This study investigated a single location within the mangroves. To obtain the vertical velocity profile in the mangrove trees, we used a three-dimensional acoustic Doppler velocimeter (ADV) (Nortek Vector, Norway) installed on a mobile frame to obtain single-point measurements at different heights above the bed of mangroves. This ADV can accurately measure the three components of the flow velocity of a sampling volume (using a cylinder with a diameter of approximately 15 mm and a height of 15 mm) at a distance of 15 cm from the probe. The range of the velocity measurements for the instrument was set to between 0 and 0.1 m/s. The measuring accuracy is 0.5% of the measurement value, and the measurement noise of the instrument is less than 1 mm/s. To obtain the profile information of the flow velocity, we developed a stainless steel observation frame (Chinese Patent No. ZL20130278911.6) that can rise and fall according to pre-selected heights once the tidal depth is sufficient. The ADV was carried by the lifting frame to observe the vertical profile. The heights of the fixed point observations are illustrated in Fig. 2a and the heights are relative to the bed of the flat.

The lifting frame is primarily made of non-magnetic stainless steel, which does not cause magnetic interference with the instrument. Electronic parts are watertight and can work under 1–2 m of water. This instrument mainly consists of five parts (Fig. 2b): (1) a support frame; (2) a transmission device that can drive the repetitive up and down motions of the instrument and can remain at a series of set heights for 5 min so that the device can complete fixed-point observations at a high frequency; (3) a platform for carrying the devices; (4) a battery compartment; and (5) a water level switch (20 cm from the bottom).

To determine the effect of mangrove plants on the vertical velocity profile, we selected the time period of the spring tides on June 19–20, 2011, to observe the tidal flows. To deploy the automatic lifting system, an area with a low canopy closure was selected so that the frame could fit into the space between the mangrove trees (Fig. 2c). The basic description of the site follows as: The lifting frame was placed at a low elevation bed without mangrove trees, and the distance between the lifting frame and the surrounding plants was approximately 1 m (Fig. 2a). The ADV sensor was positioned less than 50 cm from the adjacent trees, which allowed the measurement of the plants’ impact. The biological properties of the vegetation, including the vegetation height, canopy properties and vegetation spacing, were also measured in situ using measuring tapes. The bottom of the mangrove canopy was approximately 90 cm higher than the bottom of the lifting frame, the upper part of the canopy was approximately 180 cm high above the bed, and the central region of the canopy (i.e., the part where the leaves are the densest) was approximately 120 cm high above the bed. The ADV repeatedly moved up and down on the lifting frame (Fig. 2a). The observation heights were set at 10, 40, 70, 100 and 130 cm above the bed (same as the bottom of the mangrove trees), and the ADV remained at every height for 5 min while continuously sampling at 16 Hz to obtain three-dimensional data of the flow velocity (Fig. 2a).

It is worth noting that when the water reached the water level switch, the transmission device began to operate, and the instrument performed an observation by moving from the highest position to the lowest position. Because the instrument moved faster than the rate of a water level rise, we only obtained effective data in the middle period of the tidal cycle.

The time series of pressure and flow velocity data was output from the ADV, and the pressure data were converted to water level data. On the basis of the water level variation, the time series (5 min) of the flow velocity of each fixed point was extracted. The components of the flow velocity at each fixed point were rotated horizontally based on the main direction of the flow to obtain the velocity components u, v and w, where u is the flow in the main flow direction, v is the flow perpendicular to the main flow direction, and w is the upward flow. Before we calculated the mean velocity at the fixed location, we adopted the phase-space thresholding method developed by Goring and Nikora (2002) to denoise the original data. The water level at the fixed point was converted from the average water depth measured by the ADV pressure probe by adding the height difference between the pressure probe and the ADV measurement point.

Because the vertical movement of the instrument is uniform and slow, except for the data collected at the fixed points, the flow velocity data of the moving segments can be extracted based on the movement pattern of the instrument (each movement segment was 2 min). The horizontal flow velocity components were extracted, and the average value was obtained by rotating the component based on the main direction of the flow to supplement the results of the fixed points.

To analyze the turbulence, the instantaneous flow velocities (u, v, w) can be decomposed into the time-average flow velocities (U, V, W) and the fluctuating velocities (u_t, v_t, w_t), such as u=U+u_t. The turbulence intensities (i_u, i_v, i_w) are defined as the root-mean-square of the fluctuating velocity (Neumeier and Amos, 2006) and are calculated as follows:

The turbulent kinetic energy (TKE) (Neumeier and Amos, 2006) is calculated as follows:

where ρ is the liquid density. The three-dimensional Reynolds stress $\tau _{xyz}$ (Neumeier and Amos, 2006) is calculated as follows:

In addition, we use an autocorrelation function to calculate the energy spectral density of the three components separately.

Although the measurements lasted from the middle to spring tidal cycle, the water only reached the mangrove canopies during the spring tides to form a complete vertical profile record. Thus, we only used the data from June 19–20, 2011, when the spring tides occurred. The water levels are shown in Fig. 3, which includes a nighttime tide (Fig. 3a) and a daytime tide (Fig. 3b). The highest water level during the nighttime tide is approximately 170 cm above the bed, the average water level during the observation is 145 cm, and the average water level during the daytime tide is 80 cm. The difference in the average water level between the two tidal cycles is 65 cm; the water level reaches the canopy of the trees during the nighttime high tide, whereas it fails to submerge the canopy during the daytime high tide. On the basis of the change in the water level and the vertical biological characteristics of the plants, we divide the mangrove trees into three parts: the near-bottom part, which is composed of bare mudflat and sparse aerial roots or long hypocotyls of seedlings (0–15 cm), the trunk layer (15–90 cm) and the canopy (above 90 cm) (Fig. 1c).

Figures 3c and d show the horizontal flow velocity at different heights during the nighttime and daytime high tides, respectively, and the fit to the velocity data during the nighttime high tide. The flow velocity is very low over all of the mangroves. During the nighttime high tide, the flow velocity is less than 4 cm/s, and the flow velocity near the bottom is approximately three times that in the canopy. During the daytime high tide, the flow velocity on the bottom is less than 1 cm/s (Table 1). The directions of the flow velocity at different time and at different locations are shown by the arrows in Fig. 3a. The flow direction is essentially consistent beneath the canopy, and there is an apparent deflection in the flow direction within the canopy.

To present the final results, we calculated the average horizontal flow velocity at the fixed points and used the standard deviation as the error to plot the velocity profile (Fig. 4a, Table 1). In the vertical distribution of the flow velocity under the canopy, the flow velocity decreases as the height increases, and the vertical velocity profile exhibits an inverse logarithmic distribution. Near the bottom, the standard deviation of the flow velocity is relatively large; in the middle trunk layer, the data of the flow velocity tend to converge. On the basis of the average data obtained inside the canopy, which are relatively limited, the flow velocity inside the canopy tends to decrease slightly in comparison with the bottom of the canopy.

To supplement the data of the flow velocity at a fixed point (Fig. 4), the horizontal flow velocities of the moving segments can be joined together to form another set of profiles of the flow velocity due to the limited influence of the slow vertical velocity (30 cm in 2 min) on the horizontal flow velocity, as shown in Fig. 4b. Because the change in the water level is very limited, we can approximate the velocity profile as being measured at the same time. The profile of the flow velocity in the vertical direction after the combination essentially matches the reverse logarithmic distribution. The flow velocity near the canopy is very low (much less than 1 cm/s), and it approaches a consistent flow in the vertical direction. In the trunk part, the horizontal flow velocity decreases linearly with the increasing height. The flow velocity is the highest at the bottom, and the points of the flow velocity are relatively scattered. It is worth noting that a reverse gradient of the flow velocity is sometimes observed at the bottom (Fig. 4b, bottom right corner), which could be caused by the root system at the bottom of the mangroves, resulting in a decrease in the flow velocity near the bottom.

The flow structure over the bare mudflats is consistent with the theory of a turbulent boundary layer, the vertical flow velocity essentially agrees with a semi-logarithmic distribution (Soulsby, 1997), and the overall profile of the flow velocity has a J-shape (Fig. 8a).

When herbaceous plants appear on a tidal flat (such as Spartina) (Fig. 8), the features of the boundary layer at the bottom will change (Leonard and Luther, 1995; Shi et al., 1995; Leonard and Croft, 2006; Neumeier and Amos, 2006); the main variation is the decrease of the flow velocity in the canopy of the plants. Because the biomass of herbaceous plants is denser at the bottom than at the top, the flow velocity increases with the increasing height, but the mean flow velocity generally decreases (Fig. 8b).

Because there is a certain distance between the canopy and the bottom of the mangrove trees, the observed flow velocity feature in the boundary layer at the bottom of the mudflats with mangrove trees has a pattern in which the flow velocity below the canopy decreases as the height increases (Fig. 8c). Previous studies have found that in vegetated tidal flats, the reduction of the flow velocity is mainly caused by the resistance of the plants (Mazda et al., 1997; Furukawa et al., 1997; Nepf, 1999). Flow in the mangroves is affected not only by the bottom of the tidal flat but also by the vertical variation of the biomass of mangrove trees. In this study, we use the horizontal shear stress to estimate the resistance to flow at different heights (Thompson et al., 2003):

The results indicate that from the bottom to the canopy, the shear stress increases from 0.148×10^–3 to 1.91×10^–3 N/m² (Table 1). The profile of the flow velocity in the mud flats is assumed to follow a semi-logarithmic distribution (Soulsby, 1997); however, the observed profile of the vertical flow velocity shows an inverse logarithmic distribution in the range of the mangroves. The shear stress near the canopy is one order of magnitude higher than that in the near-bottom region, which results in the inverse logarithmic velocity profile shown in this study.

Compared with studies that have focused on the reduction of the flow velocity caused by vegetation, only limited field observations have been conducted on the energy attenuation within tidal flats with plants. The observations of Leonard and Luther (1995) indicate that the turbulence intensity on sparse Spartina alterniflora flats is one order of magnitude lower than that on the bare mudflats and the turbulence intensity of dense Spartina alterniflora flats is two orders of magnitude lower than that on the bare mudflats. The in situ observations of Neumeier and Amos (2006) in the Ria Formosa lagoon in Europe indicate that in submerged Spartina, the turbulent energy tends to be identical in the vertical direction within the canopy of plants; i.e., there is little variation from the bottom to the top. Above the canopy, the turbulence of the water is not affected by the plants, and the turbulent energy increases rapidly. On the bare mudflats, the turbulent energy increases from the bottom to the surface of the water (Soulsby, 1997). According to research results from a laboratory flume, due to the influence of rigid plants, the turbulent energy is lower at the bottom. As the height increases, the energy increases to a maximum on the top interface of the plants and then begins to decrease (López and García, 2001). This is significantly different from the spatial distribution of the turbulent energy for the mangrove trees observed in this study. The flume experiment mainly calculates the turbulent energy based on the vertical transfer of a momentum, and the model considers the plants to be vertically uniform. However, the bottom part of natural mangrove trees contains aerial roots, the middle part is the rigid trunk, and the upper part is the flexible canopy. The turbulence is generated at the interfaces between the trunk and the roots and between the trunk and the canopy. For this specific interface, the vertical transfer of momentum will be intensified, and strong turbulence usually appears, similar to the top interface of herbaceous plants (Neumeier and Amos, 2006). In addition, due to the presence of the root system and plant leaves, some small-scale vortices related to the characteristics of the plant itself could form and increase the turbulence intensity (Nepf, 2012). However, a comparison between a bare mudflat and a mangrove boundary showed that the mangroves generally dissipated turbulence rather than generating more turbulence (Chen et al., 2016).

The energy spectrum within mangrove trees is also different from those in the bare mudflats and salt marshes (Fig. 9). The energy density on the bare mudflats decreases with increasing frequency and follows a power-law pattern (Fig. 9; bare mudflat). The energy spectrum characteristics of a sparse salt marsh and a dense salt marsh are similar to those of a bare mudflat, but the salt marsh’s energy density is generally lower than that of the bare mudflat (Fig. 9). The dissipation of a high frequency turbulent energy still follows a power-law behavior with a slope of –5/3 (Leonard and Luther, 1995).

In contrast, the energy density distribution in the mangrove trees observed in this study is significantly different from that of the aforementioned three cases when the water level reaches the canopy (Fig. 9). The high-frequency energy density decreases substantially within the trunk and canopy parts, and the slope is much less than –5/3, which indicates that the canopy of the mangrove trees can effectively absorb the high-frequency turbulent energy. However, in the near-bottom part of the mangrove trees, the energy density spectrum follows the –5/3 power law, which indicates that the energy dissipation in this part is different from those in the other two parts. When the water level does not reach the canopy of the mangrove trees, the energy density distribution of the mangrove site is similar to that of a salt marsh and follows a classic power-law dissipation. However, when the water level reaches the canopy, the high-frequency part decreases rapidly, which disrupts the power-law dissipation. In such circumstances, there is an obvious peak at approximately 0.8 Hz in the low-frequency part, which corresponds to a wavelength similar to the canopy width of the mangrove trees and the space between the mangrove trees; this is likely caused by the plant geometry and the spatial arrangement of the trees. This further supports the concept that there is a difference between the canopy and the near-bottom part of the mangrove trees in terms of energy dissipation (James et al., 2006; Chen et al., 2016).