmounted on Scheimpflug adapters to account for the oblique
view angle (±42o ). A double-sided dual-plane calibration target aligned with the laser light sheet is used to determine themapping function for each setup, using a third-order polynomial fit. This resulted in a FOV of 2δ × 3δ in the (y, z)-plane.
3000 statistically independent realizations of image pairs are
acquired for each case at 0.6 Hz, with a time delay between
pulses of 20 µs, at a free-stream velocity U∞ of 20 m/s. The
velocity vector fields are subsequently obtained by interrogating particle images using a decreasing multipass scheme starting from 48 pixels × 48 pixels to a final pass of 24 pixels ×
24 pixels with 50% overlap, resulting in an effective vector
spacing of 0.55 mm.

RESULTSFrictional dragFigure 2 illustrates the response of the oil-droplet interferograms to the surface shear stress caused by both the streamwise and spanwise topographical changes. Although the magnitudes remain less evident to observe, clear directional modifications are depicted as well as a presence of a recirculation region past the streamwise step. This region herein labelled R1, is believed to be home to a highly unsteady flowcaused by the separation of the shear layer above and on theside ridges (marked in blue). As the flow reaches the streamwise step-change, these streaks deviate from the streamwisealignment and end up in the recirculation past the ridge. The
streamwise extent of the separation is estimated to be within
2-3h. Between the spanwise peak and valley symmetry planes
a “buffer” region named R2 highlighted in red, is shown to beaffected by the streamwise step as the streaks diverge and expand away from the centre plane. Past the reattachment point(marked with a dark-white dashed line) they are observed toslightly revert back showing a more parallel trajectory withrespect to the flow direction. Further away from the ridges,
the streaks labelled R3 (marked in black) remain parallel tothe flow with a very weak expansion. However at the valley
symmetry plane (z/S = 0), the streaks remain insensitive to thepresence of a step-change.

Secondary flows
Combining the oil-film and sPIV measurements, walldrag as well as flow field information can be presented as infigures 4, which show the normalised mean streamwise velocity (top) and vorticity-signed swirling strength (bottom). The
skin friction map is obtained by interpolating nearly three hundred independent (measured) points that covered a surface of
8S × 1.2S in the (x, z)-plane. On the other hand, the crossplane flow fields are obtained at x/δ =-0.65, 0.2, 4 and 8, respectively. Figure 4 indicated that the flow experienced strong
spanwise changes in the form of high- and low-momentum
pathways caused by the presence of secondary motions. Their
spanwise locations are consistent with those observed in previous studies of topographical heterogeneity (Medjnoun et al.,2020). The figure also shows that despite the presence ofa step-change, the outer region remains relatively unaffected
whilst developing downstream. As expected, the upstream2

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022
which typically accounts for viscous, turbulent and dispersive
shear stress contributions. The viscous contribution is only
present very near the wall, which in the current study remains
unresolved due to the measurement constraints.
The results are shown in figure 5, presenting comparative
maps of the turbulent, dispersive and total shear stresses fromleft to right, respectively. The maps are shown from upstreamof the step-change (top) to the farthest downstream location(bottom). The dispersive stresses are shown to be not negligible with respect to the turbulent ones, extending for nearly two
thirds of the boundary layer thickness with varying intensity
along the spanwise direction. The magnitude and distributionof the turbulent and dispersive shear stresses differ, with an
overall distribution of turbulent stress following the modulation character of the mean flow. On the other hand, the dispersive term is shown to be more localised. Right after the stepchange, substantial modifications appear for both the turbulent
and dispersive maps. Strong turbulent shear stress events areshown to occur past the ridge, while the turbulence activity inthe outer region seems to diffuse vertically and radially, which
can be caused by the flow deceleration. This observation hints
to a reduction in the overall outer-layer heterogeneity. This is
in fact substantiated by the changes that occurred in the dispersive shear stress component, which highlights a reduction in
the degree of heterogeneity in the outer region, however witha negative turbulence activity near the wall. This result seems
to have also impacted the overall shear stress which shows intense negative turbulence activity past the step. This behaviour
is due to strong negative vertical dispersive component past thediscontinuity caused by the adjustment of the upstream flow
to the new surface condition. Therefore, the reduction of the
spanwise heterogeneity comes from a dual effect of the turbulence diffusion due to deceleration as well as the negation
between the upstream upwash flow occurring above the ridges
and the downwash of the recirculation region imposed by thestreamwise step-change. At farther distances downstream thestep-change, both turbulent and dispersive shear stresses seemto adopt similar patterns to those observed upstream the step inthe outer region. Moreover, the previous observation of a negative dispersive shear stress activity near the wall does not seemto hold for such distances, confirming that it is a consequenceof the step-change. The downstream persistence of the dispersive component is in line with the mean flow and swirlingstrength maps presented before, corroborating the resiliencecharacter of these large-scale features. These results suggestthat these large-scale secondary flows posses enough inertia toself-sustain for long distances, and can maintain a good degreeof self-similarity over a homogeneous surface condition. This
also means that in order for these types of turbulent boundary
layers to recover spanwise homogeneity, very long distances
are required to allow for the diffusion of these secondary motions.

surface condition caused mean flow heterogeneity illustrated
by the high- and low-momentum pathways, themselves associated with high and low friction velocity magnitudes, respectively.
The aforementioned behaviour in the mean flow topology
is further substantiated by the identification of secondary motions through the computation of the vorticity-signed swirlingstrength. The results are shown in the bottom half of figure 4,
indicating that secondary motions made of a pair of counterrotating vortices are located on the top of either side of theridges, inducing upwash and downwash motions above theridges and valley, respectively. Right past the step, the contour level of the mean flow map seems to have reduced in theouter region, indicating a relaxation of the overall boundary
layer thickness caused by the adverse pressure gradient at thestep. Equivalently, a noticeable impact is observed near thewall with a more heterogeneous mean flow. Further downstream, only small changes can be observed from the stationsx/δ = 4 and 8 for the outer region, as opposed to the near-wallwhich seems to recover its previous form.
Besides the main large-scale secondary structures observed, a similar smaller structure constituted of a pair ofcounter-rotating vortices rotating in opposite direction to themain ones are observed above the ridge. This feature is labelled a tertiary structure in the previous study of Medjnoun
et al. (2020) which rises due to the geometry of the ridge. This
structure is shown to disappear downstream the step, as opposed to the outer region secondary structure which persists
further downstream. This observation shows that these largescale secondary motions are inherently capable of sustaining themselves for longer distances downstream of the stepchange, and are capable of maintaining a good degree of selfsimilarity when encountering homogeneous surfaces. This is
in contrast with the tertiary structures which seem incapableof self-sustain without a viscous boundary condition such as
the presence of a rectangular ridge, leading to the observedchanges in the near-wall region.
Using the triple decomposition method applied to the flow
fields in the cross-plane, the dispersive stresses caused by themean flow heterogeneity can further be examined. For instance, the streamwise velocity field can be expressed asTime-averaged velocity³¹¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ·¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹µui (y, z,t) = ⟨U(y)⟩S + ũ(y, z) + u(y, z,t) ,´¹¹ ¹ ¹ ¹ ¹ ¹ ¸¹ ¹ ¹ ¹ ¹ ¹ ¹¶´¹¹ ¹ ¹ ¹ ¹ ¸¹¹ ¹ ¹ ¹ ¹ ¶´¹¹ ¹ ¸¹¹ ¹¶ ´¹¹ ¹ ¹ ¹ ¹ ¸¹¹ ¹ ¹ ¹ ¹¶
Instantaneous
velocity

Spatial-timeaveraged
velocity

Dispersive
velocity
component(1)

Randomvelocity
component

where ui is the instantaneous velocity field measured at a fixedstreamwise location. ⟨U(y)⟩S is the time- and horizontallyaveraged velocity profile over the spanwise wavelength S.
ũ(y, z) is the time-invariant spatial deviation field and u(y, z,t)
is the time and space dependant fluctuating part from the
Reynolds double decomposition. By applying the same
method to the different velocity components, the different dispersive stress tensor terms can be evaluated and compared.
More specifically, the total shear stress term can be computedas∂Uτxy = ν− uv − ũṽ ,
∂y
´¸¶
´¸¶
´¸¶
´¹¸¹ ¶ turbulent dispersive
total
shear
stressviscousshear
stressshear
stressREFERENCES
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(2)

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

Top view
UeX

CCD Cameras

Z

60δ

Laser

w

3δ

S

37δ

PIV setup
Laser

Y

Ue
X

δ

h

Side view

SPIV setup

OFI setup

Figure 1: Schematics of the experimental arrangement of the surface step-change including the Planar/Stereo PIV setup(top) and the Oil-film interferometry setups (bottom).

Figure 2: Example of oil droplets deposited upstream the step-change at U∞ = 20 m/s with streamlines drawn to highlightthe pattern displayed by the OFI streaks.

(a)0.8Uτ (z)

0

h/S

x

-0.8
0.1
0
-0.5

x

0
z/S

0.5

Figure 3: (a) Spanwise variation of the friction velocity across different streamwise stations highlighted in dark (nearthe step) to light grey (farther). (b) Comparison of the spanwise-averaged, peak and valley skin-friction coefficient, asa function of the streamwise distance normalised by the upstream boundary layer thickness δ . (b) Comparison of the
spanwise-averaged friction coefficient with the rough-to-smooth step-change cases from Hanson & Ganapathisubramani(2016).

5

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

Figure 4: Cross-plane of the (top) normalized mean streamwise velocity and (bottom) vorticity-signed swirling strength atdifferent streamwise locations along the friction velocity map.

Figure 5: Contour maps of the normalised turbulent (left), dispersive (middle) and total (right) shear stress for the different

streamwise locations, going from top (upstream the step-change) to bottom (furthest location).
6