Four machine learning methods, i.e., self-organizing map (SOM), Gaussian mixture model (GMM), eXtreme gradient boosting (XGBoost), and contrastive learning (CL), are used to detect the irrotational boundary (IB), which represents the outer edge of the turbulent and non-turbulent interface layer. To accurately evaluate the detection methods, high-resolution databases from direct numerical simulations of a temporally evolving turbulent plane jet are used. It is found that except for the SOM method, the general contour of the IB appears to be effectively captured using the GMM, XGBoost, and CL methods, which indicate the turbulent and non-turbulent regions can be roughly recognized. Furthermore, the intrinsic features of the detected IB using the GMM, XGBoost, and the CL methods are quantitatively evaluated. Unlike the conventional vorticity norm method, the three machine learning methods do not rely on a single threshold of vorticity magnitude to separate the turbulent and non-turbulent regions. A small part of the detected IB using the three machine learning methods is characterized by the rotational motions, which are expected to be only found inside the turbulent sublayer and turbulent core region. Compared to the vorticity norm and XGBoost methods, the fractal dimensions of the IB detected by the GMM and CL methods are relatively small, which are related to the missing detection of some highly contorted elements. With the three machine learning methods, a large part of the detected IB is characterized by a convex shape, similarly as with the vorticity norm. However, the probability density function profiles of the local curvature of the detected IB differ greatly between the three machine learning methods and the vorticity norm. A mild variation of the mean conditional distributions of the vorticity magnitude can be observed across the detected IB by the three machine learning methods. This study first implies that using the machine learning methods the turbulent and non-turbulent regions can be roughly distinguished, but it is still challenging to obtain the intrinsic features of the detected IB.
REFERENCES
1.
J.
Westerweel
,
C.
Fukushima
,
J. M.
Pedersen
, and
J. C. R.
Hunt
, “
Mechanics of the turbulent-nonturbulent interface of a jet
,” Phys. Rev. Lett.
95
, 174501
(2005
).2.
C. B.
da Silva
and
J. C. F.
Pereira
, “
Invariants of the velocity-gradient, rate-of-strain, and rate-of-rotation tensors across the turbulent/nonturbulent interface in jets
,” Phys. Fluids
20
, 055101
(2008
).3.
T. S.
Silva
and
C. B.
da Silva
, “
The behaviour of the scalar gradient across the turbulent/non-turbulent interface in jets
,” Phys. Fluids
29
, 085106
(2017
).4.
Y.
Zhou
and
J.
Vassilicos
, “
Energy cascade at the turbulent/nonturbulent interface
,” Phys. Rev. Fluids
5
, 064604
(2020
).5.
H.
Zhang
and
X.
Wu
, “
Dynamics of turbulent and nonturbulent interfaces in cylinder and airfoil near wakes
,” AIAA J.
60
, 261
–275
(2021
).6.
W. J.
Yin
,
Y. L.
Xie
,
X. X.
Zhang
, and
Y.
Zhou
, “
On the structure of the turbulent/non-turbulent interface in a fully developed spatially evolving axisymmetric wake
,” Theor. Appl. Mech. Lett.
13
, 100404
(2023
).7.
T.
Watanabe
,
Y.
Sakai
,
K.
Nagata
,
Y.
Ito
, and
T.
Hayase
, “
Turbulent mixing of passive scalar near turbulent and non-turbulent interface in mixing layers
,” Phys. Fluids
27
, 085109
(2015
).8.
R.
Jahanbakhshi
and
C. K.
Madnia
, “
The effect of heat release on the entrainment in a turbulent mixing layer
,” J. Fluid Mech.
844
, 92
–126
(2018
).9.
C. B.
da Silva
,
R. R.
Taveira
, and
G.
Borrell
, “
Characteristics of the turbulent/nonturbulent interface in boundary layers, jets and shear-free turbulence
,” J. Phys.: Conf. Ser.
506
, 012015
(2014
).10.
X.
Zhang
,
T.
Watanabe
, and
K.
Nagata
, “
Turbulent/nonturbulent interfaces in high-resolution direct numerical simulation of temporally evolving compressible turbulent boundary layers
,” Phys. Rev. Fluids
3
, 094605
(2018
).11.
R. R.
Taveira
and
C. B.
da Silva
, “
Characteristics of the viscous superlayer in shear free turbulence and in planar turbulent jets
,” Phys. Fluids
26
, 021702
(2014
).12.
T.
Watanabe
,
X.
Zhang
, and
K.
Nagata
, “
Turbulent/non-turbulent interfaces detected in DNS of incompressible turbulent boundary layers
,” Phys. Fluids
30
, 035102
(2018
).13.
S.
Corrsin
and
A. L.
Kistler
, “
Free-stream boundaries of turbulent flows
,” NACA Technical Report No. TN-1244
(
NACA
, 1955
).14.
A. A.
Townsend
, The Structure of Turbulent Shear Flows
, 2nd ed. (
Cambridge University Press
,
Cambridge
, 1976
).15.
D.
Krug
,
M.
Holzner
,
I.
Marusic
, and
M.
van Reeuwijk
, “
Fractal scaling of the turbulence interface in gravity currents
,” J. Fluid Mech.
820
, R3
(2017
).16.
K. F.
Kohan
and
S.
Gaskin
, “
The effect of the geometric features of the turbulent/non-turbulent interface on the entrainment of a passive scalar into a jet
,” Phys. Fluids
32
, 095114
(2020
).17.
J.
Chen
and
O. R. H.
Buxton
, “
Spatial evolution of the turbulent/turbulent interface geometry in a cylinder wake
,” arXiv:2301.04959 (2023
).18.
D. K.
Bisset
,
J. C. R.
Hunt
, and
M. M.
Rogers
, “
The turbulent/non-turbulent interface bounding a far wake
,” J. Fluid Mech.
451
, 383
–410
(2002
).19.
R. K.
Anand
,
B. J.
Boersma
, and
A.
Agrawal
, “
Detection of turbulent/non-turbulent interface for an axisymmetric turbulent jet: Evaluation of known criteria and proposal of a new criterion
,” Exp. Fluids
47
, 995
(2009
).20.
M.
Gampert
,
J.
Boschung
,
F.
Hennig
,
M.
Gauding
, and
N.
Peters
, “
The vorticity versus the scalar criterion for the detection of the turbulent/non-turbulent interface
,” J. Fluid Mech.
750
, 578
(2014
).21.
C. B.
da Silva
,
J. C. R.
Hunt
,
I.
Eames
, and
J.
Westerweel
, “
Interfacial layers between regions of different turbulence intensity
,” Annu. Rev. Fluid Mech.
46
, 567
–590
(2014
).22.
C.
Liu
,
Y.
Gao
,
X.
Dong
et al, “
Third generation of vortex identification methods: Omega and Liutex/Rortex based systems
,” J. Hydrodyn.
31
, 205
(2019
).23.
Z.
Wu
,
J.
Lee
,
C.
Meneveau
, and
T.
Zaki
, “
Application of a self-organizing map to identify the turbulent-boundary-layer interface in a transitional flow
,” Phys. Rev. Fluids
4
, 023902
(2019
).24.
N.
Reuther
and
C. J.
Kühler
, “
Evaluation of large-scale turbulent/non-turbulent interface detection methods for wall-bounded flows
,” Exp. Fluids
59
, 121
(2018
).25.
Y.
Long
,
D.
Wu
, and
J.
Wang
, “
A novel and robust method for the turbulent/non-turbulent interface detection
,” Exp. Fluids
62
, 138
(2021
).26.
K. P.
Nolan
and
T. A.
Zaki
, “
Conditional sampling of transitional boundary layers in pressure gradients
,” J. Fluid Mech.
728
, 306
–339
(2013
).27.
N.
Otsu
, “
A threshold selection method from gray-level histograms
,” IEEE Trans. Syst., Man, Cybern.
9
, 62
–66
(1979
).28.
S. L.
Brunton
,
B. R.
Noack
, and
P.
Koumoutsakos
, “
Machine learning for fluid mechanics
,” Annu. Rev. Fluid Mech.
52
, 477
–508
(2020
).29.
D.
Kochkov
,
J. A.
Smith
,
A.
Alieva
,
Q.
Wang
,
M. P.
Brenner
, and
S.
Hoyer
, “
Machine learning-accelerated computational fluid dynamics
,” Proc. Natl. Acad. Sci.
118
(21
), e2101784118
(2021
).30.
R.
Vinuesa
and
S.
Brunton
, “
Enhancing computational fluid dynamics with machine learning
,” Nat. Comput. Sci.
2
, 358
–366
(2022
).31.
R.
Vinuesa
,
S. L.
Brunton
, and
B. J.
McKeon
, “
The transformative potential of machine learning for experiments in fluid mechanics
,” Nat. Rev. Phys.
5
, 536
–545
(2023
).32.
H.
Eivazi
and
R.
Vinuesa
, “
Physics-informed deep-learning applications to experimental fluid mechanics
,” arXiv:2203.15402 (2022
).33.
J.
Lyne
, Unsupervised Learning for Coherent Structure Identification in Turbulent Channel Flow
(
University of Waterloo
, 2023
).34.
K.
Younes
,
B.
Gibeau
,
S.
Ghaemi
, and
J.
Hickey
, “
A fuzzy cluster method for turbulent/non-turbulent interface detection
,” Exp. Fluids
62
, 73
(2021
).35.
K.
Tlales
,
K.
Otmani
,
G.
Ntoukas
,
G.
Rubio
, and
E.
Ferrer
, “
Machine learning adaptation for laminar and turbulent flows: Applications to high order discontinuous Galerkin solvers
,” arXiv:2209.02401 (2022
).36.
K.-E.
Otmani
,
G.
Ntoukas
,
O. A.
Mariño
, and
E.
Ferrer
, “
Towards a robust detection of viscous and turbulent flow regions using unsupervised machine learning
,” Phys. Fluids
35
(2
), 027112
(2023
).37.
B.
Li
,
Z.
Yang
,
X.
Zhang
,
G.
He
,
B.
Deng
, and
L.
Shen
, “
Using machine learning to detect the turbulent region in flow past a circular cylinder
,” J. Fluid Mech.
905
, A10
(2020
).38.
D.
Mistry
,
J.
Philip
,
J. R.
Dawson
, and
I.
Marusic
, “
Entrainment at multi-scales across the turbulent/non-turbulent interface in an axisymmetric jet
,” J. Fluid Mech.
802
, 690
–725
(2016
).39.
D.
Mistry
,
J. R.
Dawson
, and
A. R.
Kerstein
, “
The multi-scale geometry of the near field in an axisymmetric jet
,” J. Fluid Mech.
838
, 501
(2018
).40.
M.
Wolf
,
B.
Lüthi
,
M.
Holzner
,
D.
Krug
,
W.
Kinzelbach
, and
A.
Tsinober
, “
Investigations on the local entrainment velocity in a turbulent jet
,” Phys. Fluids
24
, 105110
(2012
).41.
T.
Watanabe
,
C. B.
da Silva
,
K.
Nagata
, and
Y.
Sakai
, “
Geometrical aspects of turbulent/non-turbulent interfaces with and without mean shear
,” Phys. Fluids
29
, 085105
(2017
).42.
T. S.
Silva
,
M.
Zecchetto
, and
C. B.
da Silva
, “
The scaling of the turbulent/non-turbulent interface at high Reynolds numbers
,” J. Fluid Mech.
843
, 156
(2018
).43.
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
).44.
S.
Laizet
,
E.
Lamballais
, and
J. C.
Vassilicos
, “
A numerical strategy to combine high-order schemes, complex geometry and parallel computing for high resolution DNS of fractal generated turbulence
,” Comput. Fluids
39
, 471
–484
(2010
).45.
S.
Laizet
and
N.
Li
, “
Incompact3d: A powerful tool to tackle turbulence problems with up to
computational cores
,” J. Numer. Methods Fluids
67
, 1735
–1757
(2011
).46.
A.
Kempf
,
M.
Klein
, and
J.
Janicka
, “
Efficient generation of initial-and inflow-conditions for transient turbulent flows in arbitrary geometries
,” Flow, Turbul. Combust.
74
, 67
(2005
).47.
C. B.
Da Silva
and
O.
Métais
, “
On the influence of coherent structures upon interscale interaction in turbulent plane jets
,” J. Fluid Mech.
473
, 103
(2002
).48.
T.
Watanabe
,
Y.
Sakai
,
K.
Nagata
,
Y.
Ito
, and
T.
Hayase
, “
Reactive scalar field near the turbulent/non-turbulent interface in a planar jet with a second-order chemical reaction
,” Phys. Fluids
26
, 105111
(2014
).49.
R.
Ramparian
and
M. S.
Chandrasekhara
, “
LDA measurements in plane turbulent jets
,” ASME J. Fluids Eng.
107
, 264
(1985
).50.
E.
Gutmark
and
I.
Wygnanski
, “
The planar turbulent jet
,” J. Fluid Mech.
73
, 465
(1976
).51.
S.
Stanley
,
S.
Sarkar
, and
J. P.
Mellado
, “
A study of the flowfield evolution and mixing in a planar turbulent jet using direct numerical simulation
,” J. Fluid Mech.
450
, 377
(2002
).52.
M.
Zecchetto
and
C. B.
da Silva
, “
Universality of small-scale motions within the turbulent/non-turbulent interface layer
,” J. Fluid Mech.
916
, A9
(2021
).53.
G.
Vettigli
, see https://github.com/JustGlowing/minisom/ for “
Minisom: Minimalistic and numpy-based implementation of the self organizing map
” (2018
).54.
F.
Pedregosa
,
G.
Varoquaux
,
A.
Gramfort
,
V.
Michel
,
B.
Thirion
,
O.
Grisel
,
M.
Blondel
,
P.
Prettenhofer
,
R.
Weiss
,
V.
Dubourg
,
J.
Vanderplas
,
A.
Passos
,
D.
Cournapeau
,
M.
Brucher
,
M.
Perrot
, and
E.
Duchesnay
, “Scikit-learn: Machine learning in Python,” J. Mach. Learn. Res.
12
, 2825
–2830
(2011
).55.
T.
Chen
and
C.
Guestrin
, “
XGBoost: A scalable tree boosting system
,” in Proceedings of 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining
(
Association for Computing Machinery
, 2016
), pp. 785
–794
.56.
E.
Patel
and
D. S.
Kushwaha
, “
Clustering cloud workloads: K-means vs Gaussian mixture model
,” Proc. Comput. Sci.
171
, 158
–167
(2020
).57.
Z.
W
,
C. D.
cunha
,
M.
Ritou
, and
B.
Furet
, “
Comparison of K-means and GMM methods for contextual clustering in HSM
,” Proc. Manuf.
28
, 154
–159
(2019
).58.
C. Q.
Liu
,
Y. S.
Gao
,
S. L.
Tian
, and
X. R.
Dong
, “
Rortex—A new vortex vector definition and vorticity tensor and vector decompositions
,” Phys. Fluids
30
, 035103
(2018
).59.
S.
Tian
,
Y.
Gao
,
X.
Dong
, and
C.
Liu
, “
Definition of vortex vector and vortex
,” J. Fluid Mech.
849
, 312
–339
(2018
).60.
Y. S.
Gao
,
J. M.
Liu
,
Y. F.
Yu
, and
C. Q.
Liu
, “
A Liutex based definition and identification of vortex core center lines
,” J. Hydrodyn.
31
, 445
–454
(2019
).61.
Y. L.
Xie
,
W. J.
Yin
,
X. X.
Zhang
, and
Y.
Zhou
, “
Visualization of the rotational and irrotational motions in a temporally evolving turbulent plane jet
,” J. Vis.
26
, 1025
–1036
(2023
).62.
W. J.
Yin
,
S. C.
Tao
,
K.
Nagata
,
Y.
Ito
,
Y.
Sakai
, and
Y.
Zhou
, “
Spatial distribution of coherent structures in a self-similar axisymmetric turbulent wake
,” Phys. Rev. Fluids
8
, 084603
(2023
).63.
S.
Er
,
J.-P.
Laval
, and
J. C.
Vassilicos
, “
Length scales and the turbulent/non-turbulent interface of a temporally developing turbulent jet
,” J. Fluid Mech.
970
, A33
(2023
).64.
X.
Zhang
,
T.
Watanabe
, and
K.
Nagata
, “
Reynolds number dependence of the turbulent/non-turbulent interface in temporally developing turbulent boundary layers
,” J. Fluid Mech.
964
, A8
(2023
).65.
66.
M. K.
Driscoll
,
C.
McCann
,
R.
Kopace
,
T.
Homan
,
J. T.
Fourkas
,
C.
Parent
, and
W.
Losert
, “
Cell shape dynamics: From waves to migration
,” PLoS Comput. Biol
8
(3
), e1002392
(2012
).67.
J. V. D.
Bossche
, see https://github.com/shapely/shapely for “
Shapely: Manipulation and analysis of geometric objects in the Cartesian plane
” (2008
).68.
Z. Q. J.
Xu
,
Y. Y.
Zhang
,
T.
Luo
,
Y. Y.
Xiao
, and
Z.
Ma
, “
Frequency principle: Fourier analysis sheds light on deep neural networks
,” arXiv:1901.06523 (2019
).© 2024 Author(s). Published under an exclusive license by AIP Publishing.
2024
Author(s)
You do not currently have access to this content.
