For a certain flowing cross-section, the momentum
of the water body on cross-section is constant. The
momentum of floodplain will increase, and the
momentum of main channel will be reduced. The
momentum exchange of lotus-root-shape channel
floodplain is more intense than that of the straight
channel. The momentum transferred from former
main channel to floodplain will be large inevitably, so
that the momentum of the main channel on lotus-root-
shape channels decreases more, and the increase in
amplitude of the momentum on floodplain is
relatively larger. Therefore, the floodplain velocity
ratio of lotus-root-shape channel is larger than that of
the straight channel. When the water depth of
floodplain is small, due to the larger floodplain
resistance, a considerable part of the reduced
momentum of the main channel is used to overcome
the floodplain resistance, and the actual momentum
obtained on the floodplain decreases. In the case of
basically equal water depths of the two channels, the
reduced momentum of main channel on lotus-root-
shape channel is larger than that of the straight
channel. It is shown that on the one hand, the main
channel of the lotus-root-shape channel reduces the
momentum more, and the floodplain indicates more
increased momentum; On the other hand, when the
momentum of the main channel of the straight
channel is reduced, the momentum of floodplain is
also less increased. Among the reduced momentum
of the main channel of the straight channel, the
momentum used to increase the velocity of floodplain
is less weighted relative to the remaining momentum
of the main channel. However, in the reduced
momentum of the main channel in the lotus-root-
shape channels, the momentum used to increase the
flow velocity of floodplain has a greater weight in the
remaining momentum of the main channel. When the
water depth of floodplain is relatively small, the
weight of the two channel types differs greatly, which
is expressed in the flow velocity ratio of floodplain,
i.e., the difference in floodplain velocity of lotus-root-
shape channels is greater than that of the straight
channel. With the increase of water depth on
floodplain, the difference in weight between the two
channels gradually decreases, and the difference in
floodplain velocity ratio also gradually decreases.
3.3 Vertical Velocity
There are some differences between the vertical
velocity distribution of lotus-root-shape compound
channel and the straight channel, which is mainly
manifested near the interface of floodplain. The
vertical velocity distribution of the straight channel is
large in the middle and small at two ends, while that
of lotus-root-shape channel basically shows the
characteristics of larger on the top while small at the
bottom, but the distribution is relatively uniform.
According to preliminary analysis, the momentum
exchange of floodplain in the straight channel is only
concentrated in a certain depth below the water
surface, which reaches the maximum at the water
surface and gradually weakens downward. This
exchange method determines that the vertical velocity
distribution is large in the middle, while small on
surface and bottom. However, in the lotus-root-shape
channels, almost the entire vertical line from water
surface to the bottom participates in the floodplain
momentum exchange, which is mainly due to the
strong momentum exchange of floodplain in lotus-
root-shape channels. The momentum exchange
process ensures that the main water body channel
with larger momentum entrains the floodplain water
body with less momentum into the main channel
water body. In addition, the main water body channel
with larger momentum in equivalent volume enters
the floodplain water body, which leads to the increase
of floodplain water body momentum. According to
the principle of conservation of momentum, it can be
shown that the momentum of main channel water
body will decrease. Due to the large difference in the
flow velocity of floodplain water body (especially
when it starts to diffuse), for the entrainment of main
water body channel on floodplain water body, almost
the entire vertical water body above the floodplain
bed surface participates in such exchange. It can be
seen from the rapid increase of floodplain flow
velocity that such exchange of massive water body
causes a sharp decrease in the momentum of the upper
water body of the main channel. The momentum
difference between the lower and upper water bodies
of the main channel becomes large sharply, so that the
upper and lower water bodies will inevitably generate
momentum exchange. This results in most of the
water bodies on the vertical line of the main channel
participating in the momentum exchange. The result
of this momentum exchange is the redistribution of
the momentum throughout the entire vertical line of
the main channel. In the vertical distribution, the
velocity is relatively uniform with small gradient, and
the distribution still shows the characteristics of larger
on the top and lower at the bottom, but the velocity
value of the entire vertical line decreases. It should be
noted that although there is also momentum exchange
in the vertical direction of water body of the straight
channel, the momentum exchange in the floodplain is
smaller than lotus-root-shape channel. Meanwhile,
momentum exchange is also gradual in the vertical