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

MECHANICS OF BOUNDARY LAYER TRANSITION INDUCED BY MULTIPLE DISCRETE
ROUGHNESS ELEMENTS
Saikishan Suryanarayanan and David B. Goldstein
Department of Aerospace Engineering and Engineering Mechanics
The University of Texas at Austin
Austin, TX 78712.
saikishan.suryanarayanan@gmail.com david@oden.utexas.edu
Edward B. White
Department of Aerospace Engineering
Texas A&M University
College Station, TX 77840.
ebw@tamu.edu
Garry L. Brown
Department of Mechanical and Aerospace Engineering
Princeton University
Princeton, NJ 08544.
glb1873@msn.com

ABSTRACTThe mechanisms of boundary layer transition caused bymultiple discrete roughness elements, as well as by a
distributed roughness patch, are studied using immersedboundary direct numerical simulations. The objective is toobtain a broad understanding of how discrete roughness
elements can affect the flow around and downstream ofneighboring roughness elements, with the aim ofextending our mechanistic understanding and mitigation
strategies for isolated-roughness-induced transition to adense array of discrete roughness elements, and possibly
distributed roughness. The results are analyzed frominstability and vorticity points of view.

been extended to pressure gradient boundary layers(Suryanarayanan et al, 2020a).
An outcome of this understanding has been in thedevelopment of transition mitigation strategies such as
roughness shielding (Kuester et al., 2014, Suryanarayanan
et al., 2020b). The shielding strategy involves placementof low amplitude distributed roughness or control strips
upstream and/or downstream of the large discreteroughness element. The downstream strips were shown to
disrupt the streamwise vortices and thus the transition
mechanisms.
In order to investigate the practical applicability ofroughness shielding and other roughness induced
transition mitigation strategies beyond isolated discreteroughness elements, a detailed understanding ofinteraction of the flow around and downstream of multiple
roughness elements is required. This paper therefore aims
to extend the vorticity dynamics viewpoint of transition
caused by an isolated discrete roughness element(Suryanarayanan et al., 2019) to more realistic situations
where there are several discrete roughness elements aswell as for a sandpaper inspired distributed roughness
strip, to enable the development of suitable transition
mitigation strategies and the eventual design of transition
resistant surfaces to be used in conjunction with laminarflow airfoils.

INTRODUCTION
Modeling and mitigation of roughness induced
transition is a fundamental problem that is relevant for
improving the operational efficiency of aircraft (Cebeci etal. 1987, Bragg & Gregorek 1989) and wind turbines(Corten & Veldkamp, 2001) that are subject to theenvironmental accumulation of leading-edge debris.
There has been significant recent progress inunderstanding roughness induced transition caused byisolated discrete roughness elements (Iyer & Mahesh
2013, Loiseau et al. 2014, Suryanarayanan et al. 2017).
Suryanarayanan et al. (2019) identified four different
stages in the transition process and provided a vorticity
point of view explanation for the mechanisms. The result
is summarized in Fig. 1A. Vortical disturbances are
generated by the interaction of the incoming boundary
layer with the discrete roughness element in the first stage
near field of the roughness element. These disturbances
are transiently amplified by the lift-up effect in Stage II.
The lifted-up structure undergoes a secondary, modal
instability in Stage III. This is followed by the‘breakdown’ to turbulence, increased wall shear stress via
counter gradient transport of the mean vorticity andspreading of the turbulent wedge. This understanding has

The objectives of the paper are to understand(1) How is the generation of vortical disturbances
downstream of a given roughness element
affected by the presence of a neighboringroughness?
(2) Is there a wave interaction or coupling between
the secondary (modal) instability of neighboring
DRE wakes? Specifically, can an unstable DRE
wake ‘infect’ otherwise stable DRE wakes in its
neighborhood?
(3) What is the effectiveness of shielding strips in a
multiple DRE situation? Can shielding the most1

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

by streamwise vorticity 𝜔𝑥 . Also shown are isolines of
𝑈 and contours of 𝜔𝑥 at a cut plane taken at 𝑥⁄𝑘1 = 20.6
from the trailing edge of DRE1. These snapshots thus
provide information on the approximate transition locationand the shape of the wake and strength of vorticity fielddownstream of the roughness element(s).
Fig 1(A) shows the roughness induced transition
caused by a single serrated DRE with 𝑘1+ =15.15 discussed in Suryanarayanan et al. (2019). In all
the other cases, the size and location of this DRE (DRE1)
remain fixed. It is of interest to examine whether thisDRE can cause nearby subcritical DREs (i.e. ones thatwould have otherwise been stable in an isolated setting) totransition. Therefore, a second DRE (DRE2) with thesame planform but with a smaller height 𝑘2 = 0.825 𝑘1 is
considered. Figure 1B shows the case with DRE2 alone,
and it can be observed that it does not cause the flow totransition. This is consistent with observations on thecritical value of 𝑘 + ~ 14 from previous work on this DRE
shape.
It can be observed from Fig. 1C that the tall DRE1 cancause the otherwise subcritical DRE2 nearby to transition.
This is because of two main reasons. The proximity
between the DREs affects the overall flow field, which
can change the “receptivity” of the shorter DRE. This canbe better observed in Fig. 1D which has two identicalshorter DREs; the strength of the streamwise vortices
behind the two are different. The second reason is that thesecondary modal instability of the taller DRE1 disturbs
the wake of the smaller DRE2 (which would have beenstable if the background was quiet).
To separate the two effects, a configuration in which
the DREs are staggered such that there is not a significant
effect on the receptivity by DRE1 upon DRE2 isconsidered as case F. The result for this case is broadly
similar to Fig. 1C; the wake of DRE2 is disturbed by theunsteady wake of DRE1. There are some differences,
however, on the detailed mechanisms, as the wake of the
DRE2 is forced by the nearly unimodal Stage III of DRE1
in case C whereas it is excited by the turbulent wedge(Stage IV) in case F. To further analyze this situation,
time averaged statistics for mean and fluctuating
streamwise velocity are compared for cases A, C and F in
Figure 2.
Shown in Fig. 2 are contours of wall shear stress withseveral stream-normal planes with isolines of mean 𝑈 and′contours of 𝑢𝑅𝑀𝑆
. Also shown are streamlines computedfrom the time averaged velocity field. It can be observed
from Fig. 2A1 (Case C) that the shape of the′𝑢𝑅𝑀𝑆
contours are similar for both DRE1 and DRE2.
In our previous work (Berger et al. 2017) the wakebehind the single DRE was examined in wind tunnel
experiments and analyzed using linear stability theory(LST). The fluctuations within the wake have three
distinct peaks, one at the top of the lifted-up structure (i.e.
low-speed streak) and one each at either side. The highest
intensity occurred at the top, suggesting that the local‘shear layer’ at the top of the low-speed streak was thedriver of this instability, what we observe to dominate inboth cases A, as well as the wakes of both DREs in case C(see Figs. 2B1 and 2B2).

dangerous disturbance ensure that nearby
subcritical DREs remain stable?
(4) Can this understanding be extended to a randomroughness trip?
To answer the above questions, a series of direct
numerical simulations involving combinations ofmarginally supercritical and marginally subcritical DREs
and control strips are performed and analyzed.
COMPUTATIONAL METHOD
An immersed boundary, pseudo spectral solver(Goldstein et al. 1993, 1995) is used for the direct
numerical simulations in this work. This solver is basedon the channel flow algorithm of Kim et al. 1987.
There is a buffer zone upstream of the usefulcomputational domain that acts as a flow straightener andinflow generator – any steady and unsteady disturbancesin the outflow are removed in the buffer zone which
forces the flow to be a steady Blasius profile of a specified
thickness. There is a virtual wall near the top of thechannel that enforces the vertical velocity of a growing
Blasius boundary layer. The combination of the bufferzone and the suction wall ensure a near zero-pressure
gradient Blasius boundary layer is developed within theuseful part of the computational domain in an undisturbed
setting. The discrete roughness elements and control
strips are created on the bottom surface using immersedboundary forces. This setup is described in detail in
Suryanarayanan et al. (2019, 2020b)
This code has been used for boundary layer transition
studies with discrete (Sharma et al. 2014, Suryanarayanan
et al. 2019) and distributed roughness (Kuester et al.
2014), examination of turbulent wedge evolution(Goldstein et al. 2017) and turbulent spots over riblets(Strand, 2007). Many of these studies include favorable
comparisons with stability theory, matched water tunnel(Suryanarayanan et al. 2019) and wind tunnel experiments(Berger et al., 2017, Suryanarayanan et al. 2020b).
The present work uses the same discrete roughness
element, inflow conditions and computational domainused in previous studies (Suryanarayanan et al. 2020a,
2020b) as the baseline case. The roughness element has anominal 𝑘 + = 𝑘𝑢𝜏 ⁄𝜈 = 15.15 and the Reynolds number
based on the boundary layer displacement thickness at theroughness location (δ*0) is approximately 1480. All thesimulations presented in this paper are carried out using
768 × 128 × 192 grid points over a domain of 164.4 δ*0 ×
8.22 δ*0 × 20.6 δ*0 in the streamwise, wall-normal andspanwise directions.
RESULTS AND DISCUSSIONInteraction between neighboring DREs
Direct numerical simulations of seven different
configurations involving one or more discrete roughness
elements are performed in this work. All the simulations
have the same computational setup and inflow conditions.
Representative instantaneous snapshots (taken after
the simulations have reached a statistically steady state)
are shown in Figure 1. Plotted in each figure are an
isosurface of streamwise velocity at 𝑈 = 0.29 𝑈∞ colored2

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

Figure 1: Instantaneous snapshots of the different DNS cases (A-G). The DREs (and control strips) are shown in orange.
Plotted in each case are an isosurface of U colored by 𝜔𝑥 and contours of 𝜔𝑥 and isolines of 𝑈 in stream-normal planes
downstream of the DRE(s).

312th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19-22, 2022′
̅Figure 2: (A1- A3) Time averaged wall shear stress, streamlines (colored by altitude) and contours of 𝑢𝑅𝑀𝑆
and isolines of 𝑈
shown in stream-normal planes for cases C, A and F. B1 and B3 zoomed in view of the same data in A1 and A3 showing theclumping mode and swaying mode occurring in the wakes of DRE2 in cases C and F. B2 and B4 show the instantaneous
snapshots with vortex lines (colored by 𝜔𝑥 ) for cases C and F to provide a mechanistic description of the two modes.

Figure 3. A Transition caused by a sandpaper-like distributed roughness trip. B. Mitigation using downstream shielding by a
low amplitude control strip.

4

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

From a vorticity point of view, this instability mode
driven by the top shear (𝜔𝑧 ) layer can be interpreted as theclumping of the heads of the vortex lines that ride on topof the lifted-up 3D structure, and this leads to tilting of thelegs (𝜔𝑦 ) generating an unsteady 𝜔𝑥 . This clumping modecan be clearly observed in Fig. 2B1 and is illustrated using
vortex lines in Fig. 2B2 (highlighted with black arrows).
Linear stability analysis (Berger et al., 2017) also
showed that there is another, longer wavelength (lowfrequency) instability that appears with peaks on eitherside of the lifted-up structure. Band pass filtering of theexperimental data confirmed the existence of this lowfrequency ‘swaying’ mode which can be interpreted as
being driven by the side (𝜔𝑦 ) shear layers.
Interestingly the wake of DRE2 in case F seems to be
dominated by this swaying mode, as observed in Fig. 2B4.
While both large and small scale vortical structures exist
within the turbulent wedge, it’s influence on the velocity
field outside the wedge is dominated by the lower
frequency - the flow field at the edge of turbulent wedges
are known to be dominated by large pancakes of 𝜔𝑥 (seeGoldstein et al., 2017). This is also consistent with the
hot-wire spectra observed well outside the DRE wake byBerger et al. (2017). This swaying mode can beunderstood from a vorticity point of view as thegeneration of unsteady 𝜔𝑥 , but this process is not driven
by the clumping of the heads and the associated tilting oflegs but rather by the spanwise swaying motion of thestructure as a whole. This results in a longer wavelengthof the instability (nearly 4 times that of the clumpingmode), consistent with the findings of Berger et al. (2017)
for a bandpass filtered single DRE dataset.

numbers for the unsteady cases, but the strips appear to
approximately cause a 50% reduction in the streamwise
vorticity magnitude. The mechanism by which the strips
work, and a theoretical model are described inSuryanarayanan at al. (2020b) and (2020c) respectively.
Case F, in which DRE2 is placed downstream andtransitions only because of the unsteady forcing of thewedge, presents an interesting case for studying control.
Case G considers just suppressing the transition behindthe larger DRE1 by disrupting it’s streamwise vortex witha finite span control strip. In this case, the control strip byitself does not directly affect the flow around DRE2; andany effect observed on the wake of DRE2 is primarily due
to the change in the wake of DRE1. The control strip
reduces the peak 𝜔𝑥 to 0.19 from a value of 0.34 for theisolated DRE case, preventing DRE1’s transition. It canbe observed that disrupting the larger DRE1’s transition inthis case, can prevent the smaller DRE2 from transitioning
too, as the modal disturbances that excite its wake are nolonger present. If we quench the unsteady disturbancessoon enough, we may be able to keep them from
‘infecting’ nearby subcritical wakes.
Extension to distributed roughness
The next step is to extend these results to the
distributed roughness case. While discrete and distributedroughness have been treated separately in literature, ourstudies (Suryanarayanan et al., 2021, manuscript underpreparation) show that there is similarity in the late-stagetransition processes that increase wall shear stress acrossboth discrete and distributed roughness induced transition.
In this paper, we consider a ‘sandpaper’ like distributedroughness trip in Fig. 3. Preliminary results show similar
mechanisms at play not just in the final stages, but
throughout the transition process, at least for this specificdistributed roughness considered here –(a) Generation of streamwise vortices by theinteraction of the roughness with the incoming
boundary layer(b) Lift-up and transient amplification(c) The most dangerous disturbances undergo modal
instability, and these may excite subcritical wakes
in their neighborhood.
A detailed analysis of this case will be presented
elsewhere, but Fig. 3B shows that shielding strips candelay transition downstream of distributed roughness aswell by reducing the magnitude of streamwise vortices,supporting the broad similarity of mechanisms. We notehowever, that random roughness strips can cause
receptivity to Tollmien–Schlichting waves that caneventually cause classical transition and the role of the
strips or other surface textures on mitigation of classicaltransition is yet to be studied.

Transition control by shielding
Regardless of the detailed mode in Stage III, the broad
picture of RIT by multiple DREs remains consistent withthe findings for the single DRE. Streamwise vortices
generated on the interaction of the DRE(s) with theboundary layer lift-up the background 𝜔𝑧 to generate 𝜔𝑦(i.e. transient growth of the amplitude of low-speed
streaks) which subsequently are subject to a secondary
instability. The main differences are that the receptivityof the DRE can be altered by other DREs in theirproximity and that stable DRE wakes can be forced by theunsteadiness present in the wakes of transitioning DREspresent nearby.
Since the mechanism of transition in a multiple DRE
system is still dominated by the lift-up caused bystreamwise vortices, the same control schemes may be
expected to work. A downstream control strip of height
0.45𝑘1 and chord 12𝑘1 placed about 5𝑘1 behind the DRE
pair (E) prevents transition. The peak value of 𝜔𝑥 /𝜔𝑧0
(where 𝜔𝑧 0 is the vorticity at the wall of the undisturbed
laminar boundary layer at the location of DRE1) in aplane 20.6 k downstream of the DREs (as observed in the
instantaneous snapshots) is significantly reduced for boththe DREs by the control strip. For DRE1 the value of𝜔𝑥 /𝜔𝑧0 decreases from 0.37 to 0.20 and in the wake of
DRE2 the streamwise vorticity is reduced from 0.33 to
0.16, thus rendering both of them subcritical. There is
likely to be some temporal variation in these precise

CONCLUDING REMARKSThe series of direct numerical simulations presented inthis paper helps extend the mechanistic understanding ofboundary layer transition caused by an isolated discreteroughness element to situations involving multiple
discrete roughness elements, as well as to certain classesof distributed roughness. The results show that DREs canaffect the flow field around other DREs in close proximity
5

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

modeled riblet covered surface. Journal
Mechanics, 302, pp.333-376.

and thus alter the vortical disturbances generated in theirwakes. Even if the DREs are not close enough to affectthe nearfield flow, a transitioning DRE wake can force (or‘infect’) otherwise subcritical wakes of neighboring or
downstream DREs and cause them to transition. This isparticularly significant in real-world situations such as
aircraft wing leading edge subject to insect splatter; asingle large roughness could potentially cause the flow
downstream of many smaller roughness elements aroundit to transition. For the DRE shapes and configurations
considered here, it is found that a transitioning DRE can
excite either the clumping mode or the swaying mode of
the subcritical DRE. The latter appears to be likely when
the subcritical wake is forced by the disturbances at theedge of a nearby turbulent wedge. Control strips aredemonstrated to mitigate transition caused by multiple
roughness elements. The control strips work by disrupting
individual streamwise vortices, and since the lift-up by
streamwise vortices continues to be a significant part of
the transition process involving multiple DREs, thecontrol strips remain effective.
The work also
demonstrates that preventing the most dangerous
disturbance from transitioning can also prevent it from
infecting neighboring subcritical wakes. Preliminary
results indicate that much of this understanding andcontrol effectiveness appear to be valid for situations
involving distributed roughness such as a sandpaper trip.

of

Fluid

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ACKNOWLEDGEMENTS
This work is sponsored by the US Air Force Office of
Scientific Research through grant# FA9550-19-1-0145.
We thank the Texas Advanced Computing Center (TACC)
at the University of Texas at Austin for providing HighPerformance Computing resources.

Suryanarayanan, S., Goldstein, D.B. and Brown, G.L.,
2019. Roughness induced transition: A vorticity point ofview. Physics of Fluids, 31(2), p.024101.

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