Two models of the flow over and through an immersed, vegetated layer are examined to study the onset of instability waves across the layer and to assess the effect of mild variations in the mean flow and in the drag force exerted by the canopy onto the frequency and growth rate of the monami instability. One of the two models, based on the use of Darcy’s equation, with a tensorial permeability, within the canopy is more robust than the other (which uses a scalar drag coefficient), i.e., it is less sensitive to the inevitable imperfections or approximations in the input data.

1.
J. D.
Ackerman
and
A.
Okubo
, “
Reduced mixing in a marine macrophyte canopy
,”
Funct. Ecol.
7
,
305
-
309
(
1993
).
2.
M.
Raupach
,
J. J.
Finnigan
, and
Y.
Brunei
, “
Coherent eddies and turbulence in vegetation canopies: The mixing-layer analogy
,”
Boundary Layer Meteorol.
78
,
351
-
382
(
1996
).
3.
C.
Py
,
E.
De Langre
, and
B.
Moulia
, “
The mixing layer instability of wind over a flexible crop canopy
,”
C. R. Mec.
332
(
8
),
613
-
618
(
2004
).
4.
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
),
1
-
12
(
2015
).
5.
G. A.
Zampogna
,
F.
Pluvinage
,
A.
Kourta
, and
A.
Bottaro
, “
Instability of canopy flow
,”
Water Resour. Res.
52
(
7
),
5421
-
5432
, doi:10.1002/2016WR018915 (
2016
).
6.
S.
Ikeda
and
M.
Kanazawa
, “
Three-dimensional organized vortices above flexible water plants
,”
J. Hydraul. Eng.
122
(
11
),
634
-
640
(
1996
).
7.
M. C.
Gambi
,
A. R. M.
Nowell
, and
P. A.
Jumars
, “
Flume observations on flow dynamics in Zostera marina (eelgrass) beds
,”
Mar. Ecol.: Prog. Ser.
61
,
159
-
169
(
1990
).
8.
J. E.
Eckman
, “
The role of hydrodynamics in recruitment, growth and survival of Argopecten irradians and Anomia simplex within eelgrass meadows
,”
J. Exp. Mar. Biol. Ecol.
106
,
165
-
191
(
1987
).
9.
R. E.
Grizzle
,
F. T.
Short
,
C. R.
Newell
,
H.
Hoven
, and
L.
Kindblom
, “
Hydrodynamically induced synchronous waving of seagrasses: ‘Monami’ and its possible effects on larval mussel settlement
,”
J. Exp. Mar. Biol. Ecol.
206
,
165
-
177
(
1996
).
10.
J. J.
Finnigan
, “
Turbulence in plant canopies
,”
Annu. Rev. Fluid Mech.
32
,
519
-
571
(
2000
).
11.
T.
Asaeda
,
T.
Fujino
, and
J.
Manatunge
, “
Morphological adaptations of emergent plants to water flow
,”
Freshwater Biol.
50
,
1991
-
2001
(
2005
).
12.
J. G.
Duan
,
B.
Barkdoll
, and
R.
French
, “
Lodging velocity for an emergent aquatic plant in open channels
,”
J. Hydraul. Eng.
132
(
10
),
1015
-
1020
(
2006
).
13.
S.
Patil
and
V. P.
Singh
, “
Characteristics of monami wave in submerged vegetated flow
,”
J. Hydrol. Eng.
15
(
3
),
171
-
181
(
2010
).
14.
M.
Ghisalberti
and
H. M.
Nepf
, “
Mixing layers and coherent structures in vegetated aquatic flows
,”
J. Geophys. Res.
107
(
C2
),
3-1
3-11
, doi:10.1029/2001jc000871 (
2002
).
15.
M.
Ghisalberti
and
H. M.
Nepf
, “
The limited growth of vegetated shear layers
,”
Water Resour. Res.
40
(
7
),
W07502
, doi:10.1029/2003WR002776 (
2004
).
16.
M.
Ghisalberti
and
H. M.
Nepf
, “
Mass transport in vegetated shear flows
,”
Environ. Fluid Mech.
5
(
6
),
527
-
551
(
2005
).
17.
A.
Bottaro
,
P.
Corbett
, and
P.
Luchini
, “
The effect of base flow variation on flow stability
,”
J. Fluid Mech.
476
,
293
-
302
(
2003
).
18.
W.
Brevis
,
M.
García-Villalba
, and
Y.
Niño
, “
Experimental and large eddy simulation study of the flow developed by a sequence of lateral obstacles
,”
Environ. Fluid Mech.
14
,
873
-
893
(
2014
).
19.
C.
Canuto
,
M. Y.
Hussaini
,
A.
Quarteroni
, and
T. A.
Zang
,
Spectral Methods in Fluid Dynamics
(
Springer-Verlag
,
Berlin
,
1987
).
20.
M.
Le Bars
and
M.
Worster
, “
Interfacial conditions between a pure fluid and a porous medium: Implications for binary alloy solidification
,”
J. Fluid Mech.
550
,
149
-
173
(
2006
).
21.
G. A.
Zampogna
and
A.
Bottaro
, “
Fluid flow over and through a regular bundle of rigid fibres
,”
J. Fluid Mech.
792
,
5
-
35
(
2016
).
22.
G. A.
Zampogna
, private communication (2016). The values of K 11 and K 22 arise from the solution of a local, microscopicproblem which accounts for inertia through the porous medium.21 It is not unexpected that K 11 approaches K 22 as we leave the Stokes regime.
23.
G. S.
Beavers
and
D. D.
Joseph
, “
Boundary conditions at a naturally permeable wall
,”
J. Fluid Mech.
30
,
197
-
207
(
1967
).
24.
C. C.
Mei
and
B.
Vernescu
,
Homogenization Methods for Multiscale Mechanics
(
World Scientific Publishing Co. Pte. Ltd.
,
Singapore
,
2010
).
25.
G. A.
Zampogna
and
A.
Bottaro
, “
The PELskin project—Part III: A homogenized model of flows over and through dense poroelastic media
,”
Meccanica
(published online).
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