The present direct numerical simulations investigate the dynamics of diverse streamwise vortices in a zero-pressure gradient incompressible laminar boundary layer and the onset of turbulence. Due to the critical role of streamwise vortices in bypass transitions, we compare the transition mechanisms induced by a single vortex and vortex pairs. We initially examine the evolution of a single vortex by employing streamwise vortex profiles at two wall-normal locations. The single streamwise vortex will prompt a more rapid eruption from the bottom part of the boundary layer if moved nearer to the wall, as observed in the experimental study by Manu et al. [“Evolution of isolated streamwise vortices in the late stages of boundary-layer transition,” Exp. Fluids 48, 431–440 (2010)]. In the late stages of boundary-layer transition, the vortex–wall interaction emerges to be particularly pronounced. The second set of simulations triggers flow transition by imposing counter-rotating vortex pairs at the inlet of the computational domain. Streamwise vortex pairs with net upward flows cause intense, sporadic ejections of near-wall fluids into the boundary-layer edge, providing the first signs of inflectional instability in all considered cases. Instead of vortex–wall interactions, flow structures created by vortex pairs penetrate deeply into the inviscid region, resulting in substantial unsteady viscous-inviscid interactions. When counter-rotating vortices accompany to form a net downward flow, the initial formation of each vortex is analogous to that of a single vortex. The instability frequency and wavelength of the transitional flow produced by a vortex introduced in the middle of the boundary layer are lower than those imposed near the wall. The transitional flow generated by the vortex pair exhibits longer-wavelength instability than the single vortex cases.

1.
Lord
Rayleigh
, “
On the stability, or instability, of certain fluid motions
,”
Proc. London Math. Soc.
s1-11
,
57
72
(
1879
).
2.
W. M.
Orr
, “
The stability or instability of the steady motions of a perfect liquid and of a viscous liquid. Part I: A viscous liquid
,”
Proc. R. Ir. Acad., Sect. A
27
,
9
68
(
1907
).
3.
W. M.
Orr
, “
The stability or instability of the steady motions of a perfect liquid and of a viscous liquid. Part II: A viscous liquid
,”
Proc. R. Ir. Acad., Sect. A
27
,
69
138
(
1907
).
4.
A.
Sommerfield
, “
Ein beitrag zur hydrodynamischen erklarung der turbulenten flussigkeisbewegung
,” in
Proceedings of the 4th International Mathematical Congress
(
Rome
,
1909
), Vol.
3
, pp.
116
124
.
5.
G. B.
Schubauer
and
H. K.
Skramstad
, “
Laminar boundary-layer oscillations and transition on a flat plate
,”
J. Res. Natl. Bur. Stand.
38
,
92
(
1947
).
6.
W.
Tollmien
, “
Über die entstehung der turbulenz
,” in
Vorträge Aus Dem Gebiete Der Aerodynamik Und Verwandter Gebiete
(
Springer
,
1930
), pp.
18
21
.
7.
T.
Herbert
, “
Secondary instability of boundary layers
,”
Annu. Rev. Fluid Mech.
20
,
487
526
(
1988
).
8.
M. V.
Morkovin
, “
On the many faces of transition
,” in
Viscous Drag Reduction
(
Springer
,
1969
), pp.
1
31
.
9.
P. S.
Klebanoff
,
K. D.
Tidstrom
, and
L. M.
Sargent
, “
The three-dimensional nature of boundary-layer instability
,”
J. Fluid Mech.
12
,
1
34
(
1962
).
10.
M.
Acarlar
and
C.
Smith
, “
A study of hairpin vortices in a laminar boundary layer. Part 1. Hairpin vortices generated by a hemisphere protuberance
,”
J. Fluid Mech.
175
,
1
41
(
1987
).
11.
M.
Acarlar
and
C.
Smith
, “
A study of hairpin vortices in a laminar boundary layer. Part 2. Hairpin vortices generated by fluid injection
,”
J. Fluid Mech.
175
,
43
83
(
1987
).
12.
P.
Klebanoff
,
W.
Cleveland
, and
K.
Tidstrom
, “
On the evolution of a turbulent boundary layer induced by a three-dimensional roughness element
,”
J. Fluid Mech.
237
,
101
187
(
1992
).
13.
A.
Bakchinov
,
G.
Grek
,
B.
Klingmann
, and
V.
Kozlov
, “
Transition experiments in a boundary layer with embedded streamwise vortices
,”
Phys. Fluids
7
,
820
832
(
1995
).
14.
J.
Zhou
,
R. J.
Adrian
,
S.
Balachandar
, and
T.
Kendall
, “
Mechanisms for generating coherent packets of hairpin vortices in channel flow
,”
J. Fluid Mech.
387
,
353
396
(
1999
).
15.
J. D.
Swearingen
and
R. F.
Blackwelder
, “
The growth and breakdown of streamwise vortices in the presence of a wall
,”
J. Fluid Mech.
182
,
255
290
(
1987
).
16.
W. S.
Saric
,
H. L.
Reed
, and
E. B.
White
, “
Stability and transition of three-dimensional boundary layers
,”
Annu. Rev. Fluid Mech.
35
,
413
440
(
2003
).
17.
R. J.
Adrian
, “
Hairpin vortex organization in wall turbulence
,”
Phys. Fluids
19
,
041301
(
2007
).
18.
C.
Lee
and
X.
Jiang
, “
Flow structures in transitional and turbulent boundary layers
,”
Phys. Fluids
31
,
111301
(
2019
).
19.
R. L.
Panton
, “
Overview of the self-sustaining mechanisms of wall turbulence
,”
Prog. Aerosp. Sci.
37
,
341
383
(
2001
).
20.
W.
Schoppa
and
F.
Hussain
, “
Coherent structure generation in near-wall turbulence
,”
J. Fluid Mech.
453
,
57
108
(
2002
).
21.
C.
Smith
and
J.
Walker
, “
Turbulent wall-layer vortices
,” in
Fluid Vortices
(
Springer
,
1995
), pp.
235
289
.
22.
J. W.
Brooke
and
T. J.
Hanratty
, “
Origin of turbulence-producing eddies in a channel flow
,”
Phys. Fluids A
5
,
1011
1022
(
1993
).
23.
F.
Waleffe
, “
On a self-sustaining process in shear flows
,”
Phys. Fluids
9
,
883
900
(
1997
).
24.
J.-C.
Loiseau
,
J.-C.
Robinet
,
S.
Cherubini
, and
E.
Leriche
, “
Investigation of the roughness-induced transition: Global stability analyses and direct numerical simulations
,”
J. Fluid Mech.
760
,
175
211
(
2014
).
25.
V.
Citro
,
F.
Giannetti
,
P.
Luchini
, and
F.
Auteri
, “
Global stability and sensitivity analysis of boundary-layer flows past a hemispherical roughness element
,”
Phys. Fluids
27
,
084110
(
2015
).
26.
D. K.
Puckert
and
U.
Rist
, “
Experiments on critical Reynolds number and global instability in roughness-induced laminar–turbulent transition
,”
J. Fluid Mech.
844
,
878
904
(
2018
).
27.
M. A.
Bucci
,
D.
Puckert
,
C.
Andriano
,
J.-C.
Loiseau
,
S.
Cherubini
,
J.-C.
Robinet
, and
U.
Rist
, “
Roughness-induced transition by quasi-resonance of a varicose global mode
,”
J. Fluid Mech.
836
,
167
191
(
2018
).
28.
J. C.
Lin
, “
Review of research on low-profile vortex generators to control boundary-layer separation
,”
Prog. Aerosp. Sci.
38
,
389
420
(
2002
).
29.
J. M.
Hamilton
and
F. H.
Abernathy
, “
Streamwise vortices and transition to turbulence
,”
J. Fluid Mech.
264
,
185
212
(
1994
).
30.
K.
Manu
,
J.
Mathew
, and
J.
Dey
, “
Evolution of isolated streamwise vortices in the late stages of boundary layer transition
,”
Exp. Fluids
48
,
431
440
(
2010
).
31.
K.
Manu
,
J.
Dey
, and
J.
Mathew
, “
Local structure of boundary layer transition in experiments with a single streamwise vortex
,”
Exp. Therm. Fluid Sci.
68
,
381
391
(
2015
).
32.
K.
Manu
,
J.
Dey
, and
J.
Mathew
, “
Boundary layer transition experiments with embedded streamwise vortices
,”
Sādhanā
43
,
165
(
2018
).
33.
S.
Laizet
and
E.
Lamballais
, “
High-order compact schemes for incompressible flows: A simple and efficient method with quasi-spectral accuracy
,”
J. Comput. Phys.
228
,
5989
6015
(
2009
).
34.
N.
Li
and
S.
Laizet
, “
2DECOMP&FFT—A highly scalable 2D decomposition library and FFT interface
,” in
Cray User Group 2010 Conference
(
2010
), pp.
1
13
.
35.
S.
Laizet
and
N.
Li
, “
Incompact3d: A powerful tool to tackle turbulence problems with up to o (105) computational cores
,”
Int. J. Numer. Methods Fluids
67
,
1735
1757
(
2011
).
36.
Q.
Ye
,
F. F.
Schrijer
, and
F.
Scarano
, “
Boundary layer transition mechanisms behind a micro-ramp
,”
J. Fluid Mech.
793
,
132
161
(
2016
).
37.
A.
Cain
,
J.
Ferziger
, and
W.
Reynolds
, “
Discrete orthogonal function expansions for non-uniform grids using the fast Fourier transform
,”
J. Comput. Phys.
56
,
272
286
(
1984
).
38.
L.
Brandt
,
C.
Cossu
,
J.-M.
Chomaz
,
P.
Huerre
, and
D. S.
Henningson
, “
On the convectively unstable nature of optimal streaks in boundary layers
,”
J. Fluid Mech.
485
,
221
242
(
2003
).
39.
R.
Jacobs
and
P.
Durbin
, “
Simulations of bypass transition
,”
J. Fluid Mech.
428
,
185
212
(
2001
).
40.
P.
Schlatter
and
L.
Brandt
, “
DNS of spatially-developing three-dimensional turbulent boundary layers
,” in
Direct and Large-Eddy Simulation VII
(
Springer
,
2010
), pp.
55
61
.
41.
P. C.
Ma
,
X.
Yang
, and
M.
Ihme
, “
Direct numerical simulations of turbulent channel flow under transcritical conditions
,”
AIAA Paper No. 2018-0582
,
2018
.
42.
X.
Wu
,
R. G.
Jacobs
,
J. C.
Hunt
, and
P. A.
Durbin
, “
Simulation of boundary layer transition induced by periodically passing wakes
,”
J. Fluid Mech.
398
,
109
153
(
1999
).
43.
P. R.
Spalart
, “
Direct simulation of a turbulent boundary layer up to rθ = 1410
,”
J. Fluid Mech.
187
,
61
98
(
1988
).
44.
L.
Brandt
and
D. S.
Henningson
, “
Transition of streamwise streaks in zero-pressure-gradient boundary layers
,”
J. Fluid Mech.
472
,
229
261
(
2002
).
45.
D. P.
Rizzetta
and
M. R.
Visbal
, “
Direct numerical simulations of flow past an array of distributed roughness elements
,”
AIAA J.
45
,
1967
1976
(
2007
).
46.
M.
Asai
,
M.
Minagawa
, and
M.
Nishioka
, “
The instability and breakdown of a near-wall low-speed streak
,”
J. Fluid Mech.
455
,
289
314
(
2002
).
47.
T. A.
Zaki
and
P. A.
Durbin
, “
Mode interaction and the bypass route to transition
,”
J. Fluid Mech.
531
,
85
111
(
2005
).
48.
P.
Schlatter
,
L.
Brandt
,
H. C.
de Lange
, and
D. S.
Henningson
, “
On streak breakdown in bypass transition
,”
Phys. Fluids
20
,
101505
(
2008
).
49.
J.
Mans
,
H. C.
de Lange
, and
A. A.
van Steenhoven
, “
Sinuous breakdown in a flat plate boundary layer exposed to free-stream turbulence
,”
Phys. Fluids
19
,
088101
(
2007
).
50.
P.
Andersson
,
L.
Brandt
,
A.
Bottaro
, and
D. S.
Henningson
, “
On the breakdown of boundary layer streaks
,”
J. Fluid Mech.
428
,
29
60
(
2001
).
51.
L.
Brandt
, “
Numerical studies of the instability and breakdown of a boundary-layer low-speed streak
,”
Eur. J. Mech.-B
26
,
64
82
(
2007
).
52.
K.
Matsuura
, “
Hairpin vortex generation around a straight vortex tube in a laminar boundary-layer flow
,” arXiv:1808.06510 (
2018
).
53.
J.
Jeong
and
F.
Hussain
, “
On the identification of a vortex
,”
J. Fluid Mech.
285
,
69
94
(
1995
).
54.
K. J.
Groot
,
J.
Serpieri
,
F.
Pinna
, and
M.
Kotsonis
, “
Secondary crossflow instability through global analysis of measured base flows
,”
J. Fluid Mech.
846
,
605
653
(
2018
).
55.
J.
Chen
,
S.
Dong
,
X.
Chen
,
X.
Yuan
, and
G.
Xu
, “
Stationary cross-flow breakdown in a high-speed swept-wing boundary layer
,”
Phys. Fluids
33
,
024108
(
2021
).
56.
R. F.
Blackwelder
and
H.
Eckelmann
, “
Streamwise vortices associated with the bursting phenomenon
,”
J. Fluid Mech.
94
,
577
594
(
1979
).
57.
J. M.
Wallace
, “
Quadrant analysis in turbulence research: History and evolution
,”
Annu. Rev. Fluid Mech.
48
,
131
158
(
2016
).
58.
C. W.
Rowley
,
I.
Mezić
,
S.
Bagheri
,
P.
Schlatter
, and
D. S.
Henningson
, “
Spectral analysis of nonlinear flows
,”
J. Fluid Mech.
641
,
115
127
(
2009
).
59.
T.
Sayadi
,
P.
Schmid
,
J.
Nichols
, and
P.
Moin
, “
Dynamic mode decomposition of controlled h-and k-type transitions
,” in
Annual Research Briefs
(
Center for Turbulence Research
,
2013
), p.
189
.
60.
Z.-H.
Wan
,
L.
Zhou
,
B.-F.
Wang
, and
D.-J.
Sun
, “
Dynamic mode decomposition of forced spatially developed transitional jets
,”
Eur. J. Mech.-B
51
,
16
26
(
2015
).
61.
D.
Lengani
,
D.
Simoni
,
M.
Ubaldi
,
P.
Zunino
, and
F.
Bertini
, “
Experimental investigation on the time–space evolution of a laminar separation bubble by proper orthogonal decomposition and dynamic mode decomposition
,”
J. Turbomach.
139
,
031006
(
2017
).
62.
A.
Alessandri
,
P.
Bagnerini
,
M.
Gaggero
,
D.
Lengani
, and
D.
Simoni
, “
Dynamic mode decomposition for the inspection of three-regime separated transitional boundary layers using a least squares method
,”
Phys. Fluids
31
,
044103
(
2019
).
63.
X.
Zhao
and
Q.
Zhang
, “
Experimental and numerical study of coherent structures in a roughness induced transition boundary layer at Mach 5
,”
Phys. Fluids
30
,
104102
(
2018
).
64.
A.
Dotto
,
D.
Lengani
,
D.
Simoni
, and
A.
Tacchella
, “
Dynamic mode decomposition and Koopman spectral analysis of boundary layer separation-induced transition
,”
Phys. Fluids
33
,
104104
(
2021
).
65.
A.
Dotto
,
D.
Barsi
,
D.
Lengani
,
D.
Simoni
, and
F.
Satta
, “
Effect of free-stream turbulence properties on different transition routes for a zero-pressure gradient boundary layer
,”
Phys. Fluids
34
,
054102
(
2022
).
66.
K.
Sarath
and
K.
Manu
, “
An investigation of bluff body flow structures in variable velocity flows
,”
Phys. Fluids
34
,
034102
(
2022
).
67.
P. J.
Schmid
, “
Dynamic mode decomposition of numerical and experimental data
,”
J. Fluid Mech.
656
,
5
28
(
2010
).
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