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).