The coverage percentage of plants as well as their location in the river cross-section influence on channel blockage (Green 2005; O’Hare 2015) and sediment deposition (Västilä and Järvelä 2018). Przyborowski et al. (2018a) showed that patches of Potamogeton pectinatus L. varied due to bed conditions and also, that an individual plant patch had a very limited impact on the flow. The present study shows that single patches of two similar species may have varying effects on the local flow field, given the major difference in the aspect ratio between these patches, which is consistent with the Nikora et al. (2008) research about the physical vegetation parameters as roughness descriptors. The obtained results of velocities and turbulence intensities downstream of M. alterniflorum (Figs. 2, 3) were in line with those of Hu et al. (2018). In particular, the water velocity in the plant wake was diminished roughly by half, which showed that the patch did not completely block the flow (Fig. 2). Downstream of M. spicatum, of which diameter was at least three times larger and the stems visually covered the whole area densely, the results showed strongly increased, in comparison with M. alterniflorum, lateral shear below its maximal height. Another significant difference between the results was decreased turbulent kinetic energy observed close to the bed; at the same distance downstream, the decrease in turbulent kinetic energy was better pronounced in the case of the M. spicatum patch (Fig. 4). On the other hand, quadrant analysis showed the same trends in occurrence of the secondary currents downstream the both patches.
Effect of patch geometry on downstream turbulence
The turbulent kinetic energy (TKE) was elevated in majority of points downstream of M. alterniflorum (Fig. 4). However, in the downstream profile 1 at Z/H = 0.3, i.e., below the maximum height of the canopy TKE was reduced, where Hu et al. (2018) showed that TKE should be increased in this layer as a sign of elevated shear stresses. In the case of M. spicatum, at the maximum canopy height, TKE was similar to the profile upstream like in the case of the first patch, profile 1 (Fig. 4). For both plants, the TKE inside the wake, i.e., below Z/H = 0.2, was reduced, in comparison with the values above (Fig. 4), similarly to the experiments of Hu et al. (2018). The differences in the magnitude of TKE at plant height might be caused by the vertical distribution of patch density, where the majority of the stems did not reach the maximum height of the canopy (Fig. 8). Thus, these results were similar to those observed by Sukhodolov and Sukhodolova (2012), where the TKE profile bias, which indicated cumulative effect of mixing and boundary layers, grew with the density of the vegetation.
The position of the measurement profile close to the M. spicatum lateral edge had impact on observed turbulence intensities and tangential Reynolds stresses, as it is closer to the plant flow lateral boundary. The highest observed peak at Z/H = 0.25 in both, longitudinal and transverse turbulence intensities, which peak also appeared in \(\left| {\overline{{u^{{\prime }} v^{{\prime }} }} } \right|\) stress, indicated the presence of a lateral shear layer (Rominger and Nepf 2011). In comparison with M spicatum, downstream of M. alterniflorum patch, \(\left| {\overline{{u^{{\prime }} v^{{\prime }} }} } \right|\) and \(\left| {\overline{{v^{{\prime }} w^{{\prime }} }} } \right|\) stresses showed about five times smaller lateral transport of momentum at Z/H = 0.4 in the first downstream profile, which corresponded to the upper part of the plant and in a lower point, i.e., Z/H = 0.25, in the second profile (Fig. 5). That difference between produced shear was the direct result of the distinct spatial dimensions of the patches (Ortiz et al. 2013).
Similar results as those presented in the paper, showing increased Reynolds stresses, were obtained by Biggs et al. (2016) in an experiment with a Ranunculus penicillatus patch; however, the \(\left| {\overline{{u^{{\prime }} w^{{\prime }} }} } \right|\) shear stress was also elevated, in contrast to the present study, which may be due to differences in bed structure, i.e., sand versus gravel/cobbles. The comparison of the observed \(\left| {\overline{{u^{{\prime }} w^{{\prime }} }} } \right|\) stress and corresponding to it turbulence intensities do not support the presence of vertical Kelvin–Helmholtz vortices in either of patches, phenomenon which was described, e.g., by Nepf (2012b). The cause of such result may be wavy motions of plant stems, which is in line with results obtained by Ghisalberti and Nepf (2006), who observed that an increase in the variability of vegetation height resulted in decreased shear stress.
The PSDs of both the longitudinal and vertical velocities in a wake should have distinct peaks at lower frequencies, marking the passage of vortices. In the case of the occurrence of a mixing layer, the spectral density should be higher than that in the free flow (Ghisalberti and Nepf 2006; Sukhodolov and Sukhodolova 2012). Such phenomenon occurred in the case of the M. spicatum patch, where a distinctive peak in the turbulence intensity (Fig. 3) translated into the higher energy visible in the PSD from that point. In this experiment, the PSD showed peaks similar in magnitude at lower frequencies; however, at higher frequencies, energy dissipated faster in the downstream profile closer to M. alterniflorum, than in the profile farther away (Fig. 6), where the turbulence intensity was elevated (Fig. 3). This indicated that the energy transport in profile 2 downstream was the same as in the free flow, but with increased mixing.
The main differences between complex natural vegetation and simplified rigid laboratory studies
The present study showed that differences in turbulent statistics describing phenomena such as a mixing layer were not as clearly distinguishable as in flumes with rigid rods (Chen et al. 2013). However, such a comparison of artificial rigid patches to real flexible vegetation has limitations. Ortiz et al. (2013) showed that flexible patches have much lower impact on the flow than its rigid counterpart. What is more, there are major differences in biomechanical properties between rigid and flexible materials, which influence plant responses to flow and thus, flow resistance (Łoboda et al. 2018a). For instance, lower flexural rigidity indicates that the plant bends and moves with the flow and thus, decreases its frontal area (Nikora 2010). Additionally, for real patches of vegetation, the majority of species such as Myriophyllum have stems reaching far beyond the area of the roots, floating above the bed, as was depicted in Siniscalchi and Nikora (2013). Therefore, it is difficult to compare the number of stems per unit bed area. Moreover, the ratio of water depth (H) to patch height (h) was considered shallow in the present case (H/h ~ 2), although there was no solid upper boundary of the patches, as observed in laboratory studies (e.g., Chen et al. 2013), thus expected velocity gradient downstream the patch was not pronounced.
In the present study, quadrant analysis at points in the wake of M. alterniflorum revealed that ejections were diminished in favor of inward and outward interactions. This behavior implies that the energy of ejections was allocated to the force needed to lift the patch canopy or that the flow in the wake was returning to its ambient state by inflow from the high-speed free flow layer above.
Limitations of the present study and future directions
One possible reason for the substantial difference in the power spectral density results for M. spicatum (Fig. 6) may be the noise contamination of the signal. Brand et al. (2016) depicted how PSD values differ when using certain bins, due to different noise contributions connected to the SNR level. Although bins were chosen using the best mean SNR in the present study, the noise contribution was found to affect higher frequencies. An effect of noise was also visible in the increased contribution of longitudinal velocity fluctuations in the quadrant analysis of point downstream of M. spicatum (Fig. 7). On the other hand, the used SNR and correlation thresholds were the same as in field experiments conducted by Cassan et al. (2015) or Afzalimehr et al. (2017), and with the used filtering procedure, the obtained results were not below accepted requirements. Though, a caution in generalization of the presented interpretation is advised due to a scarcity of similar experiments.
Nikora et al. (2008) and Cornacchia et al. (2018) showed how dimensions of aquatic plants and their positions in the river channel determine their impact on the flow. The presented outcomes of two distinct patches showed how big influence on water mixing may have patch dimensions. However, without further downstream profiles and accurate plant density values it is impossible to determine, whether the M. spicatum canopy resembles one of the patches used in laboratory studies such as in Zong and Nepf (2012), where vortex street was generated. What is more, patches with enhanced horizontal flow deflection, i.e., which are denser and with lower submergence ratio, should produce greater velocity gradient at patch edge and therefore changing the sedimentation process, while wide patches, i.e., patch width/h > 4 produce vertical deflection (Ortiz et al. 2013). However, the results of the present study, were not sufficient enough to prove this relationship, but we do believe that additional field measurement of velocity profiles at the edges of the patches of different dimensions will provide valuable information about this interaction, which finally should help in building advanced hydrodynamics flow-biota models.
In the perspective of river ecology, the existence of a large patch promotes increased sedimentation in its wake (e.g., Cotton et al. 2006; Ortiz et al. 2013) and stimulates further growth downstream (Cornacchia et al. 2018). The question arises of whether impact on the flow and the sediment of wide patches is equal to the impact of more slender ones, assuming that the covered area of the patches is the same. Further case studies including plant growing in different configurations with a denser grid of velocity profiles, sediment traps and biomechanical tests of aquatic plants should provide relevant data to unify vegetated flow models and the impact of patch characteristics on river morphology.