Turbulent channel flow with a porous wall is investigated using direct numerical simulation, where the porous media domain consists of regular or random circular cylinder arrays. We compare the statistics and structure of the mean flow and turbulence in the channel flow with a bulk Reynolds number of 2500 and two porosities (φ=0.6 and 0.8) for the porous media. It is shown that the random interface significantly affects the dynamics of turbulence and the time-averaged flow. More intense mixing is observed near the random interface due to augmented form-induced shear stresses. Due to the strong dependence of induced flow direction on the interface geometry, we segmented the flow field into two types of areas based on the slope angle formed by the top-layer cylinders: the windward area and leeward area. The conditional average of turbulence kinematic energy budget over each type of area reveals their respective role in turbulence transportation more explicitly. In addition, we use finite-time Lyapunov exponents to inspect the Lagrangian coherent structures in the flow fields, which reveal the preferential fluid trajectories in the random porous medium geometry.

1.
K.
Suga
,
Y.
Nakagawa
, and
M.
Kaneda
, “
Spanwise turbulence structure over permeable walls
,”
J. Fluid Mech.
822
,
186
201
(
2017
).
2.
A.
Chavarin
,
G.
Gomez-de Segura
,
R.
Garcia-Mayoral
, and
M.
Luhar
, “
Resolvent-based predictions for turbulent flow over anisotropic permeable substrates
,”
J. Fluid Mech.
913
,
A24
(
2021
).
3.
N.
Christopher
,
J. M. F.
Peter
,
M.
Kloker
, and
J.-P.
Hickey
, “
DNS of turbulent flat-plate flow with transpiration cooling
,”
Int. J. Heat Mass Transfer
157
,
119972
(
2020
).
4.
T.
Nguyen
,
R.
Muyshondt
,
Y. A.
Hassan
, and
N. K.
Anand
, “
Experimental investigation of cross flow mixing in a randomly packed bed and streamwise vortex characteristics using particle image velocimetry and proper orthogonal decomposition analysis
,”
Phys. Fluids
31
,
025101
(
2019
).
5.
A.
Bottaro
, “
Flow over natural or engineered surfaces: An adjoint homogenization perspective
,”
J. Fluid Mech.
877
,
P1
(
2019
).
6.
A.
Terzis
, “
On the correspondence between flow structures and convective heat transfer augmentation for multiple jet impingement
,”
Exp. Fluids
57
,
146
(
2016
).
7.
M. E.
Rosti
,
L.
Brandt
, and
A.
Pinelli
, “
Turbulent channel flow over an anisotropic porous wall–drag increase and reduction
,”
J. Fluid Mech.
842
,
381
394
(
2018
).
8.
J. J.
Voermans
,
M.
Ghisalberti
, and
G. N.
Ivey
, “
The variation of flow and turbulence across the sediment-water interface
,”
J. Fluid Mech.
824
,
413
437
(
2017
).
9.
T.
Kim
,
G.
Blois
,
J. L.
Best
, and
K. T.
Christensen
, “
Experimental evidence of amplitude modulation in permeable-wall turbulence
,”
J. Fluid Mech.
887
,
A3
(
2020
).
10.
K.
Suga
,
Y.
Okazaki
, and
Y.
Kuwata
, “
Characteristics of turbulent square duct flows over porous media
,”
J. Fluid Mech.
884
,
A7
(
2020
).
11.
G.
Shen
,
J.
Yuan
, and
M. S.
Phanikumar
, “
Direct numerical simulations of turbulence and hyporheic mixing near sediment water interfaces
,”
J. Fluid Mech.
892
,
A20
(
2020
).
12.
M. W.
McCorquodale
and
R. J.
Munro
, “
Direct effects of boundary permeability on turbulent flows: Observations from an experimental study using zero-mean-shear turbulence
,”
J. Fluid Mech.
915
,
A134
(
2021
).
13.
H. H. A.
Xu
,
S. J.
Altland
,
X. I. A.
Yang
, and
R. F.
Kunz
, “
Flow over closely packed cubical roughness
,”
J. Fluid Mech.
920
,
A37
(
2021
).
14.
W. P.
Breugem
,
B. J.
Boersma
, and
R. E.
Uittenbogaard
, “
The influence of wall permeability on turbulent channel flow
,”
J. Fluid Mech.
562
,
35
(
2006
).
15.
J.
Finnigan
, “
Turbulence in plant canopies
,”
Annu. Rev. Fluid Mech.
32
,
519
571
(
2000
).
16.
J.
Jimenez
,
M.
Uhlmann
,
A.
Pinelli
, and
G.
Kawahara
, “
Turbulent shear flow over active and passive porous surfaces
,”
J. Fluid Mech.
442
,
89
117
(
2001
).
17.
C.
Manes
,
D.
Poggi
, and
L.
Ridolfi
, “
Turbulent boundary layers over permeable walls: Scaling and near wall structure
,”
J. Fluid Mech.
687
,
141
170
(
2011
).
18.
H. M.
Nepf
, “
Flow and transport in regions with aquatic vegetation
,”
Annu. Rev. Fluid Mech.
44
,
123
142
(
2012
).
19.
M. E.
Rosti
,
L.
Cortelezzi
, and
M.
Quadrio
, “
Direct numerical simulation of turbulent channel flow over porous walls
,”
J. Fluid Mech.
784
,
396
442
(
2015
).
20.
G.
Gómez-de Segura
and
R.
García-Mayoral
, “
Turbulent drag reduction by anisotropic permeable substrates–analysis and direct numerical simulations
,”
J. Fluid Mech.
875
,
124
172
(
2019
).
21.
R.
Garcia-Mayoral
and
J.
Jiménez
, “
Drag reduction by riblets
,”
Philos. Trans. R. Soc. A
369
,
1412
1427
(
2011
).
22.
N.
Abderrahaman-Elena
and
R.
García-Mayoral
, “
Analysis of anisotropically permeable surfaces for turbulent drag reduction
,”
Phys. Rev. Fluids
2
,
114609
(
2017
).
23.
K.
Suga
,
Y.
Okazaki
,
U.
Ho
, and
Y.
Kuwata
, “
Anisotropic wall permeability effects on turbulent channel flows
,”
J. Fluid Mech.
855
,
983
1016
(
2018
).
24.
C.
Manes
,
D.
Pokrajac
,
I.
McEwan
, and
V.
Nikora
, “
Turbulence structure of open channel flows over permeable and impermeable beds: A comparative study
,”
Phys. Fluids
21
,
125109
(
2009
).
25.
H.
Fang
,
H.
Xu
,
G.
He
, and
S.
Dey
, “
Influence of permeable beds on hydraulically macro-rough flow
,”
J. Fluid Mech.
847
,
552
590
(
2018
).
26.
E.
Padhi
,
N.
Penna
,
S.
Dey
, and
R.
Gaudio
, “
Hydrodynamics of water-worked and screeded gravel beds: A comparative study
,”
Phys. Fluids
30
,
085105
(
2018
).
27.
E.
Mignot
,
E.
Barthelemy
, and
D.
Hurther
, “
Double-averaging analysis and local flow characterization of near-bed turbulence in gravel-bed channel flows
,”
J. Fluid Mech.
618
,
279
303
(
2009
).
28.
J.
Yuan
and
M. A.
Jouybari
, “
Topographical effects of roughness on turbulence statistics in roughness sublayer
,”
Phys. Rev. Fluids
3
,
114603
(
2018
).
29.
J.
Jeong
and
F.
Hussain
, “
On the identification of a vortex
,”
J. Fluid Mech.
285
,
69
94
(
1995
).
30.
C. D.
Cantwell
,
S. J.
Sherwin
,
R. M.
Kirby
, and
P. H.
Kelly
, “
From h to p efficiently: Strategy selection for operator evaluation on hexahedral and tetrahedral elements
,”
Comput. Fluids
43
,
23
28
(
2011
).
31.
X.
Chu
,
G.
Yang
,
S.
Pandey
, and
B.
Weigand
, “
Direct numerical simulation of convective heat transfer in porous media
,”
Int. J. Heat Mass Transfer
133
,
11
20
(
2019
).
32.
X.
Chu
,
W.
Wang
,
G.
Yang
,
A.
Terzis
,
R.
Helmig
, and
B.
Weigand
, “
Transport of turbulence across permeable interface in a turbulent channel flow: Interface-resolved direct numerical simulation
,”
Transp. Porous Media
136
,
165
189
(
2021
).
33.
W.
Wang
,
X.
Chu
,
A.
Lozano-Durán
,
R.
Helmig
, and
B.
Weigand
, “
Information transfer between turbulent boundary layer and porous media
,”
J. Fluid Mech.
920
,
A21
(
2021
).
34.
S.
Pandey
,
X.
Chu
,
B.
Weigand
,
E.
Laurien
, and
J.
Schumacher
, “
Relaminarized and recovered turbulence under nonuniform body forces
,”
Phys. Rev. Fluids
5
,
104604
(
2020
).
35.
M.
Lee
and
R. D.
Moser
, “
Spectral analysis of the budget equation in turbulent channel flows at high Reynolds number
,”
J. Fluid Mech.
860
,
886
938
(
2019
).
36.
I. W.
Kokkinakis
and
D.
Drikakis
, “
Implicit large eddy simulation of weakly-compressible turbulent channel flow
,”
Comput. Methods Appl. Mech. Eng.
287
,
229
261
(
2015
).
37.
P.
Tsoutsanis
,
I. W.
Kokkinakis
,
L.
Könözsy
,
D.
Drikakis
,
R.
Williams
, and
D. L.
Youngs
, “
Comparison of structured-and unstructured-grid, compressible and incompressible methods using the vortex pairing problem
,”
Comput. Methods Appl. Mech. Eng.
293
,
207
231
(
2015
).
38.
M. R.
Raupach
and
R. H.
Shaw
, “
Averaging procedures for flow within vegetation canopies
,”
Boundary-Layer Meteorol.
22
,
79
90
(
1982
).
39.
X.
Chu
,
Y.
Wu
,
U.
Rist
, and
B.
Weigand
, “
Instability and transition in an elementary porous medium
,”
Phys. Rev. Fluids
5
,
044304
(
2020
).
40.
W. P.
Breugem
and
B. J.
Boersma
, “
Direct numerical simulations of turbulent flow over a permeable wall using a direct and a continuum approach
,”
Phys. fluids
17
,
025103
(
2005
).
41.
Y.
Kuwata
and
K.
Suga
, “
Transport mechanism of interface turbulence over porous and rough walls
,”
Flow, Turbul. Combust.
97
,
1071
1093
(
2016
).
42.
S. C.
Shadden
,
F.
Lekien
, and
J. E.
Marsden
, “
Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows
,”
Physica D
212
,
271
304
(
2005
).
43.
C.
Pan
,
J. J.
Wang
, and
C.
Zhang
, “
Identification of Lagrangian coherent structures in the turbulent boundary layer
,”
Sci. China Ser. G
52
,
248
257
(
2009
).

Supplementary Material

You do not currently have access to this content.