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

TURBULENT BOUNDARY-LAYER RESPONSE TO ACTIVE ROUGHNESS

Aditya Ramani
Department of Mechanical Engineering
The University of Melbourne
Parkville, Victoria 3010, Australia
ramania@student.unimelb.edu.au

Jason P. Monty
Department of Mechanical Engineering
The University of Melbourne
Parkville, Victoria 3010, Australia
montyjp@unimelb.edu.au

Nicholas Hutchins
Department of Mechanical Engineering
The University of Melbourne
Parkville, Victoria 3010, Australia
nhu@unimelb.edu.au

ABSTRACT

dicting this increased drag from the topographical propertiesof the roughness is a highly sought after goal (Chung et al.,2021). Studies geared towards this goal often assume that theroughness is made up of rigid and invariant elements that arehomogeneously distributed. The turbulent boundary layer thatdevelops over such surfaces is said to be in ‘equilibrium’ withthe wall-condition. However, practical roughness can haveboth spatial and temporal heterogeneity. An example of theformer is patchy biofouling on ship hulls while an exampleof the latter is the soft filamentous biofouling seen on ships(Hartenberger et al., 2020). The consequence of heterogeneity
is that the boundary layer is not in equilibrium (i.e. only inthe near-wall region is the flow fully-adapted to the local wallconditions). The full-scale and generalised prediction of dragrequires studying such surfaces as well.

This experimental study investigates the response of awall-bounded turbulent flow to an oscillating rough surface.
The roughness elements are actuated between a smooth and aroughened state at a single frequency and hot-wire measurements are acquired directly above the oscillating rough wall.
The dynamic roughness has a broadband effect on the energyof the flow, increasing the energy beyond that of the static
smooth case from the wall to beyond the log region. The phaseaveraged velocity profiles suggest that, for lower frequencies,
the mean flow oscillates between two quasi-steady states: a‘rough’ state and a ‘smooth’ state. These quasi-steady states
are separated by a transition state, which is a forward leaning
front in phase that marks the departure of the phase averagemean from the static limit. As the dimensionless frequency
is increased, the transition state is seen to grow as a fractionof the phase cycle, eventually exceeding the half-cycle point
where the wall condition changes. At this point, the mean
profile is perpetually in transition and the quasi-steady states
no longer exist. This behaviour is modelled using an internal boundary layers (IBL) based method. A simple relationship to relate phase to an equivalent spatial location of a stepchange in roughness is proposed from which the IBL height
can be estimated. This is confirmed by comparison with static
streamwise heterogeneous data and a good match is seen at
the correct phase. The modelled front based on this relationship is seen to match the shape of the front identified from theexperiments, and captures the broad changes in the inclinationof the front with increasing dimensionless frequency. Thus, acase can be made that turbulent boundary-layers over oscillating roughness can be modelled as growing internal layers.

The case of spatial heterogeneity is often distilled tothe problem of streamwise step changes in roughness (either smooth-to-rough, S-R, or rough-to-smooth, R-S). In thesecases, the transition of the mean flow downstream of the stepis marked by the observation of internal boundary layers (Antonia & Luxton (1971, 1972), Li et al., 2021). In comparison,studies of temporally heterogeneous roughness are rare. While
there is some evidence to suggest that oscillating roughness elements increase skin-friction drag beyond a static equivalentsurface (Stoodley et al., 1998, Hartenberger et al., 2020), an
investigation of the dynamic properties of the roughness in relation to the flow is lacking. The work of Jacobi & McKeon(2011) showed that when a well defined dynamic roughness
impulse (sine wave) is imparted to a turbulent boundary layer,
the phase-locked effects can be discerned in both the mean andhigher-order statistics far downstream of the impulse.
The present study aims to investigate flows developing
over a well-defined dynamic roughness which can be actuatedbetween a smooth and a roughened state. The frequency of
the roughness is systematically varied and the flow is allowed
to develop over the dynamic wall. Flow statistics are acquired
directly above the dynamically actuated wall in the developing boundary layer, allowing the effects of the dimensionlessouter-scaled frequency on the boundary-layer flow to be investigated.

INTRODUCTION
Wall-bounded turbulent flows commonly occur overmany important engineering systems, such as ships, airplanes
and turbine blades. The turbulence induced drag reduces theefficiencies of these systems and therefore increases their operating costs. The presence of roughness on the surfaces ofthese systems, which is often unavoidable in practical applications, increases drag further above smooth wall levels. Pre-1

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

Figure 1: Details of the dynamic roughness experiment: (a) Cross-section of the roughness generation device showing theoperation of one element; (b) layout of the device in the wind-tunnel with the flow direction indicated by the arrow andthe green dot showing the hot-wire measurements location; (c) mapping of the roughness element height to phase for thefrequencies in the study. See Table 1 for the line-types.
EXPERIMENT SETUP

10). The plenums are connected to the reservoir with rubber
hoses (= 4mm). The cycling is achieved through miniaturesolenoid valves (Emerson ASCO 411L3305HV) that are connected in line with the hoses and located directly underneaththe plenums. Pairs of adjacent plenums are controlled by thesame valve. Custom designed circuit boards and software areused to control and switch the valves remotely. For the oscillating roughness, the valves are switched simultaneously witha square wave input thus producing a oscillating rough surface.

Table 1: Experiment details: All cases are at a free-stream velocity of U∞ = 10.03 ± 0.03 ms−1 . For the active cases, the non-dimensional roughness height, k+p =k pUτ /ν, is scaled with the Uτ for S0 case.

Label
F009
F019
F028
F047
Label
S0
R0

Active Measurementsffδk+Legendp[Hz]20.009 2140.019 196
0.028 19100.047 17

Static Measurements
pp
Uτ
k+
Reτ
p
−1
[kPa] [ms ]00.398— 118035
0.492
23 1480

The roughness device is installed in an open-return typewind-tunnel at the Walter Basset Aerodynamics Laboratory at
the University of Melbourne. The working section of the tunnel is 6.7m long with a cross-section area of 0.94m × 0.375m.
The boundary layer is tripped to turbulent at the inlet of thetunnel by a strip of P40 grit sandpaper (see Marusic & Perry,
1995 for further details on the facility). The upstream, sideand downstream portions of the tunnel floor surrounding thedevice are made up of smooth MDF panels. Flow statistics are
acquired using hot-wire anemometry. The sensor is located at
a streamwise distance of x ≈ 2.8m from the inlet of the tunnel,
which corresponds to a fetch of x̂ ≈ 0.63m over the device. See
Figure 1(b) for a schematic of the device setup and hot-wiremeasurement location. A modified Dantec 55P05 boundarylayer probe with a 5µm diameter Wollaston wire is used witha Melbourne University Constant Temperature Anemometer(MUCTA). The sensing element of the hot-wire is etched to alength of 1mm (corresponding to l + ≈ 30, where the + superscript denotes viscous scaling, i.e. l + = lUpτ /ν, where Uτ is thefriction velocity and is defined as Uτ = τw /ρ, and ν is the
kinematic viscosity) such that l/d ≈ 200 in order to minimise
end-conduction effects (Ligrani & Bradshaw, 1987). Sensor
calibration is performed prior to and after each wall-normal
traverse and drift is corrected with in-situ measurements in thefree-stream following the method of Talluru et al. (2014). The
hot-wire sensor is sampled simultaneously with the squarewave input to the valves to allow for phase averaging. Sampling frequency is set to 48kHz which gives a dimensionlesssampling frequency of f + ≈ 4.5. Sampling time is based on

LegendAn active roughness generation device is designed for thisstudy, which generates roughness elements by inflating a synthetic latex membrane through a perforated metal plate. The
peak height of the roughness elements, k p , can be varied by adjusting the input pressure, p p (gauge), to the plenum. This arrangement is illustrated in Figure 1(a). The device has an areaof 0.66m × 0.338m. In the present study, the pressure is cycled
between p p = 0kPa and a maximum of p p = 35kPa to produce a oscillating rough surface. Compressed air, regulated top p = 35kPa with a Festo MS6-LR-1/2-D5-AS manual pressure
regulator, is supplied to a common reservoir (Festo CRVZS-

2

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022(a) S0(b) F009(c) F047(d) R0Figure 2: Pre-multiplied energy spectrograms of the streamwise velocity ( f Φuu ) for cases: (a) Static smooth (S0), (b)active F009, (b) active F047 and (d) static rough (R0). Contours marked in blue are regions where f Φuu /U∞2 × 103 ≥ 1.6.
The wall-normal height with inner-scaling shown on the top is with the Uτ of the smooth (S0) case. The red dashed line
indicates the dimensionless actuation frequency for the active cases.

Figure 3: Phase averaged mean velocity profiles, ⟨U⟩, for the F009 case showing (a) Quasi steady behaviour at φ = π/2( ) and φ = 3π/2 ( ) and (b) transition behaviour at φ = 1.2π ( ). The S0 ( ) and R0 ( ) profiles are also shown.
Fluctuation of the phase average from the smooth (S0) limit (⟨U⟩ − US )/US is shown in (c) along with the roughness
element height, k p as a function of phase. The phase positions from (a) and (b) are shown with matching symbols.

the boundary layer turnover time such that TU∞ /δ > 20, 000.
Here, U∞ is the free-stream velocity and δ is the height where
the mean velocity recovers to 98% of U∞ . The free-stream
velocity for all cases is U∞ = 10.03 ± 0.03ms−1 .
Statistics are acquired for both the active and static operation of the device in a zero pressure gradient (ZPG) turbulent boundary layer. For the active operation, the frequencies studied are f ∈ [2, 4, 6, 10] Hz, which corresponds to adimensionless outer-scaled frequency of fδ = f δ /U∞ ≈ 0.009
to 0.047 ( f + ≈ (1.8 to 9.5) × 10−4 ). The roughness elementpeak height, k p , is measured as the height of the centre of theroughness element from its unactuated position. A Keyence
LK-031 laser triangulation sensor is positioned over the centreof an element and the height is sampled simultaneously withthe square-wave actuation signal. Samples are obtained overmultiple elements to check for consistency. For each of thefrequencies in this study, k p is mapped as a function of phase(φ ∈ [0, 2π]) as shown in Figure 1(c). For static operation,measurements are acquired at p p = 0kPa (i.e. ‘smooth’, caselabel S0) and p p ≈ 35kPa (i.e. ‘rough’, case label R0), corresponding to the limits of the active oscillating case. The
details of the dynamic and static cases are listed in Table
1 along with the legend for their depiction throughout thispaper. For the static cases, the friction velocity, Uτ is estimated using a modified-Clauser method in the log region(100 ≤ z+ ≤ 0.15δ + ). The roughness function varies from∆U + ≈ 0.9 for the S0 case to ∆U + ≈ 5.9 for rough R0 case(the latter corresponding to a ks+ ≈ 45 assuming fully roughconditions). Thus, switching between the S0 and R0 cases
corresponds to a Reτ = Uτ δ /ν variation between 1180 − 1480
U∞ = 10ms−1 .

RESULTSIn Figure 2(b), contours of the pre-multiplied energy
spectra, of the F009 case are shown. This spectra is the energy of the fluctuations of the streamwise velocity about the
time-averaged mean. The effect of the dynamic roughness isseen as a band of energy in the flow centered on fδ (marked
by the red-dashed line). The energy band is seen to extend into
the boundary-layer to a height of z/δ ≈ 0.3 (or z/k p ≈ 20).
This is beyond the typical upper limit of the logarithmic region (z/δ ≈ 0.15 or z+ ≈ 180). As the actuation frequency encroaches more on the energetic scales of turbulence, as shownin Figure 2(c) for case F047, the band is obscured by the energy of the flow, and the wall-normal extent into the bound-3

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

Figure 4: Fractional fluctuation of the phase averaged velocity about the smooth limit, (⟨U⟩ −US )/US , with fδ increasingfrom 0.009 to 0.047 in plots (a) to (d). The ( ) lines mark the front where the mean velocity departs from the ‘smooth’limit, i.e. the minimum of |⟨U⟩ −US |. Also shown is the IBL height, δi , modelled with Equation (3) () and Equation(4) (×). The ( ) line is at z/δ = 0.65 indicating the upper limit to which the IBL is expected to grow for the static roughsurface based on Equation 1.

nal layer growth rate is described by a power-law expression,as suggested by Li et al. (2021) and is given as:

ary layer is seen to diminish. The actuation frequencies inthis study, except for the F047 case (10Hz), are low in comparison to the largest structures in the flow, which can exceed 20δ (Hutchins & Marusic, 2007) and have a frequency
of U∞ /20δ ≈ 11Hz. In Figure 2(a) and (d), the energy spectraof the S0 and R0 cases are shown respectively. As shown by
the blue contours, which correspond to f Φuu /U∞2 × 103 > 1.6,
outside the band corresponding to the actuation frequency, thebroadband energy of the active cases appear to be elevatedabove the static smooth case S0 but lower than that of the static
rough case R0.

δi /δ = A0 (x̂/δ )α(1)where A0 = 0.094 and α = 0.75, for the fetch from the leading edge of the actuated surface to the measurement location,x̂ = 0.63m, we might expect that the maximum wall-normal
extent for the internal layer in the quasi-steady limit wouldgrow to z/δ ≈ 0.65. For the F009 case, the front is seen toreach this limit within the half-cycle (i.e. before the roughness changes at the wall), therefore reaching the quasi-steadystate where the measured flow conforms to the R0 case. However, for the F019 case and beyond, the front has failed toreach z/δ = 0.65 even at φ = 2π, where the wall conditionchanges. Therefore, at higher dimensionless frequencies, thequasi-steady state is not reached and the flow remains perpetually in a state of transition. Together, these results suggest thatthe response of the flow to oscillating roughness can be modelled as the growth of internal boundary layers. This hypothesis forms the basis for the modelling approaches discussed in
the next section.

To understand this, we look at the phase averaged mean
velocity (⟨U⟩), which is the mean velocity at the corresponding
phase of the dynamic roughness at the wall. This is shown in
Figure 3(a, b) for the lowest frequency case (F009) along withthe mean profiles for the S0 and R0 cases. At φ ≈ π/2 (opencircles) and φ ≈ 3π/2 (open squares), the phase averaged profile for case F009 matches the S0 and R0 cases respectively,
as shown in Figure 3(a). However, at φ ≈ 1.2π (open diamonds), the phase averaged profile lies in a transition state,matching the static rough profile close to the wall and transitioning to the smooth curve further away from the wall, as
shown in Figure 3(b). In Figure 3(c), contours of the fractional
fluctuation of the phase averaged mean velocity about the S0case, (⟨U⟩ − US )/US , are shown for the F009 case. Here US
is the time-averaged mean for the S0 case. The three phases
represented in Figure 3(a, b) are shown with matched symbols, along with the mapping of the roughness element height
to phase. Together, these two figures suggest that for low dimensionless frequencies the mean velocity of the flow oscillates between two quasi-steady states: a ‘smooth’ state (where⟨U⟩ ≈ US ) and a ‘rough’ state (where, ⟨U⟩ < US ). These twostates are separated by a transition state where the profile conforms to the wall condition closer to the wall, but transitions
to the previous state at some distance away from the wall.

MODELLING THE RESPONSE OF THE BOUNDARY LAYER
Let us consider a frame of reference that is advecting withthe flow over the actuating surface, as depicted in Figure 5.
The flow is developing over a smooth wall when at φtrig , thewall condition is triggered to rough. The flow now develops
over a rough wall and flows past the hot-wire sensor at somelater phase φobs . The effective fetch, x̂e that is available for the
IBL growth would depend on where on the active surface theobserved flow (at φobs ) encounters the step change in roughness, which will change as a function of φobs − φtrig . This scenario is schematically illustrated in Figure 5. For observations
just after φtrig , shown in Figure 5(a), the flow that is measured
will have experienced the temporal step change to roughness
at an effective location that is just upstream of the measurement plane. Thus only the near-wall region will be affected by
the new wall condition. At a later φobs , the flow that is measured will have encountered the temporal step change further
upstream, leading to an IBL that has developed further awayfrom the wall, which is shown in Figure 5(b). And finally,

Figure 4 (a) to (d) show similar plots of the fractional
fluctuations for all four tested dimensionless frequencies. The
transition front from the smooth response to the rough response can be demarcated as the point where the phase average (⟨U⟩) departs from the smooth limit (US ) (identified as theminimum of ⟨U⟩ −US ). The fronts are shown by the black
dashed lines in Figure 4. As fδ is increased from 0.009 to
0.047, the front becomes more forward inclined and the transition state occupies a larger fraction of each cycle (thus thequasi-steady behaviour diminishes). Assuming that the inter-4

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

Figure 5: Schematic of the model for IBL growth based on the effective fetch, x̂e , that the flow sees: the flow encounters
the step change at φtrig , and flows over the new wall condition past the hot-wire probe at φobs , where it is measured. The
effective position, x̂e at which the flow would have encountered the step change advects upstream as φobs increases from(a) to (c), with some velocity Uc . The flow direction is from left to right.

To test this hypothesis, measurements of the boundary
layer were obtained over the device with a static step change
in roughness. In Figure 6, the mean velocity profile for the
step change at x̂/δ ≈ 2.1 is shown by the dotted black linesfor (a) rough-to-smooth case (R-S) and (b) smooth-to-roughcase (S-R) along with the S0 and R0 profiles. They are seen tohave the same behaviour as the transition profile for the F009
( f = 2Hz) case in Figure 3(b). For this case, if we assume
Uc /U∞ = 0.18, and set x̂e = 2.1 × δ in Equation (2), we obtainφobs −φtrig = 0.22π. The phase averaged profiles at φ = 0.22π
and φ = 1.22π are also shown in Figure 6(a) and (b) respectively with open red symbols. The phase averaged profiles
for the active cases at the matched effective fetch are seen to
closely match the behaviour of the profiles of the static spatial
heterogeneity cases.
To complete the model, we use Equation (2) with Equation (1) to obtain an expression for the IBL height, δi , as afunction of phase which is given as:
Figure 6: Mean velocity profiles for static step change in
Uc (φobs − φtrig ) α
δi
= A0
δ
2π f δ

) and the phase averaged profiles of theroughness (active F009 case at matched phases based on Equation 2:(a) Static rough-to-smooth case at x̂/δ ≈ 2.1 and active
case at φ ≈ 0.22π ( ) and (b) Static smooth-to-roughcase at x̂/δ ≈ 2.1 and the active case at φ = 1.22π ( ).
The S0 ( ) and R0 ( ) profiles are also shown.

In Figure 4, the computed IBL height, δi /δ as a functionof phase is shown for the active cases by the red dashed line.
For the value of Uc ≈ 0.18U∞ , we find that the computed front
matches the shape of the front identified from the experimental
data. The broad changes in the inclination of this front (inphase) with increasing fδ are also well captured. However,this approach is based on empirical assumptions of the IBL
growth rate and the power-law exponent can vary from 0.22 ≤α ≤ 0.86, depending on the method used to define the IBL
height (Rouhi et al., 2019).
An alternative approach is to consider the diffusion analogy based model as proposed by Bou-Zeid et al., 2004. In
this approach, the IBL growth is considered to be proportional
to the variance of the wall-normal velocity fluctuation (wrms )and is given as Dδi /Dt = Awrms . Here, D(.)/D(.) is the total
derivative. By assuming wrms = CUτ (the downstream friction velocity), we obtain an expression for the IBL growth asa function of both time and fetch, as shown in Equation 4.

at an even later position in phase, the measured flow would
have developed over the entire fetch of the installed surface, as
shown in Figure 5(c). Therefore, an effective fetch, x̂e , can be
estimated for each φobs as:x̂e = Uc (φobs − φtrig )/2π f

(3)

(2)

where Uc is some convective velocity with which the information of the changed wall condition is considered to advect.
This effective fetch represents the virtual upstream position atwhich the flow encounters the step change. This model suggests that for the dynamically actuated surface, the mean velocity profile at some specific phase, will match the mean velocity profile of flow over a surface with a static spatial stepchange in roughness at a particular location upstream of themeasurement location.

∂ δi ∂ δi ∂ x
+
= CUτ
∂t
∂ x ∂t5(4)

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
(or rough-to-smooth) at some streamwise fetch upstream ofthe measurement location. This suggests that flow over a surface with oscillating roughness can be modelled as a series ofinternal boundary layers (IBL). An effective fetch argument
is proposed that relates the changing wall condition in phaseto an equivalent streamwise position, based on a convective
velocity, from which the IBL development can be modelled.
When compared with static streamwise heterogeneous data ata known fetch, we find a good match at the predicted equivalent phase. The modelled fronts also match the fronts identified from the experiments. This strengthens the notion that
turbulent boundary-layers developing over oscillating roughness can be modelled as internal boundary layers.

For the steady case, the time derivative term in Equation (4)is set to zero. Further, by setting ∂ x/∂t = U(δi ), which canbe evaluated by utilising an assumed form of the mean velocity profile (log + wake), Equation (4) can be numericallysolved to obtain δi as a function of x, which can then be substituted for Equation (2), yielding an alternative form of Equation(3). The IBL front estimated with this method for C = 0.9 andUc /U∞ = 0.18 is shown in Figure 4 by the red cross marks.
The front estimated with this method has excellent agreementwith the front observed from the experiments for the range of
non-dimensional frequencies studied here. An advantage ofthis method is that it is based on physical arguments and avoids
the empirical power-law expression to predict the IBL growth.
Thus, based on the argument of an effective fetch, turbulent boundary-layer flows over an actively oscillating roughsurface may be modelled as growing IBLs. The simplicity ofthe effective fetch argument allows the study of more applications of interest such as the case where the active roughness isin the form of streamwise travelling waves. If the wave velocity is denoted as c, and is defined to be positive along the flow
direction, then the effective fetch is obtained by simply modifying the convection velocity term as Uc − c. The universalityof the convection velocity term for a wider range of the dimensionless frequency as well as the strength of the perturbations
at the wall (i.e. k p of the roughness elements) remains to bestudied.
Whilst this method of effective fetch seems to reasonably
predict the flow response, it is not a true physical picture of theflow. In reality, the internal layer would develop simultaneously over the entire length of the installed roughness device.
The information of the perturbation at the wall will propagate
towards the free-stream, at some finite rate, at each streamwise
position along the length of the installed surface as the internal layer is established. Additionally, the height from the wall
to which the information travels increases as the fetch fromthe leading edge of the device increases. Thus, a challenge
for future studies is to obtain a solution for Equation (4) thatprovides the IBL height as a function of both time and fetch.

REFERENCES
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Part 1. Smooth to rough. J. Fluid Mech. 48 (4), 721–761.
Antonia, R.A. & Luxton, R.E. 1972 The response of a turbulent boundary layer to a step change in surface roughness.
Part 2. Rough-to-smooth. J. Fluid Mech. 53 (4), 737–757.
Bou-Zeid, E., Meneveau, C. & Parlange, M.B. 2004 Largeeddy simulation of neutral atmospheric boundary layer flow
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CONCLUSIONS
Measurements of a turbulent boundary layer developing
over an actively oscillating roughness with outer-scaled frequency 0.009 ≤ fδ ≤ 0.047 are presented. For the lowest frequency case ( fδ ≈ 0.009), the phase averaged velocity profile
is seen to oscillate between quasi-steady ‘rough’ and ‘smooth’states, which match the static-smooth and static-rough limitsof the roughness. The transition between the two states is identified as a forward leaning front in phase. As fδ is increased,
the transition state is seen to occupy a longer portion of the cycle. For fδ ⪆ 0.018, it is seen to extend beyond the half-cycle(φ = π), where the wall condition changes. Beyond this dimensionless frequency, the outer part of the flow continues todevelop for the previous wall condition even as the near-wall
adapts to the new wall condition. Thus, fδ ≈ 0.018 representsa critical frequency at which the mean velocity profile is perpetually in transition and no quasi-steady states are observed.
It is also demonstrated that for quasi-steady phases during the
dynamic cycle, the measured mean profile matches the profile
observed for a static spatial step change from smooth-to-rough6