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

MECHANISMS OF INTERACTION BETWEEN A STATIONARYCROSSFLOW INSTABILITY AND BACKWARD-FACING STEPS

Oleksandr Krochak
Jordi Casacuberta
Faculty of Aerospace Engineering
Faculty of Aerospace Engineering
Delft University of Technology
Delft University of Technology
Kluyverweg 1, 2629 HS Delft, the Netherlands Kluyverweg 1, 2629 HS Delft, the Netherlands
O.O.Krochak@student.tudelft.nl
J.CasacubertaPuig@tudelft.nl

Stefan Hickel
Marios Kotsonis
Faculty of Aerospace Engineering
Faculty of Aerospace Engineering
Delft University of Technology
Delft University of Technology
Kluyverweg 1, 2629 HS Delft, the Netherlands Kluyverweg 1, 2629 HS Delft, the Netherlands
S.Hickel@tudelft.nl
M.Kotsonis@tudelft.nl

heights and location, and stationary crossflow properties are
reproduced in our present work to facilitate the direct comparison of mechanisms of interaction in backward- versus forwardfacing steps. Reference data of a no-step case from their investigation is used for comparison. Unsteady perturbation effects
ultimately leading the laminar-turbulent transition process arehere discarded to isolate the stationary form of flow mechanisms; inclusion of unsteady structures in a possibly complex flow scenario would likely mask main mechanisms of thepresent analysis. The stationary perturbation field is decomposed in spanwise Fourier modes. The effect of step-induced
base-flow features, such as recirculating flow, inflectional profiles, or local pressure gradient on altering the evolution of
the stationary perturbation field is analyzed qualitatively andquantitatively.

INTRODUCTION
Subsonic swept-wing aircraft is a main mode of longdistance passenger transport; thus, improving its efficiency
carries a significant economic and environmental impact.
Laminar Flow Control (LFC) technology has shown potential
to reduce skin friction drag by delaying laminar-turbulent transition on the wings and tail parts. However, surface irregularities, such as two-dimensional steps, caused by panel junctions
and joints, may alter the stability of the boundary layer, promote premature laminar-turbulent transition (Perraud & Seraudie, 2000), and reduce the effectivity of LFC. Stationary
crossflow instabilities may typically dominate the transition
path in swept-wing flows. The goal of this article is to investigate the purely stationary interaction between an imposed
stationary crossflow instability developing in a swept-wingboundary layer and backward-facing steps of several heights.
Tufts et al. (2017) performed numerical simulations ofbackward-facing-step flows and reported rather mild stationary crossflow growth at the step, which they do not consider as the main mechanism promoting transition. Eppink(2022) studied the evolution of the crossflow instability overa backward-facing step via Particle Image Velocimetry (PIV)
measurements. It is hypothesized that, as a consequence ofthe reversal of the crossflow velocity profile downstream ofthe step, stationary crossflow vortices rotating in a sense opposite to the original primary ones may be amplified. Casacuberta et al. (2021) carried out Direct Numerical Simulations(DNS) to study the stationary interaction between incoming
crossflow and forward-facing steps. They observed that a system of near-wall streaky perturbation structures are induced at
the step; these develop underneath the incoming crossflow perturbation locally around the step. The harmonic (i.e., smaller
wavelength) components of the crossflow perturbation are significantly destabilized by the inflectional step-distorted baseflow profiles.
In this article, DNS are performed to study the purely stationary mechanisms of interaction between an incoming prescribed crossflow instability and backward-facing steps of various heights. The main elements of the setup of Casacuberta
et al. (2021, 2022), namely the free-stream evolution, step

METHODOLOGY
The incompressible swept-wing flow is modeled as flatplate flow with an externally imposed airfoil-like pressure gradient in the chordwise direction. The free-stream velocity isdecomposed into a chordwise component, u∞ , and a spanwise
component, w∞ = −1.24u∞ , to model the effect of sweep angle. Pressure measurements from wind-tunnel experiments on
a 45◦ swept wing (Rius-Vidales & Kotsonis, 2021) are used
to guide the DNS setup. The inflow boundary layer thickness,
δ0 = 7.71 × 10−4 m, and free-stream velocity, u∞ = 15.10 m/s,
are chosen as global characteristic quantities and used as nondimensionalizing values. The reader is referred to Casacuberta
et al. (2021, 2022) for further details on the flow problem andsetup.
The main coordinate system reads x = [ x y z ]T , wherex, y, and z indicate the chordwise (i.e. normal to the virtual
leading edge), wall-normal and spanwise directions, respectively. A stationary crossflow mode, computed as solution to a
local linear Orr-Sommerfeld analysis of the base flow profile,is prescribed at the inflow with an amplitude of 3.5 × 10−3 u∞for all step cases. The DNS are performed for three different
step heights, h = {0.59, 0.76, 0.97}δ0 , all of which are below
the undisturbed boundary layer thickness δ99,h at the virtual lo-

1

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022
Table 1: Base-flow properties in the near-step region.

cation of the step. Periodic boundary conditions are prescribedon the sides of the computational domain to constrain the perturbation growth in the chordwise direction. The spanwise domain length (i.e, the fundamental spanwise wavelength) is set
to λz = 7.5 mm.
The DNS of the unperturbed two-dimensional spanwiseinvariant base flow and the stationary developed threedimensional flow are performed on an indentical computational domain. Letting q = [ u v w p ]T be the vector of statevariables, the steady developed flow, q (x), obtained from DNS
is expressed as the sum of the spanwise-invariant laminar baseflow, qb (x), and a steady perturbation field, q0 (x).
To gain insight on the perturbation behaviour, the fieldq0 (x) is decomposed in spanwise Fourier modes:

N

Case

Step I

Step II

Step III

h/δ0

0.59

0.76

0.97

h/δ99,h

0.31

0.40

0.52

lrev /δ0

9.6

12.8

17.2

l∇p /δ0

13.3

17.1

20.5

lws,b /δ0

26.7

31.9

38.3

|urev | (%)

5.6

6.8

8.25

10.0

12.0

14.5

|wrev
s,b | (%)
ki(φ(0,j) + jβ0 z)

q0k = ∑ Ak(0, j) |q̃k |(0, j) e

,

(1)

j=0

RESULTS AND DISCUSSION
1

where N is the number of modes considered, k = {u, v, w, p}
expresses a component of the state vector, |q̃k |(0, j) =|q̃k |(0, j) (x, y) is the normalized shape function of a Fourierkis the phase,mode j, Ak(0, j) = Ak(0, j) (x) is the amplitude, φ(0,j)√
i = −1, β0 = 2π/λz is the fundamental spanwise wavenumber, and λz is the fundamental spanwise wavelength, which isset equal to the spanwise domain length.

BASE-FLOW FEATURES

The presence of the step distorts the organization of theboundary-layer flow and introduces new base-flow structures
which are not present in the reference, i.e., no-step, case. The
most prominent feature of the base flow is recirculating flow
immediately downstream of the step, see Figure 1(a). Its geometrical properties are here characterized by an isoline of
ub = 0; see Table 1. The xst = lrev denotes the stagnation point
further downstream. The strength of the recirculating flow,i.e., the maximum reverse velocity, |urev | with urev < 0, attains
between 6% and 8% relative to uext in the step cases (Table
1). Such values are close to the threshold for a global instability to develop in classic pressure-driven separation bubbles(Rodrı́guez et al., 2013). However, by constraining the interaction to be stationary via the usage of SFD, no manifestationof a possible global instability was captured.
The pressure field is locally altered by the presence ofthe step. A region of strong adverse pressure gradient arises
immediately downstream of the step. It extends up to approximately xst /δ0 = 20.5 in step case III (Table 1); here, l∇p denotes the distance from xst = 0 to the threshold ∂ p/∂ x = 0
downstream of the step at the wall. Furthermore, a region ofenhanced favourable pressure gradient develops immediately
upstream of the step. The pressure field around the step in thepresent DNS is in qualitative agreement with that reported byTufts et al. (2017).
Casacuberta et al. (2022) report a strong modulation of
the base-flow streamlines in z locally around the corner of aforward-facing step for a setup identical to the one presented
here. In the current backward-facing-step flow, no significant deflection of the streamlines in z upstream of the step
is observed. This may be ascribed to the different pressuregradient strength induced upstream of the forward- versus the
backward-facing step. In fact, the overall organization of theflow upstream of the step appears to not be significantly altered by the presence of the backward-facing step. Downstream of the step, the evolution of the flow in x above the flowseparation region is rather gradual. Contrary to the forwardfacing step case (Casacuberta et al., 2022), the streamlines ofthe flow do not visually display an abrupt turn in the x-z plane.
Next to flow reversal (i.e., ub < 0), the step induces reversal of the crossflow profile (i.e., ws,b < 0) as well; see Figure 1(b-g). The peak magnitude of the reserved crossflow profile in y, denoted by |wrev
s,b |, is 10% and 15% relative to uext inFollowing the discussion presented in Casacuberta et al.
(2021), the base-flow components are decomposed based on
the crossflow orientation. For that purpose, the local angle between the external inviscid streamline and the x-direction isevaluated. It reads φ (x) = arctan (w∞ /uext (x)), where uext denotes the external chordwise velocity in the outer-flow region.
Accordingly, the base-flow velocity components locally tangent and orthogonal to the inviscid streamline direction are expressed as us,b = ub cos(φ )+wb sin(φ ) and ws,b = wb cos(φ )−ub sin(φ ), where ub and wb are the base-flow chordwise andspanwise velocity components, respectively. The component
ws,b is the so-called crossflow velocity.
The incompressible Navier-Stokes equations are solved
numerically with INCA, a conservative finite-volume solver(Hickel & Adams, 2008). The Navier-Stokes equations aremarched in time with a third-order Runge-Kutta method. A
fifth-order upwind scheme is used to discretize the convective terms. The Selective Frequency Damping (SFD) method(Åkervik et al., 2006; Casacuberta et al., 2018) is applied tonumerically enforce a fully stationary solution of the developed flow. As convergence criterion, the L2 -norm of the SFD
residual is chosen to be ε = 10−6 .
The computational domain encompasses 0 ≤ x/δ0 ≤ 517,
yst /δ0 ≤ y/δ0 ≤ 26 and −4.86 ≤ z/δ0 ≤ 4.86; the baseline
flat plate is set at y = 0 and the step extends until yst /δ0 =−0.59, −0.76, −0.97 for step cases I, II, and III, respectively.
For all cases, the step is located at x/δ0 = 177.62. The coordinate expressing the chordwise distance relative to the stepis hereafter denoted by xst = x − 177.62δ0 and, downstreamof the step, the relative wall-normal distance is denoted byy∗ = y − yst . The results presented in this article have beenobtained with a grid containing 2 × 106 and 3.7 × 107 cells forthe base- and developed-flow runs, respectively. The reader isreferred to Casacuberta et al. (2022) for further details on the
topology of the computational grid.

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

y/δ0

2
1
0

lws,b

lrev
xst /δ0 = 2
3

xst /δ0 = 10
(c)

(b)

xst /δ0 = 18

xst /δ0 = 26

xst /δ0 = 42
(g)

(f )

(e)

(d)

xst /δ0 = 34y∗ /δ0

2

1

0

−0.1

0

0.1

−0.1

0

0.1

−0.1

0

0.1

−0.1

ws,b /u∞

0

0.1

−0.1

0

0.1

−0.1

0

0.1

Figure 1: Contour of base-flow velocity, ub , in step III (a). Evolution in x of the crossflow profile, ws,b , for the reference

no-step (thin solid black), step I (dash-dotted blue), step II (dotted orange), and step III (thick solid red) cases (b-g).
Isolines of velocity reversal ub = 0 (solid cyan) and crossflow inflection points ∂ 2 ws,b /∂ y2 = 0 (dash-dotted magenta).
function, Aũ(0,1) |q̃u |(0,1) , a prominent additional peak develops
in step cases II and III for xst > 0 close to the wall (Figure3(a)). This topological feature has been reported for forwardfacing (Tufts et al., 2017; Casacuberta et al., 2022), as well as
for backward-facing-step flows (Eppink, 2022). In step caseI this near-wall peak in the perturbation shape is either notpresent or very weak; see Figure 3(c). In step case III, the location of the additional peak in y reasonably matches the spatial
location of the step-induced inflection points in the base flow.

step cases I and III, respectively (Table 1). It is noteworthy
to mention that the evolution of the crossflow profile in x is
in close qualitative agreement with the behaviour reported by
Eppink (2022): surprisingly, close downstream of the step, thestrength of the crossflow reversal is approximately similar for
all steps studied here. However, when moving further in x, thereversed-flow strength is the greatest for the largest step case
(Figure 1(c,d)).
The crossflow-reversal region downstream of the step is
accompanied by additional inflection points in the crossflow
profile that do not manifest in the reference case. These new
inflection points arise close to the wall, underneath the original(primary) crossflow inflection points. The length in x of thisregion featuring secondary step-induced inflection points, lws,b ,increases with the step height; see Table 1.

2

The amplitude of the near-wall peak in step case III grows
rapidly in x and, eventually, slightly surpasses the strength ofthe primary upper peak; see Figure 3(a). The primary peakof the perturbation shape may be associated to the original
crossflow perturbation that develops further off the wall. In
recent forward-facing-step flow investigations, the secondary
near-wall peak downstream of the step was associated to the
manifestation of spanwise-alternating perturbation streaks induced at the step corner (Casacuberta et al., 2021, 2022). Despite topological similarities between such additional peaks
in forward- versus backward-facing-step flows, in the present
case, the near-wall peak in the perturbation shape may be representing a different flow mechanism than the one reported forforward-facing steps.

FUNDAMENTALPERTURBATION EVOLUTION

Next, the behaviour of the fundamental perturbation component, i.e., the primary perturbation Fourier mode β = β0 , isanalyzed. The discussion is restricted to near-step effects. Figure 2(a) portrays the chordwise evolution of the amplitude of
the primary Fourier mode. Upstream of the step, the amplitude curves of the step cases are essentially identical to thatof the no-step reference case. This was expected since, as it
was previously mentioned, the steps have only a very weak
upstream influence. Close downstream of the step, the fundamental perturbation component is significantly stabilized. This
local stabilizing effect appears to be proportional to the stepheight (Figure 2(a)). Similarly, Casacuberta et al. (2022) report a local stabilizing influence of sufficiently large forwardfacing steps to the incoming fundamental stationary crossflow
perturbation.
When considering the evolution of the overall amplitude

Eppink (2022) proposes that the destabilizing influenceof new step-induced inflection points downstream of the step
triggers stationary-crossflow growth. In the present DNS, theappearance of the secondary perturbation peak near the wallwithin the x-region featuring reversed crossflow seems to support the observations of Eppink (2022). In particular, visualcorrelation is found between the step-induced inflection point
location and the perturbation amplification near the wall (Figure 3(a)).
To shed light on the nature of the mechanism feeding perturbation growth, the perturbation shape functions and growth
rates from DNS are next compared to the results of linear sta-3

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022
0.3

0.2

(a)

(b)

0.15
Aũ(0,2) /u∞Aũ(0,1) /u∞

0.25
0.2
0.15

0.1
0.05

0.1
0

20

40
xst /δ0

60

0

80

0

20

40
xst /δ060

80

Figure 2: Evolution of the amplitude of the chordwise-velocity perturbation Fourier modes β = β0 (a) and β = 2β0 (b).
Reference no-step (thin solid black), step I (dash-dotted blue), step II (dotted orange), and step III (thick solid red).
Aũ(0, j) |q̃ũ |(0, j) + Aũ(0, j) |q̃ũ† |(0, j) /u∞

y/δ0

2

0.1

0.05

(a)

(b)

(c)

(d)

0.15

1
0
2

y/δ0

0

1
0
-10

10

30
xst /δ0

50

70

90

-10

10

30
xst /δ0

50

70

90

Figure 3: Chordwise-velocity perturbation amplitude function in step cases III (a,b) and I (c,d) for β = β0 (a,c) and

β = 2β0 (b,d) Fourier modes. Base-flow reversal ub = 0 (solid white), base-flow crossflow inflection points∂ 2 ws,b /∂ y2 = 0 (dashed yellow).

bility analysis. A linear local Orr-Sommerfeld (OS) eigenvalue problem is solved on the DNS base flow for the reference and step cases from the downstream vicinity of the step
until approximately xst /δ0 = 82. The analysis is carried out
for β = β0 to characterize fundamental perturbation effects.
While the flow field is highly non-parallel close to the step, theresults of an OS analysis are expected to elucidate on possible (in)stability effects associated to the inflectional base-flow
profiles.
Downstream of all steps, two main unstable OS eigensolutions are identified. One is associated to the original crossflow mode and, as such, it is also captured in the referencecase; this is mainly supported by the close match between the
DNS perturbation shape and the eigenfunction associated tothis eigenmode (see solid red line and blue circles in Figure4(e), respectively). In addition, a new unstable OS eigensolution is identified in all step cases, which is not present in thereference case.
The trajectory in the complex plane of the aforementioned
two families of OS eigenvalues as a function of x is depicted in
Figure 4(a-d) for all cases studied. Here, α OS = αrOS + iαiOS
denotes the corresponding eigenvalues. As mentioned previously, shortly downstream of the step, the incoming crossflow
mode is stabilized for all step cases in the DNS (Figure 2(a)).

Conformably, the eigenvalue associated to the OS crossflow
mode initially lies in (or close to) the stable region of the eigenspectrum. When moving in x, it gradually shifts towards theunstable half-plane. This is consistent with the DNS results;
see Figure 2(a). Sufficiently downstream of the step in all step
cases, the properties of the OS eigenmode originally associated to the crossflow mode gradually resemble those displayedby the reference case. Next to growth rate, the peak locationin y of the OS eigenfunction associated to the crossflow modereasonably matches that of the DNS shape function sufficiently
downstream of the step; see Figure 4(f ).
Considering the outcome of the analysis to this point, it
can be hypothesized that the second family of unstable OSeigenmodes only identified in the step cases is associated to
an inflectional instability supported by the step-distorted baseflow profiles. The fact that the wall-normal peak of the OS
eigenfunction approximately coincides with the y-location of
the step-induced inflection point in the base flow (Figure 4(e)and Figure 1(c)) would further strengthen this claim. The
growth rates of this second family of eigenmodes largely exceeds that of the original crossflow; see Figure 4(b-d). Thismay highlight the strongly unstable nature of this new instability mechanism and would serve as a plausible explanation
for the large perturbation amplification captured in the DNS

4

0
-5

(b) 4

(a)
82

-5

(e)

(f )

2
2

-10

0

xst /δ0 = 40

3

16
18

82

2

xst /δ0 = 14

(c) 4
82

20
22

y∗ /δ0Im(αiOS )δ0 (×102 ) Im(αiOS )δ0 (×102 )12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022(d) 12
82

2

28

24

1

2

-10
0.55

0.6

0.65

0.7

0.55

Re(αrOS )δ0

0.6

0.65

0

0.7

0

Re(αrOS )δ0

1
0.5


|ũ|(0,1) /max |ũ|(0,1)

0.5

1

0

Figure 4: Trajectory of Orr-Sommerfeld eigenvalues in the range xst /δ0 ∈ [2, 82] (bright-to-dark for increasing x) for thereference no-step (a), step I (b), step II (c), and step III (d) cases. Numerals indicate xst /δ0 locations. Orr-Sommerfeld
shape functions for β = β0 (orange and blue circles) and DNS (solid red) at xst /δ0 = 14 (e) and 40 (f ) for step III indicatedby magenta triangles in (d).
close to the wall in step case III; see Figure 3(a). Naturally,as the step height is decreased, the destabilizing influence of
the inflection points weakens. This is consistently observed
both in the DNS amplitude evolution (Figure 3(a,c)) and in
the OS eigenspectrum (Figure 4(b-d)). Furthermore, it should
be noted that this family of new eigenmodes in the step cases
only manifests approximately in the chordwise region where
the additional step-induced inflection points develop.

Aũ(0, j) /u∞

10−1
10−2
10−3
10−4
10−5
0

3

HARMONIC PERTURBATION EVOLUTION

The analysis is next extended to the harmonic (i.e.,
smaller wavelength) perturbation behaviour. For perturbations
with β = 2β0 , amplification is measured downstream of xst in
all step cases (Figure 2(b)). Significant amplification is observed for the harmonics β = 3β0 , β = 4β0 , and β = 5β0 aswell, see Figure 5. For the sake of simplicity, the discussion ishere focused on the β = 2β0 mode since it is representative of
the main qualitative harmonic behaviour. For the largest step
case, the amplitude of the Fourier mode β = 2β0 , Aũ(0,2) , surprisingly exceeds that of the fundamental mode, β = β0 , immediately downstream of the step (Figure 2). The main peakof the shape function |q̃u |(0,2) in y arises close to the location of
the secondary near-wall peak in the profile of the fundamental
Fourier mode (Figure 3(a,b)). This feature is observed in all
step cases. Following the discussion provided in the previous
section, the present results suggest a destabilizing influence ofthe step-induced inflection point to perturbation with β = 2β0
as well.
In a fashion similar to the analysis of the fundamental perturbation component, β = β0 , an Orr-Sommerfeld eigenvalue
problem is here solved for β = 2β0 . An unstable eigensolution is identified, which does not manifest in the reference nostep case. Figure 6(a-d) depicts the evolution of the associatedeigenvalue in the complex plane as a function of x, and Figure 6(e) portrays the corresponding OS eigenfunction together
with the DNS profile. Initially in x, the OS eigenvalue lies in
the unstable region implying that, in agreement with the DNS
results, the base flow is destabilizing. This is not the case in
the reference no-step configuration since the harmonic growthis mainly driven by non-linear perturbation interactions. Cor-2040
xst /δ060

80

Figure 5: Evolution of the amplitude of the chordwise-

velocity perturbation Fourier modes β = 0 (thick solid
black), β = 2β0 (dash-dotted blue), β = 3β0 (dashedmagenta), β = 4β0 (dotted orange), β = 5β0 (loosely
dotted teal) for step III.

respondingly, the associated OS eigenvalue remains in the stable region for all x. Interestingly, the trajectory in the complex
plane of this new unstable eigenvalue manifesting in the step
cases for β = 2β0 (Figure 6(b-d)) closely follows that of theadditional unstable eigenvalue in the β = β0 space. The peakin y of the associated β = 2β0 OS eigenfunction at xst /δ0 = 10
matches the y-location of the peak from DNS and lies close to
the step-induced inflection point (Figure 6(e) and Figure 1(c)).
Therefore, the present results provide evidence that the harmonic field is significantly destabilized at the step due to an
inflectional instability associated to the base-flow distortion introduced by the step.

CONCLUSIONS
Direct Numerical Simulations (DNS) are performed to
study the interaction between an imposed stationary crossflow
mode and backward-facing steps of several heights immersed
in an incompressible three-dimensional swept-wing boundary
layer. The behaviour of the unperturbed laminar base flow andthe stationary perturbation field at the step are presented and

5

(a)
0 82
-5
-10
-15

(b)

(e)

3

xst /δ0 = 10

82

2

2
2

(c)

(d)

0 82
-5
2
-10
-15

82

1.1

1.2

1.3

1.4

y∗ /δ0Im(αiOS )δ0 (×102 ) Im(αiOS )δ0 (×102 )12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022

1

8
1.2

1.1

Re(αrOS )δ0

1.3

Re(αrOS )δ0

1.4

0

0

1


|ũ|(0,2) /max |ũ|(0,2)
0.5

Figure 6: Trajectory of Orr-Sommerfeld eigenvalues for the reference no-step case (a), step I (b), step II (c), and step III (d)for β = 2β0 . Orr-Sommerfeld shape function (orange circles) and DNS (solid red) for step III at xst /δ0 = 10 (e) indicatedby a magenta triangle in (d).

discussed. The analysis is restricted to the near-step regime
and to perturbation effects of stationary nature. To illustrate
similarities and differences with main mechanisms and structures in forward-facing-step flows, the present setup is identical to that employed in recent numerical investigation on
forward-facing steps (Casacuberta et al., 2021, 2022).
Both the chordwise extension and peak reverse velocity of
the flow-separation region downstream of the backward-facing
steps are significantly larger than in forward-facing steps ofidentical height. The base-flow profiles downstream of the
backward-facing step display two families of inflection points
in the crossflow component; one is associated to the original
inflection point also present in the reference no-step case. The
second is induced by the presence of the step.
It is found that locally around the step, the fundamental
crossflow perturbation is stabilized. At the same time, perturbation amplification is measured close to the near-wall inflection point location, suggesting a destabilizing influence of thelatter. The DNS results are compared to the results of a linear
local Orr-Sommerfeld (OS) stability analysis on the DNS baseflow. For perturbations associated to the fundamental spanwise wavelength, two main unstable eigensolutions are identified and associated to 1) the original stationary crossflow modeand 2) an inflectional instability that would be associated to a
new family of near-wall inflection points induced by the step.
When considering the harmonic perturbation field ofsmaller wavelength, a significant destabilization is measured
close to the step. An OS unstable eigenmode is identified for
perturbations with half the fundamental wavelength; the topology of the associated OS eigenfunction and the results of theoverall analysis suggest that the step-induced near-wall inflectional profiles support an inflectional instability for harmonic
wavelengths as well. Similar as in forward-facing-step flows,
the inflectional profiles induced by the step support significant
destabilization of the harmonic perturbation components.
The underlying inflectional instability is proposed as amain step-flow mechanism purely driven by the base flow
modification imparted by the step. Furthermore, based on the
aforementioned considerations, we conclude that the results of

the OS analysis provide insightful information on the natureand evolution of the stationary perturbation field.

REFERENCES
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Phys. 375, 481–497.
Casacuberta, J., Hickel, S. & Kotsonis, M. 2021 Mechanisms
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2022 Direct Numerical Simulation of interaction between
a stationary crossflow instability and forward-facing steps.
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