3.3 Relationship between total sand transport rate and friction
velocity
The total sand transport within 70 cm height was obtained by summing the
sand transport of each layer within 0~70 cm height, and
then the total sand transport rate near the surface under different
combinations of ridge height and spacing was calculated. The results
show that under different ridge structures, the total sand transport
rate increases with the increase of friction velocity, which conforms to
the power function distribution, and the correlation of most ridge
structures is higher than 0.9 (Fig. 4). With the increase of ridge
spacing, the total sand transport rate increases rapidly, but the change
of total sand transport rate with ridge height does not show a certain
regularity. Compared with no ridges, the total sand transport rate under
different ridge structures is lower when the friction velocity is 0.34
m·s-1 and 0.42 m·s-1. When the
friction velocity increases to 0.51 m·s-1, the total
sand transport rate of a few ridge structures with large ridge spacing
increases rapidly, which has exceeded the total sand transport rate
without ridge. When the friction velocity continues to increase, the
total sand transport rate of all ridge structures with a ridge spacing
of 25H has exceeded that of no ridge.
This is because compared with the uniform bed with smooth surface, the
take-off angle and saltation height of sand particles on the rough bed
are significantly increased (Ding, 2010). When there is a ridge, the
subducted sand particles rebound violently on the ridge, which not only
increases the amount of sand transported in the upper airflow, but also
the resistance to airflow decreases as the sand particles fly farther
during the flight. The sand saltation height and horizontal distance are
small on smooth bed surface. The sand particles are close to the ground
in the transportation process, and the sand transport rate in the lower
layer increases greatly, which increases the energy consumption of the
airflow near the ground and weakens the transportation capacity of the
airflow. Therefore, under a certain wind force, the sand transport rate
on the loose bed with no ridges is smaller than that with ridge
coverage. This phenomenon is also common on the Gobi surface covered
with gravel (Zhang et al., 2007).
DISCUSSION
When there is no ridge, the sand transport rate decreases with the
increase of height in a power function law. Under different ridge
structures, the change of sand transport rate with height shows two
trends. One is that the sand transport rate decreases exponentially with
the increase of height. The other one shows an ”elephant nose” effect,
which is similar to the drifting sand flux structure in Gobi desert, as
the near surface sand transport rate increases with the increase of
height, and decreases exponentially above a certain height.
When the surface friction velocity exceeds the critical friction
velocity of sand movement, the sand particles are separated from the
surface and enter the airflow by the lifting power of wind. The movement
of sand particles in drifting sand flux is very complex, which is not
only affected by the airflow field, but also by the sand particle size,
sand shape, environmental humidity and temperature (Neuman and Maljaars,
1997; Wiggs et al., 2004). Among them, the velocity of sand particles
reflects the kinetic energy changes of airflow field and drifting sand
flux in the process of sand movement, which has an important influence
on sand transport process (Sharp, 1964; Zou et al., 2001). When the
friction velocity is low, the surface wind pressure is also low, only a
few sand particles leave the surface and begin to move, and the movement
speed of sand particles is very slow. Because the average saltation
velocity of sand particles is power function distribution with the
saltation height (Zou et al., 2001; Dong et al., 2004; Yang et al.,
2007), when the saltation height of sand particles is very low, the sand
transport rate is small, and the percentage of sand transport in the
lower layer is large. When the friction velocity increases, more sand
particles leave the bed and begin to move. Because the resistance of
sand particles in the movement process is small, they still have
considerable momentum when they falling to the bed. Therefore, not only
the falling sand particles themselves may rebound and continue to move,
but also part of the sand particles around the falling point can splash
into the motion state under its impact, and then cause a series of chain
reactions. When the saltation motion state of sand particles in the
drifting sand flux is stable, the amount of sand particles initiated by
the direct effect of wind can be ignored, and the sand particles in the
drifting sand flux mainly taking off due to the impact collision effect
(Anderson and Haff, 1991). Because the impact velocity of sand particles
increases with the increase of friction velocity, the movement velocity
and height of sand particles also increase with the increase of friction
velocity. For the above reason, the larger the friction velocity, the
larger the sand transport rate, the higher the proportion of sand
transport in the higher height level. However, the sand movement mainly
occurs in the limited height near the surface (Shao and Li, 1999; Kok
and Renno, 2009), the proportion of sand transport in the near surface
height layer is much larger than that in the higher height layer under
different friction velocities.
Due to the influence of ridge, the wind velocity near surface decreases,
the total sand transport decreases, the sand transport in the lower
layer decreases as a whole, while the sediment concentration in the
upper layer changes relatively little, and the surface sand transport
rate decreases exponentially with the increase of height. This is due to
the variation of drifting sand flux structure caused by the influence of
underlying surface (Ma, 1988). Taking a ridge height of 5 cm as an
example, the drifting sand flux structure of five ridge spacings under
different experimental wind velocities conforms exponential
distribution, which can be expressed by the formulaq =A exp(-Bh ). Haas et al. (2004) pointed out in the
study on the vertical distribution of surface sand transport rate of
dunes in Tengger desert that the fitting coefficient A refers to
the near surface sand transport, and B refers to the decreasing
rate of surface sand transport rate with height. It can be seen that
with the increase of wind velocity the value of A increases
continuously, and the change of B value is not obvious. When the
ridge spacing is 5H, the friction velocity increases from 0.42
m·s-1 to 0.68 m·s-1, the value ofA increases from 0.003 to 0.056, and the value of B first
increases and then decreases. This shows that the sand transport rate
increases continuously within the height of 0~10 cm on
the surface, and the decreasing rate of sand transport rate with height
increases first and then decreases. When the friction velocity is 0.68
m·s-1, the ridge spacing increases from 5H to 25H, the
value of A increases from 0.056 to 6.696, and the value ofB changes little. That is, when the ridge height is 5 cm, the
sand transport rate within the height of 0~10 cm
increases with the increase of ridge spacing, and the decrease rate of
sand transport rate among the five ridge spacings with height does not
change significantly.
There are two reasons why the surface drifting sand flux structure
covered by ridges has the ”elephant nose” effect which is similar to
that on Gobi surface. One reason is that, the sand transport in the low
height layer is greatly affected by the ridge, especially for the
structure of the last row ridge in the downwind direction which is close
to the sand sampler. Due to the barrier action of ridges, the sand
particles with low saltation height between ridges can not reach the end
of the sample trough, so the sand transport in the low height layer
mainly comes from the wind erosion of the bed surface behind the last
row of ridges. With the increase of height, the mean diameter of wind
erosion sediment decreases. Compared with coarse particles, fine
particles have long transport distance and large transport height (Arens
et al., 2002). Therefore, a large number of saltation fine particles
from upwind ridges can reach the end of the sample trough, which
increases the sand transport rate of the middle height layer of the sand
sampler. The second reason is that, the collision properties between
sand and ridge is different from that between sand and bare soil. Qu et
al. (2005) considered that the ”elephant nose” effect of the drifting
sand flux structure on the Gobi surface is because the Gobi surface is
mainly composed of gravel with large compactness, and the collision
between moving particles and the surface is similar to elastic
collision, resulting in large take-off angle and initial velocity of
sand particles. When sand particles move to a higher space, they can
make more use of the energy of high-level air flow, while the collision
between sand particles and bare soil is opposite. Through field
observation, Bagnold (1941) found that the maximum saltation height of
sand particles can reach 2 m in gravel area, while the maximum saltation
height of sand is 9 cm on the sandy surface. There is a certain
similarity between the surface of ridge cover and the surface of Gobi.
The ridge model is a rigid barrier, and the saltation particles are
elastic collision when they collide with it. After the collision, the
sand particles can rebound higher and farther, and make full use of the
energy of the high-level air flow, resulting in the drifting sand flux
mainly concentrated near the ridge height, which is similar to the
”elephant nose” effect of the Gobi surface.
Compared with no ridges, the transport height of sand particles
increased. Under most ridge structures, the sand transport height
reached a height layer of 60~70 cm. Since more than 90%
of the saltation sand particles transport within the height of 30 cm
near the surface (Ding, 2010), the sand particles in the higher layer
are mainly suspended. This also proves the conclusion of Fryear and
Saleh (1993) that the variation of saltation sand transport with height
follows a power function distribution law, while the suspension follows
an exponential function distribution.
CONCLUSIONS
Using wind tunnel experiments, we measured the near-surface drifting
sand flux structure and sand transport rate with different combinations
of height and spacing for non-erodible ridges. The results show that:
(1) Under the condition of no ridges, the sand transport rate within the
height of 0~70 cm above the sand bed decreases with the
increase of height, but the decline rate between each height layer is
becoming smaller and smaller. With the increase of friction velocity,
the sand transport rate continues to increase, and the proportion of
sand transported in the drifting sand flux layer near the bed decreases
relatively, and the proportion of sand transported in the upper layer
increases accordingly. More than 97% of the sand transport is
concentrated in the height of 0~10 cm, the sand
transport rate decreases with the increase of height in a power
function. (2) The sand transport rate at 0~70 cm height
with different ridge structure increases continuously with the increase
of friction velocity, while the change of sand transport rate with
height can be divided into two cases. One is that the sand transport
rate decreases with the increase of height, and the fitting relationship
between surface sand transport rate and height deviates from the power
function law with no ridges, but mostly conforms the exponential
function law of particle distribution of reaction saltation. The second
one is that the sand transport rate increases with the increase of
height below a certain height, and decreases with the increase of height
above the certain height, showing the ”elephant nose” effect similar to
the drifting sand flux structure in Gobi desert. (3) The total sand
transport rate in 0~70 cm height increases with the
increase of friction velocity, which conforms to the power function
distribution. With the increase of ridge spacing, the total sand
transport rate increases rapidly, but the change of total sand transport
rate with ridge height does not show a certain regularity. When the
friction velocity is low, the total sand transport rate under different
ridge structures is lower than that with no ridges, but when the
friction velocity and ridge spacing are high, the total sand transport
rate of some ridge structures exceeds that with no ridges.