3 Methods and Materials
3.1 Vegetation measurements
The dominant vegetations of all cases in present study were Carex cinerascens , Artemisia selengensis , and Phalaris arundinacea (Table 1). For each case, 15 strains of plant were randomly selected during velocity measurement and the vegetation height (hv ), stem diameter (d ), and the blade width were measured to describe the plant morphology. C. cinerascens is a kind of herbaceous plant. It has basal blades with a mean of 12 blades for each plant. The blades of C. cinerascensare lanceolate and the blade width decreased gradually from the base to the top. According to our survey, the mean blade width was 0.3 cm.A. selengensis has rigid and cylinder-like stems with a mean diameter of 0.5 cm for each. Several stems are grown for each individual plant and these stems are divided at the base. The blades of A. selengensis are palmate and distributed uniformly from top to bottom of the stem. P. arundinacea has stem with a mean diameter of 0.5 cm, and usually 6 ~ 8 knots where blades grow are distributed for each stem. The blades of P. arundinacea are lanceolate with the length of 6 ~ 30 cm and maximum width of 1.8 cm for each. For A. selengensis and P. arundinacea , the blade width near the top of stem is smaller than that of the rest part of stem because new and fresh blades always grow at the top.
The stem density (m , stems per bed area) was measured one week after the velocity measurements when the flood had already receded to Ganjiang River and the measurement points in sites A and B were exposed to the air. For each case, the stem density was estimated by randomly choosing three 1 m × 1 m quadrats within a 5-m radius of the measurement point. As the stems of C. cinerascens are very short, its stem density was estimated as the number of blades, not individual plants, per unit area in our study. The stem density for each case was listed in Table 1.
3.2 Velocity measurements
Instantaneous velocities were collected using a 3-D Acoustic Doppler Velocimeter (ADV, Nortek Vector) in the East-North-Up (ENU) coordinate system. With ENU coordinate system the instantaneous velocities in the east, north, and upward directions can be represented asue , un , anduu , respectively. As ADV measures flow velocity at a specific point (i.e., 15 cm below the probe tip), the measurements of velocity profile need to move ADV vertically, and this was accomplished by using a self-made field observation system, which was described by Zhang et al. (2020) in detail. Velocity was recorded for 150 s with sampling frequency of 32 Hz at each measurement point. For all cases except the bare-bed case S0, velocity was measured starting from 5 cm above the bed (i.e., z = 5 cm with z = 0 representing the bed bottom) at 5 cm vertical increment. With large water depth, velocity profile of the case S0 was measured at 10 cm vertical increment to reduce the uncertainty caused by the variation of hydrodynamic and meteorological conditions (i.e., water level, flow velocity, and wind speed) during measurements. To keep too many blades from blocking the ADV beams, vegetation was removed within a 15 cm diameter of the measurement position.
3.3 Data processing
In flows with both waves and currents, the variance in velocity associated with waves is often much larger than that associated with turbulence, and some form of wave–turbulence decomposition must be performed (Trowbridge, 1998 ). For combined wave-current flow, the instantaneous velocity, taking velocity in the east direction (ue ) for example, can be decomposed into three parts:
\(u_{e}=U_{e}+u_{\text{we}}+u_{e}^{{}^{\prime}}\) (1)
in which Ue is the time-averaged velocity,uwe is the unsteady wave velocity, andue is the turbulent velocity fluctuation, and similarly for un and uu . Spikes in the velocity record were removed using the acceleration threshold method that the instantaneous acceleration (i.e., the difference between two adjacent instantaneous velocity records divided by the sampling interval) should be less than the acceleration of gravity (Goring & Nikora, 2002 ). After de-spiking, the time-averaged velocity was calculated as:
\(U_{e}=\frac{1}{T_{d}}\int_{0}^{T_{d}}{u_{e}\left(t\right)}\text{dt}\)(2)
in which Td is the time duration for each measurement point, and similar for Un andUu . As the flow direction was not the same for all cases, the time-averaged horizontal velocity,Uhoriz , was used for comparison between different cases and can be calculated as:
\(U_{\text{horiz}}=\sqrt{U_{e}^{2}+U_{n}^{2}}\) (3)
The time-averaged vertical velocity, Uvert , can then be expressed as Uvert =Uu .
In present study, a method of spectral decomposition was employed to decompose the wave and turbulent velocities. In the power spectral density (PSD) of the instantaneous velocity of flow with both waves and currents, wave signal (grey circles in Fig. 3a) is indicated as peaks around the dominant wave frequency and spectra outside the wave domain (black line in Fig. 3a) indicate the signal of flow turbulence. Velocity in east direction was used as an example to show the specific procedures of wave-current decomposition. First, the Fast Fourier Transform (FFT) of a time series of instantaneous velocity (ue (t )) is computed (labeled asFue ), and the real and imaginary parts ofFue are labeled asR (Fue ) andI (Fue ), respectively. Second, the frequency window of wave signal is chosen and the boundaries are represented as fl (low frequency boundary) andfh (high frequency boundary) (Fig. 3a). The amplitude (As =\(\sqrt{\left(R\left(F_{\text{ue}}\right)\right)^{2}+\left(I\left(F_{\text{ue}}\right)\right)^{2}}\)) and phase angle (φ ) of the signal within the wave frequency window are determined. Third, a broader frequency window (with its boundaries labeled as fL andfH ) containing the wave domain is chosen, and a straight line is fit between the amplitudes within the frequency range of fL~fl and fh~ fH . Within the wave frequency range (i.e., fl ~fh ), the interpolated amplitudes constitute the amplitudes of turbulence (At ) infl ~ fh , and the amplitudes of wave signal are computed asAw = AsAt . Percentage of wave signal amplitudes on total power energy in PSD was then estimated by\(P_{w}=\frac{\int_{f_{l}}^{f_{h}}{A_{w}\text{df}}}{\int_{0}^{F}{A_{s}\text{df}}}\)(with F (= 16 Hz) representing the half of sampling rate), andPw > 10% indicates that water motion was influenced by wind waves (Hansen & Reidenbach, 2013 ). Fourth, combined the As outside wave frequency window (i.e., f < fland f > fh ) and the interpolated amplitudes within fl~ fh , the Fourier coefficients of turbulence are determined by Ft =At [cos(φ )+i sin(φ )] assuming the phase angles are not altered. SettingAw = 0 outside wave frequency window, the Fourier coefficients of wave are determined by Fw =Aw [cos(φ )+i sin(φ )]. Fifth, the Inverse Fast Fourier Transform (IFFT) ofFt and Fw is computed to reconstruct the time series of turbulent (ue (t )) and wave (uwe (t )) velocities, respectively. Similar procedures are employed for velocities in north and upward directions. The velocity record measured near the water surface (i.e., z = 55 cm) of case A4 was used as an example to show the time series of turbulent (blue line in Fig. 3b) and wave (red line in Fig. 3b) velocity after decomposition.
The wave orbital velocity was defined as the root mean square (RMS) of the wave velocity time series, i.e.,
\(U_{\text{we}}=\sqrt{\frac{1}{T_{d}}\int_{0}^{T_{d}}{\left(u_{\text{we}}\left(t\right)-\overset{\overline{}}{u_{\text{we}}}\right)^{2}\text{dt}}}\)(4)
in which \(\overset{\overline{}}{u_{\text{we}}}\) is the time-averaged value of uwe (t ), and similar forUwn and Uwu . Considering the wave velocity in the east and north directions, the horizontal component of wave orbital velocity, Uw_horiz , was defined as
\(U_{w\_horiz}=\sqrt{U_{\text{we}}^{2}+U_{\text{wn}}^{2}}\) (5)
The vertical wave orbital velocity Uw_vert =Uwu . From linear wave theory for small amplitude, monochromatic waves, the horizontal and vertical wave orbital velocities were computed as (Dean & Dalrymple, 1991 )
\(U_{w\_horiz}=\sqrt{\frac{1}{2\pi}\int_{0}^{2\pi}{\left(a_{w}\omega\frac{\cosh\left(\text{kz}\right)}{\sinh\left(\text{kh}\right)}\cos\left(kx-\omega t\right)\right)^{2}\text{dφ}}}=\frac{1}{\sqrt{2}}a_{w}\omega\frac{\cosh\left(\text{kz}\right)}{\sinh\left(\text{kh}\right)}\)(6)
and
\(U_{w\_vert}=\sqrt{\frac{1}{2\pi}\int_{0}^{2\pi}{\left(a_{w}\omega\frac{\sinh\left(\text{kz}\right)}{\sinh\left(\text{kh}\right)}\sin\left(kx-\omega t\right)\right)^{2}\text{dφ}}}=\frac{1}{\sqrt{2}}a_{w}\omega\frac{\sinh\left(\text{kz}\right)}{\sinh\left(\text{kh}\right)}\)(7)
respectively, in which aw is the wave amplitude near the water surface, ω (= 2π /T with T the wave period) is the wave radian frequency, k (= 2π /λ with λ the wave length) is the wave number,h is the water depth, and z is the vertical coordinate. The instantaneous turbulent fluctuations (σe ,σn , σu ) were defined as the standard deviation of the reconstructed time series of turbulent velocity (ue (t ),un (t ),uu (t )), and the turbulent kinetic energy (TKE ) is expressed as:
\(TKE=\frac{1}{2}\left(\sigma_{e}^{2}+\sigma_{n}^{2}+\sigma_{u}^{2}\right)\)(8)
The horizontal and vertical TKE can then be expressed asTKEhoriz = (σe 2+σn 2)/2 and TKEvert =σu 2/2, respectively.
For each case, the wave amplitude, aw , was estimated by fitting the measured Uw_horiz to eq. (6) at the highest three measurement points. The peak frequency (fp ) of the wave domain in the PSD of instantaneous velocity was used to determine the wave period, i.e.,T = 1/fp . Based on the linear wave theory, the wave length (λ ) can be estimated using the relationship ofω 2= (kg )tanh(kh ) with g representing the gravitational acceleration. Wave parameters for each case are listed in Table 1.