Plants in aquatic canopies deform when subjected to a water flow and so, unlike a rigid bluff body, the resulting drag force FD grows sub-quadratically with the flow velocity U ̄ . In this article, the effect of density on the canopy reconfiguration and the corresponding drag reduction is experimentally investigated for simple 2D synthetic canopies in an inclinable, narrow water channel. The drag acting on the canopy, and also on individual sheets, is systematically measured via two independent techniques. Simultaneous drag and reconfiguration measurements demonstrate that data for different Reynolds numbers (400–2200), irrespective of sheet width (w) and canopy spacing (ℓ), collapse on a unique curve given by a bending beam model which relates the reconfiguration number and a properly rescaled Cauchy number. Strikingly, the measured Vogel exponent V and hence the drag reduction via reconfiguration is found to be independent of the spacing between sheets and the lateral confinement; only the drag coefficient decreases linearly with the sheet spacing since a strong sheltering effect exists as long as the spacing is smaller than a critical value depending on the sheet width.

1.
W. O.
Ree
and
V. J.
Palmer
,
Flow of Water in Channels Protected by Vegetative Linings
(
US Department of Agriculture
,
Washington, D.C.
,
1949
).
2.
H. M.
Nepf
, “
Flow and transport in regions with aquatic vegetation
,”
Annu. Rev. Fluid Mech.
44
,
123
142
(
2012
).
3.
S. M.
Haslam
,
River Plants: The Macrophytic Vegetation of Watercourses
(
CUP Archive
,
1978
).
4.
E.
de Langre
, “
Effects of wind on plants
,”
Annu. Rev. Fluid Mech.
40
(
1
),
141
168
(
2008
).
5.
G.
Bornette
and
S.
Puijalon
, “
Response of aquatic plants to abiotic factors: A review
,”
Aquat. Sci.
73
(
1
),
1
14
(
2011
).
6.
C.
Sanchez
,
H.
Arribart
, and
M. M.
Giraud Guille
, “
Biomimetism and bioinspiration as tools for the design of innovative materials and systems
,”
Nat. Mater.
4
(
4
),
277
288
(
2005
).
7.
B.
Bhushan
, “
Biomimetics: Lessons from nature–an overview
,”
Philos. Trans. R. Soc., A
367
(
1893
),
1445
1486
(
2009
).
8.
J.
Finnigan
, “
Turbulence in plant canopies
,”
Annu. Rev. Fluid Mech.
32
,
519
571
(
2000
).
9.
P.
Naden
,
P.
Rameshwaran
,
O.
Mountford
, and
C.
Robertson
, “
The influence of macrophyte growth, typical of eutrophic conditions, on river flow velocities and turbulence production
,”
Hydrol. Processes
20
(
18
),
3915
3938
(
2006
).
10.
H. M.
Nepf
, “
Hydrodynamics of vegetated channels
,”
J. Hydraul. Res.
50
(
3
),
262
279
(
2012
).
11.
R.-M.
Li
and
H. W.
Shen
, “
Effect of tall vegetations on flow and sediment
,”
J. Hydraul. Div.
99
(
5
),
793
814
(
1973
).
12.
F.
Lopez
and
M.
Garcia
, “
Open-channel flow through simulated vegetation: Suspended sediment transport modeling
,”
Water Resour. Res.
34
(
9
),
2341
2352
, doi:10.1029/98WR01922 (
1998
).
13.
J.
Järvelä
,
J.
Aberle
,
A.
Dittrich
,
H. P.
Rauch
, and
I.
Schnauder
, “
Flow-vegetation-sediment interaction: Research challenges
,” in
River Flow 2006
, edited by
R. M. L.
Ferreira
,
E. C. T. L.
Alves
,
J. G. A. B.
Leal
, and
A. H.
Cardoso
(
Taylor & Francis
,
2006
), Vol.
2
, pp.
2017
2026
.
14.
N.
Kouwen
and
M.
Fathi-Moghadam
, “
Friction factors for coniferous trees along rivers
,”
J. Hydraul. Eng.
126
(
10
),
732
740
(
2000
).
15.
H. M.
Nepf
, “
Drag, turbulence, and diffusion in flow through emergent vegetation
,”
Water Resour. Res.
35
(
2
),
479
489
, doi:10.1029/1998WR900069 (
1999
).
16.
F. C.
Wu
,
H. W.
Shen
, and
Y. J.
Chou
, “
Variation of roughness coefficients for unsubmerged and submerged vegetation
,”
J. Hydraul. Eng.
125
(
9
),
934
942
(
1999
).
17.
N.
Kouwen
and
T. E.
Unny
, “
Flexible roughness in open channels
,”
J. Hydraul. Div.
99
,
713
728
(
1973
).
18.
M.
Righetti
and
A.
Armanini
, “
Flow resistance in open channel flows with sparsely distributed bushes
,”
J. Hydrol.
269
(
1-2
),
55
64
(
2002
).
19.
E.
de Langre
, “
Methodological advances in predicting flow-induced dynamics of plants using mechanical-engineering theory
,”
J. Exp. Biol.
215
,
914
921
(
2013
).
20.
M.
Ghisalberti
and
H. M.
Nepf
, “
Mixing layers and coherent structures in vegetated aquatic flows
,”
J. Geophys. Res.
107
,
3-1
3-11
, doi:10.1029/2001JC000871 (
2002
).
21.
C.
Py
,
E.
de Langre
, and
B.
Moulia
, “
A frequency lock-in mechanism in the interaction between wind and crop canopies
,”
J. Fluid Mech.
568
,
425
449
(
2006
).
22.
S. M.
Cameron
,
V. I.
Nikora
,
I.
Albayrak
,
O.
Miler
,
M.
Stewart
, and
F.
Siniscalchi
, “
Interactions between aquatic plants and turbulent flow: A field study using stereoscopic PIV
,”
J. Fluid Mech.
732
,
345
372
(
2013
).
23.
R.
Singh
,
M. M.
Bandi
,
A.
Mahadevan
, and
S.
Mandre
, “
Linear stability analysis for monami in a submerged seagrass bed
,”
J. Fluid Mech.
786
,
R1
(
2016
).
24.
S. G.
Monismith
, “
Hydrodynamics of coral reefs
,”
Annu. Rev. Fluid Mech.
39
,
37
55
(
2007
).
25.
M.
Luhar
and
H. M.
Nepf
, “
Wave-induced dynamics of flexible blades
,”
J. Fluids Struct.
61
,
20
41
(
2016
).
26.
J. S.
Madin
and
S. R.
Connolly
, “
Ecological consequences of major hydrodynamic disturbances on coral reefs
,”
Nature
444
,
477
480
(
2006
).
27.
D.
Lopez
,
S.
Michelin
, and
E.
de Langre
, “
Flow-induced pruning of branched systems and brittle reconfiguration
,”
J. Theor. Biol.
284
,
117
124
(
2011
).
28.
R.
Nathan
,
G.
Katul
,
H.
Horn
,
S.
Thomas
, and
R.
Oren
, “
Mechanisms of long–distance dispersal of seeds by wind
,”
Nature
418
,
409
413
(
2002
).
29.
R.
Nathan
and
G.
Katul
, “
Foliage shedding in deciduous forests lifts up long-distance seed dispersal by wind
,”
Proc. Natl. Acad. Sci.
102
,
8251
8256
(
2005
).
30.
S.
Vogel
, “
Drag and flexibility in sessile organisms
,”
Am. Zool.
24
(
1
),
37
44
(
1984
).
31.
S.
Vogel
, “
Drag and reconfiguration of broad leaves in high winds
,”
J. Exp. Bot.
40
(
217
),
941
948
(
1989
).
32.
S.
Vogel
,
Life in Moving Fluids: The Physical Biology of Flow
(
Princeton University Press
,
1994
).
33.
T.
Barois
and
E.
de Langre
, “
Flexible body with drag independent of the flow velocity
,”
J. Fluid Mech.
735
,
R2
(
2013
).
34.
K.
Sand-Jensen
, “
Drag and reconfiguration of freshwater macrophytes
,”
Freshwater Biol.
48
(
2
),
271
283
(
2003
).
35.
O.
Speck
and
H.-C.
Spatz
, “
Damped oscillations of the giant reed Arundo donax (Poaceae)
,”
Am. J. Bot.
91
(
6
),
789
796
(
2004
).
36.
M.
Rudnicki
,
S. J.
Mitchell
, and
M. D.
Novak
, “
Wind tunnel measurements of crown streamlining and drag relationships for three conifer species
,”
Can. J. For. Res.
34
(
3
),
666
676
(
2004
).
37.
S.
Vollsinger
,
S. J.
Mitchell
,
K. E.
Byrne
,
M. D.
Novak
, and
M.
Rudnicki
, “
Wind tunnel measurements of crown streamlining and drag relationships for several hardwood species
,”
Can. J. For. Res.
35
(
5
),
1238
1249
(
2005
).
38.
S.
Alben
,
M. J.
Shelley
, and
J.
Zhang
, “
Drag reduction through self-similar bending of a flexible body
,”
Nature
420
(
6915
),
479
481
(
2002
).
39.
S.
Alben
,
M. J.
Shelley
, and
J.
Zhang
, “
How flexibility induces streamlining in a two-dimensional flow
,”
Phys. Fluids
16
(
5
),
1694
(
2004
).
40.
F. P.
Gosselin
,
E.
de Langre
, and
B. A.
Machado-Almeida
, “
Drag reduction of flexible plates by reconfiguration
,”
J. Fluid Mech.
650
,
319
341
(
2010
).
41.
J. T.
Dijkstra
and
R. E.
Uittenbogaard
, “
Modeling the interaction between flow and highly flexible aquatic vegetation
,”
Water Resour. Res.
46
(
12
),
W12547
, doi:10.1029/2010WR009246 (
2010
).
42.
M.
Luhar
and
H. M.
Nepf
, “
Flow-induced reconfiguration of buoyant and flexible aquatic vegetation
,”
Limnol. Oceanogr.
56
(
6
),
2003
2017
(
2011
).
43.
L.
Schouveiler
and
A.
Boudaoud
, “
The rolling up of sheets in a steady flow
,”
J. Fluid Mech.
563
,
71
80
(
2006
).
44.
I.
Albayrak
,
V.
Nikora
,
O.
Miler
, and
M. O.
Hare
, “
Flow-plant interactions at a leaf scale: Effects of leaf shape, serration, roughness and flexural rigidity
,”
Aquat. Sci.
74
(
2
),
267
286
(
2012
).
45.
R. D.
Blevins
,
Flow-Induced Vibration
(
Van Nostrand Reinhold Co.
,
New York
,
1977
).
46.
A. S.
Thom
, “
Momentum absorption by vegetation
,”
Q. J. R. Meteorol. Soc.
97
,
414
428
(
1971
).
47.
H. M.
Nepf
and
E. R.
Vivoni
, “
Flow structure in depth-limited, vegetated flow
,”
J. Geophys. Res.
105
(
C12
),
28547
28557
, doi:10.1029/2000JC900145 (
2000
).
48.
F. P.
Gosselin
and
E.
de Langre
, “
Destabilising effects of plant flexibility in air and aquatic vegetation canopy flows
,”
Eur. J. Mech., B: Fluids
28
,
271
282
(
2009
).
49.
M. R.
Hoffmann
, “
Application of a simple space-time averaged porous media model to flow in densely vegetated channels
,”
J. Porous Media
7
(
3
),
183
(
2004
).
50.
O.
Doaré
,
B.
Moulia
, and
E.
de Langre
, “
Effect of plant interaction on wind-induced crop motion
,”
J. Biomech. Eng.
126
(
2
),
146
151
(
2004
).
51.
J.
Favier
,
A.
Dauptain
,
D.
Basso
, and
A.
Bottaro
, “
Passive separation control using a self-adaptive hairy coating
,”
J. Fluid Mech.
627
,
451
483
(
2009
).
52.
F. P.
Gosselin
and
E.
de Langre
, “
Drag reduction by reconfiguration of a poroelastic system
,”
J. Fluids Struct.
27
(
7
),
1111
1123
(
2011
).
53.
Y.
Brunet
,
J. J.
Finnigan
, and
M. R.
Raupach
, “
A wind tunnel study of air flow in waving wheat: Single-point velocity statistics
,”
Boundary-Layer Meteorol.
70
,
95
132
(
1994
).
54.
M. D.
Novak
,
J. S.
Warland
,
A. L.
Orchansky
,
R.
Ketler
, and
S.
Green
, “
Wind tunnel and field measurements of turbulent flow in forests. Part I: Uniformly thinned stands
,”
Boundary-Layer Meteorol.
95
,
457
495
(
2000
).
55.
C. H.
Peterson
,
R. A.
Luettich
,
F.
Micheli
, and
G. A.
Skilleter
, “
Attenuation of water flow inside seagrass canopies of differing structure
,”
Mar. Ecol.: Prog. Ser.
268
,
81
92
(
2004
).
56.
D.
Poggi
,
A.
Porporato
,
L.
Ridolfi
,
J. D.
Albertson
, and
G. G.
Katul
, “
The effect of vegetation density on canopy sub-layer turbulence
,”
Boundary-Layer Meteorol.
111
,
565
587
(
2004
).
57.
T.
Leclercq
and
E.
de Langre
, “
Drag reduction by elastic reconfiguration of non-uniform beams in non-uniform flows
,”
J. Fluids Struct.
60
,
114
129
(
2016
).
58.
L.
Chevalier
,
Mécanique des Systèmes et des Milieux Déformables
(
Ellipses Edition
,
1994
).
59.
D. M.
Temple
,
K. M.
Robinson
,
R. M.
Ahring
, and
A. G.
Davis
,
Stability Design of Grasslined Open Channels
Vol.
667
(
US Department of Agriculture, Agricultural Research Service
,
1987
).
60.
H.
Glauert
, “
Wind tunnel interference on wings, bodies and airscrews
,”
Technical Report 1566
,
DTIC Document
,
1933
.
61.
G. K.
Batchelor
,
An Introduction to Fluid Dynamics
(
Cambridge University Press
,
2000
).
You do not currently have access to this content.