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

IMPLICATIONS OF SPANWISE WAKE INSTABILITY ON THE FORMATION
OF SECONDARY STRUCTURES BEHIND OSCILLATING FOILS

Suyash Verma & Arman Hemmati*
Department of Mechanical Engineering, University of Alberta, Edmonton, AB, Canada T6G 2R3* arman.hemmati@ualberta.ca

ABSTRACT

dimensionality in turbulent wakes of oscillating rigid foils.
Since the foil kinematics closely mimic the motion of biological propulsors (e.g., insect wings, bird wings, and fish tail fins)and robotic maneuvering systems in underwater applications,the understanding gained here will present unique insights foradvancement of highly efficient micro-aerial vehicles and marine robotic swimmers.
Investigations of the wake of stationary bluff bodies, suchas circular cylinders, revealed the presence of primary and secondary instabilities that were associated with either outflux
of core vorticity or the straining of braid shear layer (Mittal& Balachandar, 1995; Zhang et al., 1995; Williamson, 1996;
Brede et al., 1996). Mittal & Balachandar (1995) described
the time-evolution of wake structures behind a stationary circular cylinder while highlighting the presence of horse-shoeand rib−like formations associated with the primary and secondary vorticity. The spatio-temporal growth of dislocations
via core vorticity outflux and braid vorticity straining therefore presented an important mechanism for transition to turbulence in the wake of bluff bodies (Mittal & Balachandar, 1995;
Williamson, 1996). Extensive efforts on the characterizationof primary and secondary instability modes differentiated thedislocation features in terms of their spanwise wavelength (λz )or periodicity of paired streamwise ribs (Zhang et al., 1995;
Brede et al., 1996). Further studies also involved investigating different stationary geometries, such as square cylinders(Robichaux et al., 1999), bluff elongated trailing edge airfoils(Ryan et al., 2005) and oscillating foils mimicking kinematics of bird wings and fish tail fins (Deng & Caulfield, 2015;
Sun et al., 2018; Chiereghin et al., 2020). The association of
spanwise instabilities and turbulence in the wake of oscillating
foils, however, needs a more detailed investigation.
Quantitative determination of ‘long’ and ‘short’ wavelength instability modes using perturbation analysis of flows
around purely pitching foils revealed λz ≈ 1c and 0.2c, respectively, where c denotes the foil chord length (Deng &Caulfield, 2015; Deng et al., 2015). Similarly, Sun et al.
(2018) characterized the instability modes A, B, QP and S, detected for purely heaving foils that varied from 0.196c to 1.05c.
However, extensive characterization of the instability features
were concerned with deflected wake topology. Further, thequalitative insights into the presence or evolution of spatial
dislocations, and their association with the leading edge vortex(LEV) dynamics in particular, was rather limited. Chiereghin
et al. (2020) observed spanwise undulations of leading edge
vortex filament for a heaving airfoil and suggested that a morethorough quantitative analysis is still needed in order to confirm if a model in terms of an oscillating wake, mixing layer
or a vortex filament is sufficient to explain the flow dynamics.
Verma & Hemmati (2021b) presented detailed quantitative and

The wake of an oscillating hydrofoil in combined heaving and pitching motion is numerically evaluated at a range ofreduced frequency (0.32 ≤ f ∗ ≤ 0.64) and phase offset (90◦≤ φ ≤ 270◦ ) at Reynolds number of Re = 8000. At f ∗ = 0.32
and φ = 90◦ , a dominant spanwise elliptic instability feature
is observed due to the presence of a paired primary and secondary leading edge vortex roller over the foil boundary. Subsequent outflux of vorticity from the secondary leading edge
vortex leads to the formation of streamwise hairpin structuresthat evolve downstream on account of straining in the braid
vorticity region. The spanwise wavelength (λz ) of the growing
streamwise secondary hairpin legs is approximately 0.86c before the leading edge vortex structures shed from the foil. Thisis followed by a reduction in λz , which coincided with continuous ejection of vorticity from secondary leading edge structures, and the rearrangement of growing hairpin legs. However, the dominant association between spanwise instability
and growth of secondary streamwise structures at φ = 90◦ reduces with increasing φ towards 270◦ . At φ = 180◦ , there
is a delay in the emergence of secondary structures that coincide with the disintegration and re-growth of secondary leading edge structures. Further increase in φ to 225◦ and 270◦
depicts the absence of secondary hairpin structures, despite theapparent local instability features on the leading edge rollers.

INTRODUCTION
The fundamentals of vortex dynamics and interactions
have been of great interest to the fluid mechanics and turbulence community for decades (Leweke et al., 2016). The
mechanisms of formation, evolution and early dismantlementof straight vortical filaments, especially in the wake of aircrafts and submarines, are greatly important for minimizing
wake hazards and noise propagation (Leweke & Williamson,
1998; Dizès & Laporte, 2002; Ortega et al., 2003; Meunier &Leweke, 2005). Jacquin et al. (2003) briefly outlined the critical role of increasing turbulence and promotion of the cooperative instability, in terms of an increased radius for a system
of vortices, that contributed to a decreased rolling moment on
the aircraft. Characterization of instabilities on wake structures have further gained motivation in terms of their association with the propulsive performance of natural bird flights andswimming mammals (Deng & Caulfield, 2015; Deng et al.,2016; Sun et al., 2018). Deng & Caulfield (2015) reported thatthe transition of symmetric reverse Von Kàrmàn (rBvK) to deflected wake modes coincided with the appearance of threedimensional instability features and a large thrust generation.
The current study extends the present understanding of the association between vortex instability characteristics and three-1

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
qualitative evidence for the possible association of spanwise
undulation of LEVs to the elliptic instability of vortex pair for
foils that executed coupled pitching and heaving kinematics.
They further evaluated and discussed the spanwise dislocation
features and the formation of conjoint hairpin-horseshoe structure for different wake topologies. These provided unique insights into the association of spanwise instability and growthof streamwise vortical structures in the wake of oscillating hydrofoils (Verma & Hemmati, 2021b).
In this study, we particularly expand on the implicationsof characteristic spanwise instability of the leading edge vortex
on the formation and evolution of secondary wake structures
for foils oscillating in coupled heaving and pitching motion.
The observations will provide fundamental insights and hints
with regards to the association of LEV dynamics and growth ofsecondary structures in the wake. We discuss the effects of increasing phase offset (φ ) between the heaving and pitching, on
the evolution of LEV instability and secondary wake structuresthat has not been assessed for oscillating foils. The methodology for conducting the numerical study is briefly highlighted
in the Problem Description, followed by assessment of major observations in the Results & Discussion section. A briefsummary of important findings is then presented in the Conclusions section.

z

30c

y

52.5c

Figure 2: Computational domain (not to scale) employed in
the current study

et al., 2009). The phase offset (φ ) was varied in the range of90◦ ≤ φ ≤ 270◦ , which ensured a heave dominated kinematics, and thereby allowing LEVs to develop and advect along
the foil boundary. Contrarily, pitch dominated kinematics coincided with either a weak LEV formation or their apparent
disintegration during an early stage of the oscillation cycle(Verma & Hemmati, 2021b). Here, we limit the results to thecase of f ∗ = 0.32 to mainly detail the changes in evolution of
instability and secondary structures at increasing φ .
The computational domain shown in Figure 2 closely followed that of Verma & Hemmati (2021b). The domain extends 2πc in the spanwise (z−) direction to capture the dominant spanwise instability features along with multiple paired
streamwise secondary structures. More details on the validation and verification of the numerical methodology canbe found in our previous studies (Verma & Hemmati, 2020,
2021b).

PROBLEM DESCRIPTION
Three-dimensional wake evolution of an oscillating hydrofoil is assessed by solving the Navier-Stokes equations directly at Re = 8000. Overset Grid Assembly (OGA) method,
implemented in OpenFOAM, was employed for simulating the
combined heaving and pitching motion of the foil. The infinite span of the oscillating teardrop foil (see Figure 1) preserves the developing spanwise instability on primary vortex(rollers) and secondary structures (ribs) in the wake (Mittal &Balachandar, 1995; Verma & Hemmati, 2021a,b). The heaving and pitching motion of the foil can be mathematically expressed as:

RESULTS & DISCUSSION
The time evolution and advection of the leading edge vortex structures are initially evaluated in an oscillation cycle forkinematics corresponding to φ = 90◦ and f ∗ = 0.32. The
origination of spanwise undulations and its links to instability
mechanisms are qualitatively evaluated, along with their implications on growth of secondary streamwise structures. The
quantified spanwise wavelength (λz ) of paired rib filaments is
estimated using autocorrelation of streamwise vorticity (ωx )at increasing streamwise distance, which will highlight their
growth and rearrangement process. The effects of increasing
φ from 90◦ to 270◦ is then evaluated qualitatively, primarily
depicting the delay and a gradual disappearance of secondary
structures.
Figures 3a-3e depict the formation and advection of LEV
rollers at successive quarter phases of one oscillation cycle.
At t = 0, the anti-clockwise roller LEV1ac is formed near
the leading edge of the foil with no visible spanwise undulation. At t = T /4 in Figure 3b, however, LEV1ac depicts a low
amplitude spanwise undulation. We further notice a counterrotating secondary roller (LEV1sc ) that forms on account of
the vorticity outflux resulting from the mutual interaction of
LEV1ac and the foil boundary. It is reasonable to speculatethat the presence of two counter-rotating rollers will initiate
an elliptic instability mechanism featuring the spanwise undulations observed on LEV1ac (Leweke et al., 2016).
As LEV1ac and the paired secondary vortex (LEV1sc ) approach the trailing edge at t = T /2, it is apparent that a few

h = ho sin 2π f t
θ (t) = θo sin(2π f t + φ )Here, the oscillation frequency ( f ) can be expressed in termsof the reduced frequency f ∗ = f c/U∞ , which varied as 0.32
≤ f ∗ ≤ 0.64. This corresponds to an amplitude based Strouhal
number (StA = 2 f A/U∞ ) in the range of 0.2 ≤ StA ≤ 0.8, whichfurther coincide with highly propulsive wakes observed forfoils in coupled motion at a similar range of StA (Schnipper

θFigure 1: Schematic representing teardrop foil geometry andkinematics

2

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

FL
OW

4

FL
OW

4

LEV1acs

LEV1c
LEV1ac

+
z

+
z

-4

-4

1.875

1.875

1.25

1.25
0

0

0.625

0.625
1.25
+ 1.875z+-0.625

x

2.5

0.625

0.625

0

0

1.25
+ 1.875-0.625

x

-1.25

2.5

-1.25
-1.875-1.875

(a)
4

(b)

FL
OW

LEV1ac

-4

-4

S
OF S
E
H
1.875
T UR
OW CT
1.25
R
G RU
ST
0.625

0.625

2.5

P
IR 0
HA
-0.6250.625+-0.625

S
1.875
RE
TU
C
U
1.25
R
ST
0.625
IN

0

0

1.25
+ 1.875

LEV1ac

+
z

RY
DA
N
O
EC

x

FL
OW

4

+
z

0

z+

z

1.25
+ 1.875

x

-1.25

2.5

z+

-1.25
-1.875-1.875

(d)

(c)

FL
OW

4

LEV2ac

+
z
-4

1.875
1.25
0

0.625

0.625

0

1.25

x+

-0.625

z+

1.875
-1.25

2.5

-1.875(e)
Figure 3: Time evolution of LEVs for φ = 90◦ at (a) t = 0, (b) t = T /4, (c) t = T /2, (d) t = 3T /4 and (e) t = T . The vortical structures
are identified using iso-surfaces of λ2+ = λ2 c2 /U∞2 = -0.032, colored with spanwise vorticity (|ωz+ | = ωz c/U∞ = 4).

paired streamwise vortex filaments start to grow. The amplitude of undulation on rollers also appears enhanced, whichcoincides with the appearance of paired rib filaments. It is important to mention here that the origin of rib filaments appears
associated with the developing elliptic instability feature on
LEV1ac and LEV1sc . As the weaker LEV1sc experiences straining in the presence of the stronger LEV1ac , a core vorticity
outflux occurs from LEV1sc . This grows to form rib filament
pairs along the spanwise direction. At t = 3T /4, a more vividalignment of stronger hairpin structures is observed, which coincides with large amplitude undulations of LEV1ac . LEV1sc
eventually loses its coherence on account of the consistent vorticity outflux and straining due to elongation of secondary hair-pin structures. The hairpin legs further elongate in the streamwise direction at t = T , which eventually result in paired ribalignment along the spanwise direction.
Formation of the secondary roller (i.e. LEV 1sc ) and its
interaction within the neighborhood of primary LEVs (i.e.,
LEV1ac ) is also captured using contours of coefficient of pressure, C pr = P/(0.5ρU∞2 ). This is presented on the pressure
side of the foil in Figures 4a and 4b. The low magnitude
pressure signature for weaker secondary LEV1sc is observed
alongside a stronger pressure dominated region that highlights
LEV1ac at t = T /4 (Figure 4a). Faint undulations of both primary and secondary rollers are also visible, which indicate theonset of elliptic instability for the vortex pair. At t = T /2,

3

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

s

OW
FL

LEV1c
LEV1acCpr

x+= 0.875
x+= 1.75

1.875

x+ = 2.5

1.25

C(Δz)

0.625
0
-0.625

0

x+

0.625

z+

-1.25
1.25

-1.875

Δz+
(a)
(a)

OW
FL

DIFFUSEDs
LEV1c
LEV1ac

Cpr

1.875
1.25
0.625
0
-0.625

0

x+

0.625

z+

-1.25
1.25

-1.875(b)(b)

Figure 5: (a) Variation of C(∆z) with ∆z+ = ∆z/c and (b) Depiction of ωx+ pairs on spanwise slices at increasing x+ . Here,decreasing opacity of rib pairs ensures a complete streamwise
and spanwise views in the wake.

Figure 4: Surface pressure (C pr ) distribution on foil for φ =90◦ at (a) t = T /4 and (b) T /2.

the diffused secondary LEV1sc is captured on account of its
core vorticity outflux, thus forming the rib filaments shown in
Figure 3c. While the primary LEV1ac shed at t = T /2, the instability feature is amplified compared to the undulations captured at t = T /4.
We now estimate the spanwise wavelength (λz ) for the rib
filaments at increasing streamwise distance (i.e. x+ = 0.875,
1.75 and 2.5) to highlight the evolution features of secondary
structures in the wake. Autocorrelation of streamwise vorticity(ωx+ = ωc/U∞ ) on specific spanwise slices is used to estimate
λz , following Verma & Hemmati (2021b). The mathematical
function for the coefficient of autocorrelation (C(∆z)) is:C(∆z) =

while the core vorticity outflux occurs via mechanism of elliptic instability (Leweke & Williamson, 1998). At x+ = 1.75
and 2.5, the ωx+ pairs become more symmetric and developed
compared to those observed at x+ = 0.875, while supporting
the smaller λz observed in Figure 5a. The decreasing λz withincreasing x+ can therefore be linked to the rearrangement
mechanism for the evolving hairpin legs, which depends on
the action of continuous straining within the braid vorticity region between two successive rollers. Qualitative observationsin Figure 3c further provide a vivid indication that the newly
formed hairpin legs continuously feed upon the core vorticity
outflux from the secondary LEV roller (LEV1sc ) before attaining a strong coherence at some distance downstream of thetrailing edge.
The onset of elliptic spanwise instability on LEVs andits association with the growth of secondary hairpin structures at φ = 90◦ provided unique insights into the wake threedimensionality behind oscillating foils. We now evaluate theeffects of increasing φ on the spanwise instability features andthe associated growth of secondary structures. Figure 6 depicts the evolution of LEV rollers, spanwise undulations andgrowth of secondary hairpin structures for the cases corresponding to φ = 180◦ , 225◦ and 270◦ , respectively. The instantaneous snapshots of wake evolution are shown at eachquarter phase of one oscillation cycle (i.e. from t = T /4 tot = T ). At φ = 180◦ (Figures 6a, 6d, 6g and 6j), we observea primary LEV3ac along with remnants of a disintegrated secondary LEV neighboring LEV3ac . We also observe a tertiaryωx+ (yo , z0 ,ti ) · ωx+ (yo , z0 + ∆z,ti )++ωx,rms (yo , z0 ,ti ) ωx,rms(yo , z0 + ∆z,ti )Here, ∆z represents the spanwise lag used for obtaining C(∆z).
Figure 5(a) depicts the variation of C(∆z) for spanwise slices at
x+ = 0.875, 1.75 and 2.5, respectively. The estimated λz willcorrespond to twice the distance of first minimum observedfor C(∆z) in Figure 5a (Verma & Hemmati, 2021b). At x+ =0.875, λz is close to 0.86c which then decreases to 0.71c and
0.57c at x+ = 1.75 and 2.5, respectively. The qualitative visualization of the counter-rotating hairpin legs and the spanwise
slice at x+ = 0.875, 1.75 and 2.5, respectively, are also shownin Figure 5b. The counter-rotating ωx+ pairs at x+ = 0.875 appear to be in their early stages of spatio-temporal development

412th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
FLOW

LEV3ac

FLOW

T

LEV4acc

FLOW

4

+
z

-4
T
LEV3ac

4

+
z

4

+
z

-4

-4
-1.25

-1.25

-1.25
-0.625-0.625-0.625

y+

0

1.25

0.625
0.625

DISIN

1.25

y+

TEG

0

RAT

ION

0.625

OF S

1.25

0

ECO
NDA
RY

1.875

t = T/4+

LEV4 s

1.25

c

s

LEV5c

1.25

LEV4ac

z

0

0.625

-0.625

0.625

1.25

-0.625
1.875

-1.25

t = T/4

2.5

+

x

3.125

1.875

FLOW

-1.25
3.125

3.75

3.75

(b)
T

(c)
FLOW

FLOW

c
LEV4ac2.5x+t = T/4

-1.25

z+

0

LEV5ac

+

0

(a)

+
z

0.625

0

3.75

T
LEV3ac

1.25

0

0.625

1.25

3.125

LEV3ac

y+

0.625

0.625

z+

-0.625

LEV

2.5

x

1.25

0

T

4
-4

LEV5ac

4

+
z

4

+
z

-4

-4
-1.25

-1.25

-1.25
-0.625-0.625-0.625

y+ 0

1.25

0.625
0.625
1.25

LEV3 s

0

0

c

0.625
1.25

y+

1.25

0

0.625

0.625

z+

LEV4 s1.25

c0-0.625

0.625

1.875

t = T/2

0.625

-1.25

3.125

z+

T

x+

1.875

FLO
W

(e)
FLOW

T

-1.25

-1.25
-0.625

y+ 0

1.25

DEL
AY
SECO ED GRO
NDAWTH
1.25 STOF
RUC RY
TUR
0
ES

y+

1.25

0

y+

0.625

0

0.625

0.625

z+

1.25

0.625

LEV4 s

LEV4ac0-0.625

0.625
1.25

1.25

0

s
LEV5c

0.625

z+

0

c

1.875

1.25

3.75

2.5

x+

t = 3T/4

(g)

-1.25

3.125

0.625

0.625

1.25

1.875

x+

t = 3T/4-0.625
2.5

-1.25
3.125

3.75

3.75

(h)
FLOW

FLOW

z+

0

LEV5ac0-0.625

1.875

-1.25

3.125

'

LEV6ac-4-4-0.625

LEV5ac

4

+
z

-1.25

2.5

3.75

(f)

-0.625t = 3T/4

-1.25
3.125

FLOW

4

+
z

LEV3ac

2.5

x+

3.75

T

4

x+

1.25

t = T/2

-1.25

3.125

c
LEV4ac

-4

1.25

0.625

-0.6252.5z+0LEV5ac-0.6250

1.875

t = T/2(d)
LEV3ac

0.625

s
LEV5c

1.25

0

LEV4ac

3.75

+
z

1.25

0

0.625

1.25

2.5

x+

y+

(i)

FLOW
T

+
z

4
-4

-1.25

LEV5ac

4

+
z

4

+
z

-4

-1.25

-1.25

-0.625-0.625'

LEV6ac-4-0.625

+

y

0

1.25

0.625
0.625
1.25
0
0.625

HAIR
P
STRU IN
CTU
RES

0

1.25

1.875

x+

2.5

-0.625

LEV3ac

1.25

0

0.625

LEV T
4a

1.25

c

0.625

LEV4 s

0

cc

0
0.625
1.875

-1.25
3.75

y+

1.25

0

s

0.625

1.25

3.125

t=T

z+

y+

t=T

(j)

x+

LEV4ac-0.625

2.5

0

1.25
0

0.625

LEV5ac
1.25

-1.25

3.125
3.75

(k)

z+

0.625

LEV5c

t=T

1.875

x+

2.5

z+

-0.625
-1.25
3.125

3.75

(l)

Figure 6: Iso-surfaces of λ2+ = -0.032 criterion colored with |ωz+ | = 4, for φ = 180◦ (a,d,g,j), 225◦ (b,e,h,k) and 270◦ (c,f,i,l). The
instantaneous snapshots correspond to t = T /4, T /2, 3T /4, T , respectively.

LEV3Tac that remains in close vicinity of LEV3ac . This tertiary LEV did not appear to have a coherent presence at φ =90◦ (Figure 3). At t = T /2 (Figure 6d), we now observe asecondary LEV3sc which forms on account of the combined
vorticity outflux of LEV3ac and LEV3Tac . The spanwise undu-

lations on LEVs also become evident at t = T /2, while mutual straining of LEV3sc from LEV3ac and LEV3Tac , leads tocore vorticity outflux and subsequent growth of small hairpin
legs observed at t = 3T /4 (Figure 6g). These small rib-likeformations evolve further downstream and form strong coher-

512th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
REFERENCES

ent hairpin structures at t = T (Figure 6j). In comparison to
the growing secondary structures at φ = 90◦ , which became
evident at an earlier streamwise distance and advective time(t = T /2 in Figure 3(c)), a delayed growth of secondary structures is quite clear for the case of φ = 180◦ . This delay is attributed to an early disintegration and regeneration of the secondary roller (i.e. LEV3sc ) noticed for φ = 180◦ at t = T /4
and t = T /2, respectively.
At φ = 225◦ , Figure 6b depicts a peculiar series formation of primary (LEV4ac ), secondary (LEV4sc ) and tertiary(LEV4Tac ) LEVs at t = T /4. Besides a localized inception of
an instability feature at t = T /2 (Figure 6e), an initial disintegration of secondary LEV4sc is not apparent here. At t = 3T /4(Figure 6h), while LEV4ac , LEV4sc and LEV4Tac shed from thetrailing edge of the foil, there seems to be no evident growthof secondary structures. This absence also remains persistent
at t = T (Figure 6k). We further observe a similar evolution
process of LEVs at φ = 270◦ (Figures 6c, 6f, 6i, and 6l)). A
series formation of counter-rotating LEVs (LEV5ac , LEV5sc
and LEV5Tac ) is observed at t = T /2 (Figure 6f), which evolveand shed in the wake at subsequent phases of the oscillation
cycle. Although spanwise instability features remain dominant on LEVs, the growth of secondary structures is entirely
absent for φ = 270◦ as well. We speculate that an inherent
dependence between the circulation strength of rollers andthe growth of secondary structures must hold. Wherein, theformer plausibly decreases with increasing φ , which thereby
lower the intensity of straining in the braid shear layer. The
quantitative measurements are currently underway and will bepresented in upcoming studies. Overall, there is vivid evidence
that the association of spanwise instability features and growthof secondary structures is most dominant at φ = 90◦ , while it
successively fades away with increasing φ to 270◦ .

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CONCLUSION
Three-dimensional wake assessments for an oscillating
foil in coupled heaving and pitching motion were describedat f ∗ = 0.32 and Re = 8000, while the phase offset (φ ) variedin the range of 90◦ to 270◦ . The spatio-temporal wake evolution revealed an association of elliptic spanwise instability
characteristics on primary, secondary and tertiary LEVs thatformed over the foil boundary, and the growth of paired secondary streamwise structures in the form of hairpin vortices.
These hairpin structures are the result of core vorticity outflux,
particularly from the secondary LEV, via a mechanism detailed
previously by Mittal & Balachandar (1995). The concerned association is strongly dominant at φ = 90◦ where the secondary
LEV, located in close vicinity of the primary LEV, encounteredstrong straining on account of the existing spanwise instability.
However, the dominant association faded away as φ increased
above 90◦ . At φ = 180◦ , the LEV evolution depicts a disintegration and re-emergence of the secondary LEV, which coincides with a delay in the growth of secondary hairpin structureswith respect to advective time. Further increasing φ towards
225◦ and 270◦ shows a complete absence of secondary structures despite the presence and inception of spanwise instability
features on rollers. Possibly, an increasing φ from 90◦ to 270◦
promotes a weaker LEV formation (e.g., circulation strength),which leads to an insufficient core vorticity outflux necessary
for the growth of secondary structures. Quantitative assessment of the circulation of LEV is currently underway, which
supports the qualitative observations presented here.

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