We numerically study the spatiotemporal dynamics of a turbulent coaxial jet in a model rocket engine combustor from the viewpoints of symbolic information-theory quantifiers and complex networks. The dynamic behavior of flow velocity undergoes a significant transition from a stochastic to chaotic state as the turbulent jet moves downstream. The small-world nature exists in the near field forming a stochastic state, whereas it disappears by the formation of a chaotic state in the far field. The dynamic behavior of hydrogen and oxygen concentrations in the far field also represents deterministic chaos. The simultaneous dynamic behavior with chaotic mixing forms the phase-synchronization state.

1.
C. W.
Kulp
and
L.
Zunino
,
Chaos
24
,
033116
(
2014
).
2.
L.
Zunino
,
M. C.
Soriano
, and
O. A.
Rosso
,
Phys. Rev. E
86
,
046210
(
2012
).
3.
J.
Zhang
,
J.
Zhou
,
M.
Tang
,
H.
Guo
,
M.
Small
, and
Y.
Zou
,
Sci. Rep.
7
,
7795
(
2017
).
4.
Y.
Kuramoto
,
Chemical Oscillations, Waves, and Turbulence
(
Dover
,
2003
).
5.
H.
Kantz
and
T.
Schreiber
,
Nonlinear Time Series Analysis
(
Cambridge University Press
,
1997
).
6.
M.
Small
,
Applied Nonlinear Time Series Analysis
(
World Scientific
,
2005
).
7.
S.
Kondo
,
H.
Gotoda
,
T.
Miyano
, and
I. T.
Tokuda
,
Physica D
364
,
1
(
2018
).
8.
H.
Gotoda
,
M.
Pradas
, and
S.
Kalliadasis
,
Phys. Rev. Fluids
2
,
124401
(
2017
).
9.
H.
Gotoda
,
H.
Kobayashi
, and
K.
Hayashi
,
Phys. Rev. E
95
,
022201
(
2017
).
10.
H.
Kinugawa
,
K.
Ueda
, and
H.
Gotoda
,
Chaos
26
,
033104
(
2016
).
11.
K.
Takagi
,
H.
Gotoda
,
I. T.
Tokuda
, and
T.
Miyano
,
Phys. Rev. E
96
,
052223
(
2017
).
12.
K.
Takagi
and
H.
Gotoda
,
Phys. Rev. E
98
,
032207
(
2018
).
13.
K.
Takagi
,
H.
Gotoda
,
I. T.
Tokuda
, and
T.
Miyano
,
Phys. Lett. A
382
,
3181
(
2018
).
14.
H.
Gotoda
,
H.
Kinugawa
,
R.
Tsujimoto
,
S.
Domen
, and
Y.
Okuno
,
Phys. Rev. Appl.
7
,
044027
(
2017
).
15.
H.
Kobayashi
,
H.
Gotoda
,
S.
Tachibana
, and
S.
Yoshida
,
J. Appl. Phys.
122
,
224904
(
2017
).
16.
H.
Kobayashi
,
H.
Gotoda
, and
S.
Tachibana
,
Physica A
510
,
345
(
2018
).
17.
H.
Kasuya
,
H.
Gotoda
,
S.
Yoshida
, and
S.
Tachibana
,
Chaos
28
,
033111
(
2018
).
18.
S.
Murayama
,
H.
Kinugawa
,
I. T.
Tokuda
, and
H.
Gotoda
,
Phys. Rev. E
97
,
022223
(
2018
).
19.
S.
Murayama
and
H.
Gotoda
,
Phys. Rev. E
99
,
052222
(
2019
).
20.
A. K. M. F.
Hussain
,
J. Fluid Mech.
173
,
303
(
1986
).
21.
D.
Liepmann
,
Phys. Fluids A
3
,
1179
(
1991
).
22.
I.
Danaila
,
J.
Dušek
, and
F.
Anselmet
,
Phys. Fluids
9
,
3323
(
1997
).
23.
H.
Rehab
,
E.
Villermaux
, and
E. J.
Hopfinger
,
J. Fluid Mech.
345
,
357
(
1997
).
24.
T.
Matsuda
and
J.
Sakakibara
,
Phys. Fluids
17
,
025106
(
2005
).
25.
G.
Balarac
and
O.
Métais
,
Phys. Fluids
17
,
065102
(
2005
).
26.
J.
Kim
and
H.
Choi
,
J. Fluid Mech.
620
,
383
(
2009
).
27.
T. A.
Casey
,
J.
Sakakibara
, and
S. T.
Thoroddsen
,
Phys. Fluids
25
,
025102
(
2013
).
28.
S.
Matsuyama
,
D.
Hori
,
T.
Shimizu
,
S.
Tachibana
,
S.
Yoshida
, and
Y.
Mizobuchi
,
J. Propul. Power
32
,
628
(
2016
).
29.
T.
Hashimoto
,
H.
Shibuya
,
H.
Gotoda
,
Y.
Ohmichi
, and
S.
Matsuyama
,
Phys. Rev. E
99
,
032208
(
2019
).
30.
B.
Luque
,
L.
Lacasa
,
F. J.
Ballesteros
, and
A.
Robledo
,
Chaos
22
,
013109
(
2012
).
31.
C.
Bandt
and
B.
Pompe
,
Phys. Rev. Lett.
88
,
174102
(
2002
).
32.
O. A.
Rosso
,
H. A.
Larrondo
,
M. T.
Martin
,
A.
Plastino
, and
M. A.
Fuentes
,
Phys. Rev. Lett.
99
,
154102
(
2007
).
33.
Q. L.
Li
and
Z. T.
Fu
,
Phys. Rev. E
89
,
012905
(
2014
).
34.
W.
Zhang
,
P.
Liu
,
H.
Guo
, and
J.
Wang
,
Phys. Rev. E
96
,
052215
(
2017
).
35.
M. B.
Kennel
,
R.
Brown
, and
H. D. I.
Abarbanel
,
Phys. Rev. A
45
,
3403
(
1992
).
36.
K.
Taira
,
A. G.
Nair
, and
S. L.
Brunton
,
J. Fluid Mech.
795
,
R2
(
2016
).
37.
C. W.
Kulp
,
L.
Zunino
,
T.
Osborne
, and
B.
Zawadzki
,
Phys. Rev. E
96
,
022218
(
2017
).
38.
H.
Gotoda
,
Y.
Okuno
,
K.
Hayashi
, and
S.
Tachibana
,
Phys. Rev. E
92
,
052906
(
2015
).
39.
A. K.
Charakopoulos
,
T. E.
Karakasidis
,
P. N.
Papanicolaou
, and
A.
Liakopoulos
,
Chaos
24
,
024408
(
2014
).
40.
L.
Lacasa
,
B.
Luque
,
F.
Ballesteros
,
J.
Luque
, and
J. C.
Nuño
,
Proc. Natl. Acad. Sci. U.S.A.
105
,
4972
(
2008
).
41.
X.
Xu
,
J.
Zhang
, and
M.
Small
,
Proc. Natl. Acad. Sci. U.S.A.
105
,
19601
(
2008
).
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