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 = As –At . 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.