4 Results and Discussion
4.1 Flow structures in bare bed
To set a base line, the condition without vegetation (i.e., case S0) was
first considered. Under wave-current conditions, the vertical
distribution of time-averaged horizontal velocity
(Uhoriz , grey circles shown in Fig. 4a) was
characterized by a logarithmic profile and the time-averaged vertical
velocity (Uvert , blue triangles in Fig. 4a) was
vertically uniform near the value of zero. This was similar to the
time-averaged velocity profile under pure-current conditions (e.g.,Zhang, Lai, & Jiang, 2016 ). The percentages of wave portion on
total energy in the PSD of instantaneous velocity (i.e.,Pw ) decreased gradually from the water surface to
the bed (Fig. 4b), indicating that the influence of surface waves on
water motion became weaker and weaker with decreasing z . However,
with Pw of vertical velocityPw_u > 10% through the entire
water column (blue circles in Fig. 4b), water motion over the full-depth
was affected by wave energy. Under wind-driven waves with typical periodT = 1 ~ 5 s, the water orbital motions can
penetrate down from water surface to bed when h <λ /2
(Green & Coco, 2014 ). For the case S0 in present study, the
water depth was 2.2 m, smaller than half of the wave length (λ =
6.1 m, Table 1). Besides, Pw of horizontal
velocities (i.e., Pw_e andPw_n ) was smaller thanPw_u at the same vertical height (Fig. 4b)
because of the small total energy of velocity caused by weaker
hydrodynamics (especially the smaller flow velocity, Fig. 4a) in the
vertical direction than the horizontal directions. The measured wave
orbital velocity in both horizontal (Uw_horiz )
and vertical (Uw_vert ) directions decreased with
decreasing z (Fig. 4c), and agreed (within 25%) with the
predictions of linear wave theory by eqs. (6) and (7), respectively.
Therefore, eqs. (6) and (7) were used to estimate the natural wave
attenuation with water depth for the vegetated cases. The turbulent
kinetic energy (TKE ) was dominated by the horizontal component
and decreased gradually from the water surface to the bed (Fig. 4d), a
trend that was also observed by Pujol et al. (2010) andZhang et al. (2018) .
4.2 Time-averaged velocity within vegetation
Compared with bare bed, vertical profiles of the time-averaged
horizontal velocity (Uhoriz ) were altered by the
presence of AV. Velocity profiles can be divided into two categories
based on the vegetation was under emergent (i.e., cases A1, A2, B1, B3,
and B4) and submerged (i.e., cases A3, A4, A5, B2, and B5) conditions.
For the cases A1, A2, and B1, the vegetation height was larger than the
water depth (i.e., hv > h ).
Restricted by the setup of ADV measurements (with the sampling volume 15
cm downward the probe tip) and the fluctuation of water surface, the
highest position for velocity measurement was only half or less than
half of the canopy height. For these three cases, the measuredUhoriz distributed uniformly through the water
column (Fig. 5a, 5b, and 5f), whereas Uhorizincreased gradually with increasing z for cases B3 and B4 (Fig.
5h and 5i), for which the vegetation was just emergent withhv = h . According to Lightbody &
Nepf (2006) , the mean velocity within emergent vegetation varied
inversely with the canopy frontal area (a = md withm and d representing the stem density and stem diameter,
respectively) under conditions with pure current. In present study, the
dominant vegetations for the emergent cases were P. arundinaceaand A. selengensis (Table 1). With blades uniformly distributed
from top to bottom of the stem, the a of both P.
arundinacea and A. selengensis was uniform through most part of
the stem. Near the top of vegetation, a decreased with increasingz as fresh blades with small length and width always grew at the
top. Therefore, the velocity profiles, withUhoriz uniformly distributed through the entire
water column for cases A1, A2, B1 and Uhorizgradually increasing with increasing z for cases B3 and B4, were
consistent with observations by Lightbody & Nepf (2006) .
The time-averaged velocity profiles can be separated at the top of
canopy (z = hv ) when the vegetation was
under submerged condition (i.e., hv <h ). Within vegetation (z <hv ), Uhoriz was small and
uniformly distributed in the lower part of vegetation, and increased
with increasing z in the upper part of vegetation (e.g., cases A3
and B5 in Fig. 5c and 5j, respectively). The velocity distribution
within canopy in present study was very similar to observations byNepf & Vivoni (2000) . Regions in the lower and upper part of
canopy corresponded to the “longitudinal exchange zone” and “vertical
exchange zone”, respectively, in Nepf & Vivoni (2000) .
Defined as the distance from the top of vegetation to the point within
canopy at which Uhoriz has decayed to 10% of its
maximum value, the thickness of “vertical exchange zone”
(δe ), or the penetration depth called byNepf & Vivoni (2000) , was 50, 10, 15, 25, and 20 cm for the
submerged cases A3, A4, A5, B2, and B5, respectively. Under
unidirectional current, a model was proposed by Nepf et al.
(2007) to predict the penetration depth and it gave thatδe = 0.23/(CDa ).CD was the vegetative drag coefficient and a
relatively constant value of CD = 1.1 forad ≤ 0.01 (Nepf, 1999) . With ad = 0.003
~ 0.013 for all cases in present study,CD = 1.1 was used, and the prediction gaveδe = 34.8, 5.5, 8.0, 14.9, and 13.9 cm for cases
A3, A4, A5, B2, and B5, respectively, smaller than the measured. AsNepf et al. (2007) model was built under unidirectional current
condition, its underestimation indicated that the vertical exchange of
momentum can penetrate a deeper depth within canopy when water motion
was also affected by wind-induced waves.
In present study with the hydrodynamic environment dominated by combined
wave and current, the vertical distributions of time-averaged velocity
were more similar to that under unidirectional current than waves. Under
pure wave conditions the presence of AV can alter the mean flow
structure, and a significant mean current in the direction of wave
propagation is generated within vegetation when the ratio of wave
excursion (Ew =uwmaxT /(2π), with uwmaxthe maximum velocity in wave cycle) to stem spacing (distance between
two adjacent stems, S = m -1/2) larger
than one (Luhar, Coutu, Infantes, Fox, & Nepf, 2010 ). Using
the velocity measured at the middle height within vegetation (i.e.,z = h /2 and hv /2 for emergent and
submerged cases, respectively), Ew /S =
0.03 ~ 0.3, indicating weak wave-plant interaction, for
all cases in present study (Table 1). Therefore, under combined
wave-current conditions the time-averaged velocity was determined by the
magnitude of current when the Ew /S was
small. However, the existence of waves enhanced the momentum transfer
between the canopy and its overlying water column, leading to a larger
penetration depth present within the canopy.
4.3 Wave orbital velocity within vegetation
Vertical profiles of the wave orbital velocity,Uw , for cases with vegetation were shown in
Figure 6. Measurement points with Pw_u< 10% (indicating the water motion was not affected by
surface waves) were excluded from the velocity profiles. For all
vegetated cases tested here, both the horizontal
(Uw_horiz , grey circles in Fig. 6) and vertical
(Uw_vert , blue triangles in Fig. 6) components
of wave orbital velocity decreased from the water surface to the bed. To
determine the extent to which reduction of wave velocity by the
interaction with AV, linear wave theory (i.e., eqs. (6) and (7)) was
used to estimate the natural attenuation of wave velocity with depth.
For both the horizontal and vertical components of wave velocity, the
measured Uw_horiz andUw_vert (symbols in Fig. 6) agreed with the
predictions (red and blue dashed curves in Fig. 6) through the entire
water column, suggesting that the wave orbital velocity within
vegetation was not attenuated compared with that above the vegetation or
near the water surface in present study. As noted by Low et al.
(2005) , the significance of wave orbital velocity reduction within
vegetation, for which we can call the wave attenuation in vertical
direction, can also be indicated by Ew /S ,
and this vertical attenuation by vegetation is significant forEw /S >1. WithEw /S = 0.03 ~ 0.3 in
present study, the wave orbital motion was not significantly altered by
the interaction with vegetation. This finding is similar to laboratory
measurements of flow structure within and above a model Z. marinameadow (Luhar, Coutu, Infantes, Fox, & Nepf, 2010 ) and field
observations by Hansen & Reidenbach (2013) in coastal regions.
As AV can efficiently inhibit the wave amplitude (e.g., Bradley
& Houser, 2009; Luhar, Infantes, & Nepf, 2017 ), the presence of AV
can decrease the wave orbital velocity by attenuating wave amplitude
(i.e., eqs. (6) and (7)) compared with bare bed, which we can refer as
the attenuation of wave orbital velocity in horizontal direction. The
extent to which reduction of wave amplitude was determined by the
relative velocity between vegetation and water motion and the distance
the wave propagated into the vegetation (e.g., Luhar, Infantes,
& Nepf, 2017; Mendez, Losada, & Losada, 1999; Mullarney & Henderson,
2010 ). Therefore, the attenuation of wave orbital velocity in both the
horizontal and the vertical directions should be considered to fully
evaluate the impact of vegetation on wave orbital velocity by measuring
the velocity in the vegetation region and its adjacent bare-bed region
simultaneously.
4.4 Turbulent kinetic energy within vegetation
The presence of vegetation also altered the vertical distribution of
turbulent kinetic energy (TKE ). For emergent conditions (i.e.,hv > h ), TKE was
uniformly distributed through the entire water column (i.e., cases A1,
A2, and B1 shown in Figs. 7a, 7b, and 7f, respectively) or increased
from bed to water surface (i.e., cases B3 and B4 as shown in Figs. 7h
and 7i, respectively). This distribution also occurred within the lower
part of canopy (e.g., A3, A5, and B5 in Figs. 7c, 7e, and 7j,
respectively) when the vegetation was under submerged conditions (i.e.,hv < h ). Near the top of
vegetation, TKE increased with increasing z and reached
its maximum near canopy interface, and then decreased toward the water
surface (e.g., Figs. 7c, 7d, 7e, and 7j).
Within the emergent vegetation and lower part of submerged vegetation
with Uhoriz small and uniformly distributed, stem
wakes were the main source of turbulence (e.g., Nepf & Vivoni,
2000; Zhang, Tang, & Nepf, 2018 ). Under unidirectional currents,
vortices shed behind stems when the stem Reynolds numberRed (= Uhorizd /νwith ν the water kinematic viscosity) > 120
(Liu & Nepf, 2016 ). For all cases tested here, theRed within the canopy varied between 3 and 90
(Table 1), indicating that no turbulence was generated by the
interaction of vegetation and mean current. Stem vortices by wave-plant
interaction are governed by the Keulegan-Carpenter number,KC (= uwmaxT /d ), and vortex
shedding occurs near the stem for KC > 6(Sumer, Christiansen, & Fredsoe, 1997 ). Using theuwmax measured at z =hv /2, the KC of all cases in present study
ranged 2 ~ 24 (Table 1), suggesting that the stem
turbulence was generated for some cases (e.g., B1 and B4). However, with
weak wave-plant interaction (i.e., Ew /S< 0.5) in present study the stem-generated turbulence cannot
enhance the turbulence level within canopy (Zhang, Tang, &
Nepf, 2018 ), leading to the turbulence level within vegetation for
cases with KC > 6 was not elevated compared with
cases with KC < 6. Besides, with weak wave-plant
interaction the TKE distributions near the top of vegetation for
submerged cases in present study were similar to that by pure currents
(e.g., Zhang, Lai, & Jiang, 2016; Zhang et al., 2020 ). Recall
that Uhoriz increased with increasing znear the top of vegetation. This can lead to the generation of shear
turbulence (Nepf & Vivono, 2000 ), making TKE reach its
maximum near the canopy interface and decrease toward bottom and water
surface. The presence of shear turbulence can also give explanation for
the increased TKE toward water surface for the emergent cases B3
and B4 in which the Uhoriz gradually increased
with increasing z near the water surface (see Fig. 5h and 5i).