This study assesses the capability of extended proper orthogonal decomposition (EPOD) and convolutional neural networks (CNNs) to reconstruct large-scale and very-large-scale motions (LSMs and VLSMs respectively) employing wall-shear-stress measurements in wall-bounded turbulent flows. Both techniques are used to reconstruct the instantaneous LSM evolution in the flow field as a combination of proper orthogonal decomposition (POD) modes, employing a limited set of instantaneous wall-shear-stress measurements. Due to the dominance of nonlinear effects, only CNNs provide satisfying results. Being able to account for nonlinearities in the flow, CNNs are shown to perform significantly better than EPOD in terms of both instantaneous flow-field estimation and turbulent-statistics reconstruction. CNNs are able to provide a more effective reconstruction performance employing more POD modes at larger distances from the wall and employing lower wall-measurement resolutions. Furthermore, the capability of tackling nonlinear features of CNNs results in estimation capabilities that are weakly dependent on the distance from the wall.
REFERENCES
1.
S. J.
Kline
, W. C.
Reynolds
, F.
Schraub
, and P.
Runstadler
, “The structure of turbulent boundary layers
,” J. Fluid Mech.
30
, 741
–773
(1967
).2.
A.
Favre
, J.
Gaviglio
, and R.
Dumas
, “Structure of velocity space-time correlations in a boundary layer
,” Phys. Fluids
10
, S138
–S145
(1967
).3.
R. F.
Blackwelder
and L. S.
Kovasznay
, “Time scales and correlations in a turbulent boundary layer
,” Phys. Fluids
15
, 1545
–1554
(1972
).4.
C. E.
Wark
and H.
Nagib
, “Experimental investigation of coherent structures in turbulent boundary layers
,” J. Fluid Mech.
230
, 183
–208
(1991
).5.
K.
Kim
and R.
Adrian
, “Very large-scale motion in the outer layer
,” Phys. Fluids
11
, 417
–422
(1999
).6.
N.
Hutchins
and I.
Marusic
, “Evidence of very long meandering features in the logarithmic region of turbulent boundary layers
,” J. Fluid Mech.
579
, 1
–28
(2007
).7.
J.
Monty
, J.
Stewart
, R.
Williams
, and M.
Chong
, “Large-scale features in turbulent pipe and channel flows
,” J. Fluid Mech.
589
, 147
–156
(2007
).8.
S.
Discetti
, G.
Bellani
, R.
Örlü
, J.
Serpieri
, C. S.
Vila
, M.
Raiola
, X.
Zheng
, L.
Mascotelli
, A.
Talamelli
, and A.
Ianiro
, “Characterization of very-large-scale motions in high-Re pipe flows
,” Exp. Therm. Fluid Sci.
104
, 1
–8
(2019
).9.
N.
Hutchins
and I.
Marusic
, “Large-scale influences in near-wall turbulence
,” Philos. Trans. R. Soc., A
365
, 647
–664
(2007
).10.
R.
Mathis
, N.
Hutchins
, and I.
Marusic
, “Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers
,” J. Fluid Mech.
628
, 311
–337
(2009
).11.
S.
Hoyas
and J.
Jiménez
, “Scaling of the velocity fluctuations in turbulent channels up to Reτ=2003
,” Phys. Fluids
18
, 011702
(2006
).12.
S.
Hoyas
and J.
Jiménez
, “Reynolds number effects on the Reynolds-stress budgets in turbulent channels
,” Phys. Fluids
20
, 101511
(2008
).13.
I.
Marusic
, R.
Mathis
, and N.
Hutchins
, “Predictive model for wall-bounded turbulent flow
,” Science
329
, 193
–196
(2010
).14.
R.
Mathis
, N.
Hutchins
, and I.
Marusic
, “A predictive inner–outer model for streamwise turbulence statistics in wall-bounded flows
,” J. Fluid Mech.
681
, 537
–566
(2011
).15.
B.
Ganapathisubramani
, N.
Hutchins
, J.
Monty
, D.
Chung
, and I.
Marusic
, “Amplitude and frequency modulation in wall turbulence
,” J. Fluid Mech.
712
, 61
–91
(2012
).16.
R.
Mathis
, I.
Marusic
, S. I.
Chernyshenko
, and N.
Hutchins
, “Estimating wall-shear-stress fluctuations given an outer region input
,” J. Fluid Mech.
715
, 163
–180
(2013
).17.
J.
Jiménez
and A.
Pinelli
, “The autonomous cycle of near-wall turbulence
,” J. Fluid Mech.
389
, 335
–359
(1999
).18.
M.
Abbassi
, W.
Baars
, N.
Hutchins
, and I.
Marusic
, “Skin-friction drag reduction in a high-Reynolds-number turbulent boundary layer via real-time control of large-scale structures
,” Int. J. Heat Fluid Flow
67
, 30
–41
(2017
).19.
H.
Bai
, Y.
Zhou
, W.
Zhang
, S.
Xu
, Y.
Wang
, and R.
Antonia
, “Active control of a turbulent boundary layer based on local surface perturbation
,” J. Fluid Mech.
750
, 316
–354
(2014
).20.
K.
Gouder
, M.
Potter
, and J. F.
Morrison
, “Turbulent friction drag reduction using electroactive polymer and electromagnetically driven surfaces
,” Exp. Fluids
54
, 1441
(2013
).21.
C.
Lee
, J.
Kim
, D.
Babcock
, and R.
Goodman
, “Application of neural networks to turbulence control for drag reduction
,” Phys. Fluids
9
, 1740
–1747
(1997
).22.
R. J.
Adrian
, “Stochastic estimation of the structure of turbulent fields
,” in Eddy Structure Identification
(Springer
, 1996
), pp. 145
–195
.23.
C.
Tinney
, F.
Coiffet
, J.
Delville
, A.
Hall
, P.
Jordan
, and M. N.
Glauser
, “On spectral linear stochastic estimation
,” Exp. Fluids
41
, 763
–775
(2006
).24.
C. E.
Tinney
, L.
Ukeiley
, and M. N.
Glauser
, “Low-dimensional characteristics of a transonic jet. Part 2. Estimate and far-field prediction
,” J. Fluid Mech.
615
, 53
–92
(2008
).25.
W. J.
Baars
, N.
Hutchins
, and I.
Marusic
, “Spectral stochastic estimation of high-Reynolds-number wall-bounded turbulence for a refined inner-outer interaction model
,” Phys. Rev. Fluids
1
, 054406
(2016
).26.
T.
Suzuki
and Y.
Hasegawa
, “Estimation of turbulent channel flow at Reτ = 100 based on the wall measurement using a simple sequential approach
,” J. Fluid Mech.
830
, 760
–796
(2017
).27.
S. J.
Illingworth
, J. P.
Monty
, and I.
Marusic
, “Estimating large-scale structures in wall turbulence using linear models
,” J. Fluid Mech.
842
, 146
–162
(2018
).28.
M. P.
Encinar
, A.
Lozano-Durán
, and J.
Jiménez
, “Reconstructing channel turbulence from wall observations
,” in Proceedings of CTR Summer School
(Stanford University
, 2018
).29.
J.
Borée
, “Extended proper orthogonal decomposition: A tool to analyse correlated events in turbulent flows
,” Exp. Fluids
35
, 188
–192
(2003
).30.
S.
Discetti
, M.
Raiola
, and A.
Ianiro
, “Estimation of time-resolved turbulent fields through correlation of non-time-resolved field measurements and time-resolved point measurements
,” Exp. Therm. Fluid Sci.
93
, 119
–130
(2018
).31.
F.
Rosenblatt
, “The perceptron: A probabilistic model for information storage and organization in the brain
,” Psychol. Rev.
65
, 386
(1958
).32.
Y.
LeCun
, Y.
Bengio
, and G.
Hinton
, “Deep learning
,” Nature
521
, 436
(2015
).33.
P.
Baldi
and K.
Hornik
, “Neural networks and principal component analysis: Learning from examples without local minima
,” Neural Networks
2
, 53
–58
(1989
).34.
J.
Ling
, A.
Kurzawski
, and J.
Templeton
, “Reynolds averaged turbulence modelling using deep neural networks with embedded invariance
,” J. Fluid Mech.
807
, 155
–166
(2016
).35.
J.-L.
Wu
, J.-X.
Wang
, H.
Xiao
, and J.
Ling
, “A priori assessment of prediction confidence for data-driven turbulence modeling
,” Flow, Turbul. Combust.
99
, 25
–46
(2017
).36.
R.
Maulik
, O.
San
, A.
Rasheed
, and P.
Vedula
, “Subgrid modelling for two-dimensional turbulence using neural networks
,” J. Fluid Mech.
858
, 122
–144
(2019
).37.
Z.
Nikolaou
, C.
Chrysostomou
, L.
Vervisch
, and S.
Cant
, “Progress variable variance and filtered rate modelling using convolutional neural networks and flamelet methods
,” Flow, Turbul. Combust.
103
, 485
(2019
).38.
M.
Raissi
, Z.
Wang
, M. S.
Triantafyllou
, and G. E.
Karniadakis
, “Deep learning of vortex-induced vibrations
,” J. Fluid Mech.
861
, 119
–137
(2019
).39.
M. P.
Hack
and T. A.
Zaki
, “Data-enabled prediction of streak breakdown in pressure-gradient boundary layers
,” J. Fluid Mech.
801
, 43
–64
(2016
).40.
S.
Brunton
, B.
Noack
, and P.
Koumoutsakos
, “Machine learning for fluid mechanics
,” Annu. Rev. Fluid Mech.
52
, 1
(2020
).41.
M.
Milano
and P.
Koumoutsakos
, “Neural network modeling for near wall turbulent flow
,” J. Comput. Phys.
182
, 1
–26
(2002
).42.
R.
Maulik
and O.
San
, “A neural network approach for the blind deconvolution of turbulent flows
,” J. Fluid Mech.
831
, 151
–181
(2017
).43.
K.
Fukami
, K.
Fukagata
, and K.
Taira
, “Super-resolution reconstruction of turbulent flows with machine learning
,” J. Fluid Mech.
870
, 106
–120
(2019
).44.
B.
Lusch
, J. N.
Kutz
, and S. L.
Brunton
, “Deep learning for universal linear embeddings of nonlinear dynamics
,” Nat. Commun.
9
, 4950
(2018
).45.
P.
Srinivasan
, L.
Guastoni
, H.
Azizpour
, P.
Schlatter
, and R.
Vinuesa
, “Predictions of turbulent shear flows using deep neural networks
,” Phys. Rev. Fluids
4
, 054603
(2019
).46.
K.
Fukushima
, “Neocognitron: A self-organizing neural network model for a mechanism of pattern recognition unaffected by shift in position
,” Biol. Cybern.
36
, 193
–202
(1980
).47.
Y.
LeCun
, “A learning scheme for asymmetric threshold networks
,” in Proceedings of COGNITIVA
(1985
), Vol. 85, pp. 599
–604
.48.
K.
Fukushima
, “Neocognitron: A hierarchical neural network capable of visual pattern recognition
,” Neural Networks
1
, 119
–130
(1988
).49.
Y.
LeCun
, B.
Boser
, J. S.
Denker
, D.
Henderson
, R. E.
Howard
, W.
Hubbard
, and L. D.
Jackel
, “Backpropagation applied to handwritten zip code recognition
,” Neural Comput.
1
, 541
–551
(1989
).50.
W.
Liu
, Z.
Wang
, X.
Liu
, N.
Zeng
, Y.
Liu
, and F. E.
Alsaadi
, “A survey of deep neural network architectures and their applications
,” Neurocomputing
234
, 11
–26
(2017
).51.
J.
Ou
and Y.
Li
, “Vector-kernel convolutional neural networks
,” Neurocomputing
330
, 253
–258
(2019
).52.
K.
Sasaki
, R.
Vinuesa
, A. V.
Cavalieri
, P.
Schlatter
, and D. S.
Henningson
, “Transfer functions for flow predictions in wall-bounded turbulence
,” J. Fluid Mech.
864
, 708
–745
(2019
).53.
L.
Guastoni
, M. P.
Encinar
, P.
Schlatter
, H.
Azizpour
, and R.
Vinuesa
, “Prediction of wall-bounded turbulence from wall quantities using convolutional neural networks
” J. Phys.: Conf. Ser.
(in press
).54.
J. L.
Lumley
, “The structure of inhomogeneous turbulent flows
,” in Atmospheric Turbulence and Radio Wave Propagation
(1967
).55.
Y.
Wu
, “A study of energetic large-scale structures in turbulent boundary layer
,” Phys. Fluids
26
, 045113
(2014
).56.
L.
Sirovich
, “Turbulence and the dynamics of coherent structures. I. Coherent structures
,” Q. Appl. Math.
45
, 561
–571
(1987
).57.
V.
Nair
and G. E.
Hinton
, “Rectified linear units improve restricted Boltzmann machines
,” in Proceedings of the 27th International Conference on Machine Learning (ICML-10)
(2010
), pp. 807
–814
.58.
D. P.
Kingma
and J.
Ba
, “Adam: A method for stochastic optimization
,” preprint arXiv:1412.6980 (2014
).59.
Y.
Li
, E.
Perlman
, M.
Wan
, Y.
Yang
, C.
Meneveau
, R.
Burns
, S.
Chen
, A.
Szalay
, and G.
Eyink
, “A public turbulence database cluster and applications to study Lagrangian evolution of velocity increments in turbulence
,” J. Turbul.
9
, N31
(2008
).60.
H.
Yu
, K.
Kanov
, E.
Perlman
, J.
Graham
, E.
Frederix
, R.
Burns
, A.
Szalay
, G.
Eyink
, and C.
Meneveau
, “Studying Lagrangian dynamics of turbulence using on-demand fluid particle tracking in a public turbulence database
,” J. Turbul.
13
, N12
(2012
).61.
Z.
Liu
, R.
Adrian
, and T.
Hanratty
, “Large-scale modes of turbulent channel flow: Transport and structure
,” J. Fluid Mech.
448
, 53
–80
(2001
).62.
M.
Guala
, S.
Hommema
, and R.
Adrian
, “Large-scale and very-large-scale motions in turbulent pipe flow
,” J. Fluid Mech.
554
, 521
–542
(2006
).63.
C.
Sanmiguel Vila
, R.
Örlü
, R.
Vinuesa
, P.
Schlatter
, A.
Ianiro
, and S.
Discetti
, “Adverse-pressure-gradient effects on turbulent boundary layers: Statistics and flow-field organization
,” Flow, Turbul. Combust.
99
, 589
–612
(2017
).64.
Z.
Deng
, Y.
Chen
, Y.
Liu
, and K. C.
Kim
, “Time-resolved turbulent velocity field reconstruction using a long short-term memory (LSTM)-based artificial intelligence framework
,” Phys. Fluids
31
, 075108
(2019
).65.
M. P.
Encinar
and J.
Jiménez
, “Logarithmic-layer turbulence: A view from the wall
,” Phys. Rev. Fluids
4
, 114603
(2019
).66.
Z.-C.
Liu
, R. J.
Adrian
, and T. J.
Hanratty
, “Reynolds number similarity of orthogonal decomposition of the outer layer of turbulent wall flow
,” Phys. Fluids
6
, 2815
–2819
(1994
).67.
H.
Nakamura
and S.
Yamada
, “Quantitative evaluation of spatio-temporal heat transfer to a turbulent air flow using a heated thin-foil
,” Int. J. Heat Mass Transfer
64
, 892
–902
(2013
).68.
M.
Raiola
, C. S.
Greco
, M.
Contino
, S.
Discetti
, and A.
Ianiro
, “Towards enabling time-resolved measurements of turbulent convective heat transfer maps with IR thermography and a heated thin foil
,” Int. J. Heat Mass Transfer
108
, 199
–209
(2017
).69.
F.
Mallor
, M.
Raiola
, C. S.
Vila
, R.
Örlü
, S.
Discetti
, and A.
Ianiro
, “Modal decomposition of flow fields and convective heat transfer maps: An application to wall-proximity square ribs
,” Exp. Therm. Fluid Sci.
102
, 517
–527
(2019
).70.
R.
Mayer
, R. A. W. M.
Henkes
, and J. L.
Van Ingen
, “Quantitative infrared-thermography for wall-shear stress measurement in laminar flow
,” Int. J. Heat Mass Transfer
41
, 2347
–2356
(1998
).© 2019 Author(s).
2019
Author(s)
You do not currently have access to this content.
