Impact of turbulence on aeolian particle entrainment: results from wind-tunnel experiments

Abstract

We hypothesize that large eddies play a major role in the entrainment of aeolian particles. To test this, wind-tunnel experiments are carried out to measure the particle entrainment rate for various sizes and flow conditions. Wind-tunnel flows are usually neutrally stratified with no large eddies, which are typically seen in convective atmospheric boundary layers. Here, a novel technique is applied, by deploying a piece of randomly fluttering cloth, to generate large eddies similar to convective eddies, here referred to as quasi-convective turbulence. The characteristics of quasi-convective turbulence are analyzed with respect to neutral turbulence in the Monin–Obukhov similarity framework, and the probability distributions of surface shear stress are examined. We show that for a given mean flow speed and in comparison with neutral flow conditions, quasi-convective turbulence increases the surface shear stress and alters its probability distribution and hence substantially enhances the entrainment of sand and dust particles. Our hypothesis is thus confirmed by the wind-tunnel experiments. We also explain why large eddies are important to aeolian entrainment and transport.

1 Introduction

The entrainment of sand and dust particles is among the most important quantities to determine in aeolian studies. Based on , showed that the vertically integrated saltation flux $Q$ can be expressed as

1$$Q=\left\{\begin{array}{lr}{c}_{\mathrm{0}}\frac{\mathit{\rho }}{g}{u}_{*}^{\mathrm{3}}\left(\mathrm{1}-\frac{u_{*\mathrm{t}}^{\mathrm{2}}}{u_{*}^{\mathrm{2}}}\right)& \text{for}{u}_{*}>u_{*\mathrm{t}}\\ \mathrm{0}& \text{otherwise}\end{array}\right.,$$ where $c_{\mathrm{0}}$ is the Owen coefficient, $\mathit{\rho }$ air density, $g$ acceleration due to gravity, $u_{*}$ friction velocity and $u_{*\mathrm{t}}$ threshold friction velocity. By definition, $u_{*}=\sqrt{\mathit{\tau }/\mathit{\rho }}$ is a descriptor of the surface shear stress $\mathit{\tau }$. Although challenged by some researchers e.g.,, it has been shown in numerous studies that Eq. (1) is valid in general, but $c_{\mathrm{0}}$ scatters over a wide range if Eq. (1) is fitted to $Q$ observations . While the large scatter of $c_{\mathrm{0}}$ is not yet fully explained, it is most likely because both $u_{*}$ and $u_{*\mathrm{t}}$ are stochastic variables, and hence saltation driven by atmospheric-boundary-layer (ABL) flows is also turbulent . In this sense, Eq. (1) is valid only for mean quantities, $\stackrel{\mathrm{‾}}{Q}$ and ${\stackrel{\mathrm{‾}}{u}}_{*}$, if we assume $u_{*\mathrm{t}}$ is constant (this assumption is sufficient for the purpose of our study, but see , , and for discussions on $u_{*\mathrm{t}}$ as a stochastic variable).

Our question here is how turbulence influences aeolian processes, especially the entrainment of sand and dust particles into the atmosphere. Numerous studies on aerodynamic sand and dust entrainment have been carried out e.g.,, but in most of these studies, flow is assumed to be steady, and the effect of turbulence on the entrainment is not accounted for. In reality, the flows and flow-driven aeolian processes are both impossible to stabilize. Although people can analyze the relevant average variables, the existence of nonlinear relations (e.g., Eq. 1) makes it difficult to determine the quantitative relations between the average variables. investigated the behavior of saltating grains in unsteady flows and found that both the frequency and strength of wind gusts influence the rate of sand transport. observed that saltation intermittently occurs even when $u_{*}<u_{*\mathrm{t}}$, a phenomenon known as saltation intermittency. reported that turbulence decreases $u_{*\mathrm{t}}$ or the threshold wind velocity $u_{\mathrm{t}}$ and increases saltation intensity and the dust entrainment rate. and developed a parameterization scheme for dust emission by convective turbulence and explained how dust emission can be produced by large eddies in weak mean wind conditions. Based on extensive field measurements, showed that neglecting saltation intermittency causes biases in the model estimated saltation fluxes. reported that saltation in unstable ABLs is generally more fully developed than in stable ABLs.

Saltation intermittency in the sense of is a special case of saltation fluctuation at ${\stackrel{\mathrm{‾}}{u}}_{*}\sim u_{*\mathrm{t}}$, with ${\stackrel{\mathrm{‾}}{u}}_{*}$ being the time-averaged friction velocity. In general, if $u_{*}={\stackrel{\mathrm{‾}}{u}}_{*}+u_{*}{}^{\prime }$ (where $u_{*}{}^{\prime }$ is the $u_{*}$ derivation from ${\stackrel{\mathrm{‾}}{u}}_{*}$) and $u_{*}{}^{\prime }>\mathrm{0}$, then we have $Q=Q\left({\stackrel{\mathrm{‾}}{u}}_{*}\right)+Q{}^{\prime }$ with $Q{}^{\prime }>\mathrm{0}$. The saltation intermittency studied is for the case ${\stackrel{\mathrm{‾}}{u}}_{*}=u_{*\mathrm{t}}$ and $Q\left({\stackrel{\mathrm{‾}}{u}}_{*}\right)=\mathrm{0}$ but $Q{}^{\prime }>\mathrm{0}$. The above discussion suggests that the turbulent (or probabilistic) behavior of $u_{*}$ is of great importance to $Q$ and naturally also to sand and dust entrainment. Because the turbulent behavior of $u_{*}$ is closely related to ABL turbulence, our hypothesis is thus that ABL turbulence significantly influences the entrainment of sand and dust particles.

In stable and neutral ABLs, turbulence is generally weak and more homogeneous and isotropic, but in unstable (or convective) ABLs, turbulence is generally strong due to buoyancy production of turbulent kinetic energy and less homogeneous and isotropic due to the structure of large eddies. It is thus particularly interesting to study the influences of convective turbulence on aeolian processes. pointed out that dust particle size at emission is dependent on ABL stability. compared some features of saltation and dust emission in convective and stable ABLs based on the field observations of the Japan-Australian Dust Experiment JADE;, but due to the limitations of the field measurements, the role of turbulence in aerodynamic sand and dust entrainment could not be explicitly examined. We are thus motivated to acquire additional data to test our hypothesis.

Wind tunnels are a powerful tool for studying aeolian problems under controlled flow conditions e.g.,. Although several methods have been proposed to generated turbulence in wind tunnels, including spires, roughness elements and grids, all these methods are designed to increase the intensity of turbulence in neutral ABLs but are inadequate for generating large eddies similar to those commonly seen in convective ABLs. Generating convective turbulence in wind tunnels usually requires the use of additional thermal forcing from the surface e.g., EnFlo stratified flow wind tunnel,, temperature control of recirculating air and floor panels e.g.,, and thermally stratified wind tunnels e.g.,. Applying surface heating normally requires a very large wind tunnel. To the best of our knowledge, studying the effect of convective eddies on aeolian processes has never been done in wind-tunnel experiments, mainly because we have so far no adequate means to generate convective turbulence in a wind tunnel for aeolian experiments. Here we apply a simple forced-perturbation technique (using a piece of randomly fluttering cloth) to generate quasi-convective turbulence, namely, turbulence in a neutrally stratified flow but with characteristics of convective turbulence. Aerodynamic sand and dust entrainment rates under various mean-wind and quasi-convective turbulence conditions are measured. We use these wind-tunnel data to study how and why turbulence influences the aerodynamic sand and dust entrainment rate.

2 Wind-tunnel experiment and instrumentation

We carried out the experiment in the Lanzhou University wind tunnel, which is specially designed for aeolian studies. The technical details of the wind tunnel can be found in , and hence only the most relevant information is given here. Figure  shows the wind-tunnel configuration for the experiment. The working section of the tunnel is about 15 m long, with the first 6 m being the roughness-element section for generation of a turbulent boundary layer. The remaining section is covered by 40-grit sandpaper to simulate a non-erodible sandy surface. One end of the piece of cloth is attached to a horizontal bar located 6 m downstream the roughness-element section and 0.7 m above the tunnel floor, and the other end is allowed to flutter freely. The cloth is a woven fabric (grammage 200 g m${}^{-\mathrm{2}}$) with a size of 1 m in width and 1.5 m in length. The cloth size was empirically determined by a series of tests before the formal experiment, to satisfy the requirement on generating quasi-convective turbulence. Two sand trays (285 mm wide, 150 mm long and 13 mm deep, which have been tested as a suitable option for the study of aerodynamic entrainment ) are placed 1.5 m downstream of the end of the fluttering cloth. The trays filled with sand are mounted flush to the tunnel floor. The sand surface is smoothed before every test. Each tray is weighted before and after each test by an electronic balancer with a precision of 0.01 g in the range 5 kg, to determine the net mass loss of the tested surface. The anemometers, including the hot-wire anemometer (1-D, fixed at 10 mm height and employed only in clear air condition) and the wind profiler (combined by nine pitot tubes and placed at the levels of 6.5, 10, 15, 30, 60, 120, 201, 351 and 501 mm), were located between the trays. The outer diameter of the pitot tubes of the wind profiler is 1 mm, and the inner diameter is 0.5 mm. The wind profiler measures the profile of the mean flow speed with a sampling frequency of 1 Hz, while the hot-wire anemometer measures turbulent fluctuations with a sampling frequency of 1000 Hz. An Irwin sensor is mounted on the central axis of the wind-tunnel floor and is located upwind of the tray. Irwin sensors are omnidirectional devices for measuring the surface shear stress, which have been used successfully in a number of earlier studies e.g.,. We manufactured the Irwin sensors used in this study ourselves according to the dimensions given in , as shown in Fig. c. The Irwin-sensor pressure differences are sampled at a frequency of 100 Hz using a Scanivalve attached to a pressure transducer (ZOC33). Prior to the wind-tunnel experiment, the Irwin sensors are calibrated in the wind-tunnel against the wind profiler for various flow conditions.

Figure 1

(a) Top view of the wind-tunnel configuration. (b) Side view of the wind-tunnel configuration, where a piece of randomly fluttering cloth generates quasi-convective turbulence. (c) The probes employed. The Irwin sensor has a diameter of 12.5 mm. Its inner port has a diameter of 1.65 mm and a height of 1.75 mm, and its outer port diameter is 2.57 mm. (d) The size distributions of four tested soils, where ${\mathit{\varphi }}_{\mathrm{p}}$ is the volume fraction, and $d_{\mathrm{p}}$ is the particle diameter.

[Figure omitted. See PDF]

A key requirement for our experiment is to generate turbulence in the wind tunnel with characteristics similar to convective turbulence. In convective ABLs, large eddies develop due to the buoyancy production of turbulent kinetic energy. While horizontal velocity fluctuations are approximately Gaussian-distributed, vertical velocity fluctuations are typically non-Gaussian with a positive skewness, resulting in a positive skewed probability distribution of surface shear stress. As already discussed, convective turbulence is difficult to generate in wind-tunnel flows which are usually neutrally stratified. Here, we use a “forced perturbation” technique to generate turbulence in the wind-tunnel flow, that mimics convective turbulence with energy-containing large eddies and positively skewed velocity probability distribution function (PDF). Such turbulence is referred to here as quasi-convective turbulence. Forced perturbation is achieved using a piece of cloth which flutters (rapid and lightly swing) randomly in the wind-tunnel flow to produce small eddies and flaps with a longer period and greater amplitude to produce large eddies, superposed on the background turbulence. Although quasi-convective turbulence is not the same as convective turbulence, the forced-perturbation method is both simple and efficient to remedy the critical deficit of wind-tunnel flows which lack large eddies with skewed structures.

The wind tunnel is a blow tunnel, with the inlet flow speed controlled by a rotating fan. For our experiment, the fan speed is fixed for each run between 7000 and 12 000 rpm with an interval of 1000 rpm, and the corresponding inlet free wind speed is between 7.7 and 13.7 m s${}^{-\mathrm{1}}$. We call the runs with forced perturbation WP runs and those with no forced perturbation NP runs. The entrainment rates are measured for various flow and turbulence combinations, as listed in Table . For each run, at least three successful repetitions are made, and the measurement period for each repetition is 5 min. Four different soils are used in the experiment, labeled S1–S4. The mean particle size of the four soils is, respectively 75, 140, 215 and 398 $\mathrm{\mu }$m. The particle size distributions are approximately lognormal, as shown in Fig. d, measured by a Microtrac S3500 laser diffractometer (Microtrac, Montgomeryville, USA). We use NP70_S1 to denote the NP run for fan speed 7000 rpm and soil S1, and following this convention, we name the other runs.

Table 1

Summary of wind-tunnel experiments.

Fan speed ($\times \mathrm{100}$ rpm)	Repetitions
	70	75	80	85	90	95	100	105	110	120
Particle size	NP/WP	NP/WP	NP/WP	NP/WP	NP/WP	NP/WP	NP/WP	NP/WP	NP/WP	NP/WP
O (no soil)	1	/	1	/	1	/	1	/	1	1
S1 (75 $\mathrm{\mu }$m)	5/3	/	5/5	/	5/5	/	5/5	/	5/5	3/5
S2 (140 $\mathrm{\mu }$m)	5/5	/5	5/5	/4	5/5	3/3	3/	/	/	/
S3 (215 $\mathrm{\mu }$m)	5/5	/	5/5	/5	5/5	/	5/5	5/	6/	/
S4 (398 $\mathrm{\mu }$m)	3/3	/	3/5	/	3/5	/	5/5	/	5/5	5/

Note that NP – no cloth and WP – with cloth. The tests of 0.5 $\times$ 1000 rpm are supplementary. In the case of large surface shear, the erodible surface (S2 and S3) rapidly appeared to be concave, which could affect the test results. We therefore added several tests for low surface shear.

3 Results

3.1 Forced perturbation

We first examine whether turbulence generated using the forced-perturbation technique has the desired features of convective turbulence. In Fig. , the characteristics of $V_{\mathrm{10}\mathrm{mm}}$ (horizontal flow velocity in height of 10 mm sensed by the hot-wire anemometer) are compared between the NP70_O and WP70_O runs, including its time series, PDF and power spectrum. As $V_{\mathrm{10}\mathrm{mm}}$ is measured using a one-dimensional hot-wire anemometer, it is the resultant velocity of its horizontal component, $u_{\mathrm{10}\mathrm{mm}}$, and vertical component, $w_{\mathrm{10}\mathrm{mm}}$. As seen, the forced-perturbation technique effectively generates quasi-convective turbulence, as turbulence for the WP70_O run has an increased variance and a positive skewness, while turbulence for the NP70_O run is weaker and almost Gaussian-distributed. It is shown that the effect of cloth not only enhances the average value of instantaneous wind speed, but also causes the probability of strong wind to increase in the distribution of instantaneous wind speed. While depending on the fluttering mode of the cloth, the quasi-convective turbulence has coherent structures as observed in convective ABLs . As our main interest is how convective eddies affects aeolian particle entrainment, we did not study the intrinsic mechanisms of how cloth induces large eddies.

Figure 2

(a) A section of 10 s of the $V_{\mathrm{10}\mathrm{mm}}$ time series for the NP70_O and WP70_O runs, (b) probability density functions of $V_{\mathrm{10}\mathrm{mm}}$ (estimated using a time series of 300 s) and (c) normalized power spectra of $V_{\mathrm{10}\mathrm{mm}}$ for WP70_O and NP70_O compared with field-observed power spectra in the atmospheric boundary layer . $Z_{\mathrm{0}\mathrm{WT}}$ is 1.33 $\times$ ${\mathrm{10}}^{-\mathrm{2}}$ mm, and $Z_{\mathrm{0}\mathrm{ABL}}$ is set to 3.10 mm .

[Figure omitted. See PDF]

In the MOST (Monin–Obukhov similarity theory) framework, $\mathit{\zeta }=z/L$, with $z$ being height and $L$ the Obukhov length, is used as a measure of ABL stability: the ABL is stable, neutral and unstable if $\mathit{\zeta }>\mathrm{0}$, $=\mathrm{0}$ and $<\mathrm{0}$, respectively. examined the characteristics of surface-layer turbulence using the MOST and found that the nondimensionalized power spectra of ABL quantities collapse to universal functions, with $\mathit{\zeta }$ being the only parameter. They showed that as the ABL stability decreases, the inertial subrange extends to lower frequencies. Plotted in Fig. c are the normalized power spectra of $V_{\mathrm{10}\mathrm{mm}}$ for NP70 and WP70, denoted as $P_{\mathrm{NP}\mathrm{70}}$ and $P_{\mathrm{WP}\mathrm{70}}$, respectively. Following , we express the normalized frequency as $f=nz/u$ (with $n$ being frequency) and normalized energy spectral density as 2$$P=nS\left(n\right){\stackrel{\mathrm{‾}}{u}}_{*}^{-\mathrm{2}}{\mathit{\varphi }}_{\mathit{ϵ}}^{-\mathrm{2}/\mathrm{3}},$$ with $S$ being the energy density per frequency and ${\mathit{\varphi }}_{\mathit{ϵ}}$ the MOST similarity function for the dissipation rate of turbulent kinetic energy: 3$${\mathit{\varphi }}_{\mathit{ϵ}}=\mathrm{1}+\mathrm{0.5}{\left|\mathit{\zeta }\right|}^{\mathrm{2}/\mathrm{3}}.$$ Following , our analysis does not involve the cases of $\mathit{\zeta }>\mathrm{0}$. For the wind-tunnel runs, $nS\left(n\right)$ is obtained by analyzing the horizontal wind velocity component measured by the hot-wire anemometer, ${\stackrel{\mathrm{‾}}{u}}_{*}$ is measured by the Irwin sensor and ${\mathit{\varphi }}_{\mathit{ϵ}}$ is calculated using Eq. (3) with $\mathit{\zeta }=\mathrm{0}$ for the NP70_O run and $\mathit{\zeta }=-\mathrm{2}$ for the WP70_O run. For comparison, the ABL velocity power spectra, denoted as $P_{\mathrm{ABL}}$, for three different stabilities $\mathit{\zeta }=\mathrm{0}$, $-\mathrm{0.8}$ and $-\mathrm{2}$ are plotted. The empirical form given by , 4$$P_{\mathrm{ABL}}=\mathrm{105}f/{\left(a+\mathrm{33}f\right)}^{\mathrm{5}/\mathrm{3}},$$ is used, where $a$ is an empirical constant set to 1, 0.4 and 0.1 for $\mathit{\zeta }=\mathrm{0}$, $-\mathrm{0.8}$ and $-\mathrm{2}$, respectively. In Fig. c, $P_{\mathrm{ABL}}\mathrm{\times }{z}_{\mathrm{0}\mathrm{WT}}/z_{\mathrm{0}\mathrm{ABL}}$ is plotted, where $z_{\mathrm{0}\mathrm{WT}}$ is the roughness length for the wind-tunnel flows and $z_{\mathrm{0}\mathrm{ABL}}$ that for the field ABL flows. The ratio $z_{\mathrm{0}}/L$ is the MO number which was excluded in . The exclusion is justified because the differences in $z_{\mathrm{0}}$ in their data are not large. However, because $z_{\mathrm{0}\mathrm{WT}}$ (Table ) is 2 orders of magnitude smaller than $z_{\mathrm{0}\mathrm{ABL}}$, the effect of $z_{\mathrm{0}}/L$ needs to be considered, and hence the mentioned multiplication is necessary.

Figure c reveals that $P_{\mathrm{NP}\mathrm{70}}$ and $P_{\mathrm{WP}\mathrm{70}}$ are almost the same in the (normalized) frequency range of $f<\mathrm{3}\times {\mathrm{10}}^{-\mathrm{3}}$, as turbulence in this frequency range is attributed to the upstream roughness elements. They are also the almost the same in the high-frequency range of $f>\mathrm{0.1}$. In the energy-containing range $\mathrm{3}\times {\mathrm{10}}^{-\mathrm{3}}<f<\mathrm{0.1}$, $P_{\mathrm{WP}\mathrm{70}}$ shows much increased energy with respect to $P_{\mathrm{NP}\mathrm{70}}$, implying that the forced-perturbation technique generated large eddies in the wind-tunnel flow.

Figure c also shows that it is generally difficult for the wind tunnel to reproduce the turbulence observed in the ABL. Clearly, compared with $P_{\mathrm{ABL}}(\mathit{\zeta }=-\mathrm{0.8})$ and $P_{\mathrm{ABL}}(\mathit{\zeta }=-\mathrm{2})$, $P_{\mathrm{NP}\mathrm{70}}$ lacks energy in the frequency range of $\mathrm{3}\times {\mathrm{10}}^{-\mathrm{3}}\sim \mathrm{1}\times {\mathrm{10}}^{-\mathrm{1}}$. In contrast, power spectral density in this frequency range is substantially increased if forced perturbation is applied as a comparison of $P_{\mathrm{WP}\mathrm{70}}$ and $P_{\mathrm{NP}\mathrm{70}}$ reveals. It is seen that $P_{\mathrm{WP}\mathrm{70}}$ is fairly similar to $P_{\mathrm{ABL}}(\mathit{\zeta }=-\mathrm{2})$, although it still lacks energy for $f<{\mathrm{10}}^{-\mathrm{2}}$. In summary, Fig.  shows that the forced-perturbation technique is effective in generating quasi-convective turbulence, which has a degree of similarity with ABL convective turbulence. This simple technique can be further optimized (e.g., using a combination of fluttering cloths of different materials and different dimensions) to overcome the critical lack of convective eddies in wind-tunnel flows, which has so far seriously limited the usefulness and generalization of the wind-tunnel results.

3.2 Mean wind profile and shear stress

Figure  shows the mean wind profiles measured using the pitot tubes. For height $z$ smaller than 0.2 m, the mean wind profiles for both NP runs and WP runs are approximately logarithmic. In the WP runs, the flow speed for $z>\mathrm{0.2}$ m is reduced due to the fluttering cloth which acts as a momentum sink. For $z<\mathrm{0.2}$ m in WP runs, the air flow seems to be accelerated ($\sim$ 0.5 m s${}^{-\mathrm{1}}$). It could be a wind-tunnel artifact associated with a small degree of compression of the flow that was redirected beneath the cloth and between the confining walls. For a given fan speed, the fluttering cloth not only enhances the turbulent kinetic energy (Fig. ), but also modifies the wind profile for $z<\mathrm{0.2}$ m, which will be proved by the following analysis.

Figure 3

Mean flow speed profiles for different runs. For all cases, the wind-tunnel floor is covered by sandpaper. The trays filled with particles and mounted flush to the tunnel floor do not affect the measured profiles.

[Figure omitted. See PDF]

Based on the MOST, the similarity relationship between the mean flow speed $\stackrel{\mathrm{‾}}{U}$ and height $z$, can be expressed as 5$$\stackrel{\mathrm{‾}}{U}\left(z\right)={\displaystyle \frac{{\stackrel{\mathrm{‾}}{u}}_{*}}{\mathit{\kappa }}}\left[\ln \left({\displaystyle \frac{z}{z_{\mathrm{0}}}}\right)+{\mathrm{\Psi }}_{\mathrm{m}}\right],$$ where $\mathit{\kappa }$ is the von Karmen constant, and 6$${\mathrm{\Psi }}_{\mathrm{m}}=\underset{z_{\mathrm{0}}}{\overset{z}{\int }}\left(\mathrm{1}-{\mathit{\varphi }}_{\mathrm{m}}\right)\mathrm{d}\ln z$$ and 7$${\mathit{\varphi }}_{\mathrm{m}}={\left(\mathrm{1}-{\mathit{\gamma }}_{\mathrm{m}}\mathit{\zeta }\right)}^{-\mathrm{1}/\mathrm{4}},\mathit{\zeta }\le \mathrm{0}$$ are the similarity functions. For ABL flows, ${\mathit{\gamma }}_{\mathrm{m}}=\mathrm{16}$ is an empirical coefficient . For the NP runs, ${\mathrm{\Psi }}_{\mathrm{m}}=\mathrm{0}$ is assumed. By fitting Eq. (5) to $\stackrel{\mathrm{‾}}{U}$ measured at $z<\mathrm{0.2}$ m, we estimate ${\stackrel{\mathrm{‾}}{u}}_{*}$ and $z_{\mathrm{0}}$. The shear stress $\stackrel{\mathrm{‾}}{\mathit{\tau }}=\mathit{\rho }{\stackrel{\mathrm{‾}}{u}}_{*}^{\mathrm{2}}$ (here, air density $\mathit{\rho }=\mathrm{1.2}$ kg m${}^{-\mathrm{3}}$) is then used to calibrate the shear stress measured using the Irwin sensor, ${\stackrel{\mathrm{‾}}{\mathit{\tau }}}_{\mathrm{Irwin}}$. But if ${\mathrm{\Psi }}_{\mathrm{m}}$ is set to 0 for the case of WP, the obtained $u_{*}$ obviously diverges from the data of Irwin sensor. Only when a nonzero ${\mathrm{\Psi }}_{\mathrm{m}}$ is considered, does the deduced $u_{*}$ agree with the data of Irwin sensor (Table ). That is why we state that the wind profile for $z<\mathrm{0.2}$ m modifies to be more similar to the one in convective ABL. As both ${\mathit{\gamma }}_{\mathrm{m}}$ and $L$ are unknown for the quasi-convective turbulent flows, it is sensible to write Eq. (7) as 8$${\mathit{\varphi }}_{\mathrm{m}}={\left(\mathrm{1}-{\mathit{\eta }}_{\mathrm{m}}z\right)}^{-\mathrm{1}/\mathrm{4}},$$ with ${\mathit{\eta }}_{\mathrm{m}}\sim {\mathit{\gamma }}_{\mathrm{m}}/L$. By combining the $\stackrel{\mathrm{‾}}{U}$ measurements at $z<\mathrm{0.2}$ m and the shear stress measured using the Irwin sensors for the WP runs, ${\mathit{\eta }}_{\mathrm{m}}$ can be estimated. The results are summarized in Table .

Table 2

Friction velocity ${\stackrel{\mathrm{‾}}{u}}_{*}$ and roughness length $z_{\mathrm{0}}$ estimated for runs with and with no forced perturbation and different wind-tunnel fan speeds ($R^{\mathrm{2}}=\mathrm{99}$ %). The Irwin sensor is calibrated based on the data of wind profiles under the NP condition.

		NP		WP
		Profile(${\mathrm{\Psi }}_{\mathrm{m}}=\mathrm{0}$)		Profile(${\mathrm{\Psi }}_{\mathrm{m}}\ne \mathrm{0}$)			Irwin
Fan speed	$U_{\mathrm{501}\mathrm{mm}}$	$u_{*}$	$z_{\mathrm{0}}$	$u_{*}$	$z_{\mathrm{0}}$	${\mathit{\eta }}_{\mathrm{m}}$	$u_{*}$
($\times$100 rpm)	(m s${}^{-\mathrm{1}}$)	(m s${}^{-\mathrm{1}}$)	(mm)	(m s${}^{-\mathrm{1}}$)	(mm)	(mm${}^{-\mathrm{1}}$)	(m s${}^{-\mathrm{1}}$)
70	7.68	0.29 $\pm$ 0.0087	0.0133 $\pm$ 0.0044	0.31 $\pm$ 0.0077	0.0150 $\pm$ 0.0034	$-$0.0229	0.32 $\pm$ 0.0128
75	8.32	/	/	0.34 $\pm$ 0.0062	0.0153 $\pm$ 0.0025	$-$0.0213	0.34 $\pm$ 0.0064
80	8.95	0.34 $\pm$ 0.0068	0.0146 $\pm$ 0.0024	0.36 $\pm$ 0.0067	0.0159 $\pm$ 0.0016	$-$0.0200	0.37 $\pm$ 0.0101
85	9.56	/	/	0.39 $\pm$ 0.0051	0.0167 $\pm$ 0.0013	$-$0.0188	0.39 $\pm$ 0.0069
90	10.18	0.38 $\pm$ 0.0083	0.0159 $\pm$ 0.0020	0.41 $\pm$ 0.0087	0.0156 $\pm$ 0.0022	$-$0.0178	0.42 $\pm$ 0.0080
95	10.80	/	/	0.44 $\pm$ 0.0038	0.0165 $\pm$ 0.0007	$-$0.0168	0.44 $\pm$ 0.0031
100	11.42	0.43 $\pm$ 0.0106	0.0164 $\pm$ 0.0024	0.46 $\pm$ 0.0083	0.0166 $\pm$ 0.0016	$-$0.0160	0.47 $\pm$ 0.0109
110	12.55	0.47 $\pm$ 0.0204	0.0175 $\pm$ 0.0043	0.50 $\pm$ 0.0067	0.0165 $\pm$ 0.0010	$-$0.0146	0.51 $\pm$ 0.0077
120	13.72	0.51 $\pm$ 0.0180	0.0166 $\pm$ 0.0035	0.55 $\pm$ 0.0033	0.0162 $\pm$ 0.0008	$-$0.0133	0.55 $\pm$ 0.0085

Table  shows that forced perturbation leads to an increased ${\stackrel{\mathrm{‾}}{u}}_{*}$, corresponding to an increase of $\stackrel{\mathrm{‾}}{\mathit{\tau }}$ by about 22 % at a fan speed of 7000 rpm and about 16 % at a fan speed of 12 000 rpm. As pointed out in several earlier studies , we emphasize again that surface shear stress $\mathit{\tau }$ is a stochastic variable, which satisfies a probability distribution function $p$($\mathit{\tau }$). To facilitate discussions, we explicitly write 9$$\mathit{\tau }=\stackrel{\mathrm{‾}}{\mathit{\tau }}+\mathit{\tau }{}^{\prime },$$ with $\mathit{\tau }{}^{\prime }$ being the perturbation of $\mathit{\tau }$.

3.3 Aeolian particle entrainment in quasi-convective turbulence

The entrainment rate of sand and dust particles $F$ is estimated from the mass loss of the trays as

10$$F={\displaystyle \frac{\mathrm{1}}{I}}\sum _{i=\mathrm{1}}^{i=I}{\displaystyle \frac{\mathrm{\Delta }{m}_i}{A\mathrm{\Delta }{T}_i}},$$ where $\mathrm{\Delta }{m}_i$ is the net mass loss (integrated over $\mathrm{\Delta }{T}_i$) from the tray during the $i$th run with run time $\mathrm{\Delta }{T}_i$, $A$ is the tray surface area and $I$ is the number of repetitions. Figure  shows the entrainment rates of the various particle-size groups measured in the NP and WP runs. It is seen that for all four soils, for a given $\stackrel{\mathrm{‾}}{\mathit{\tau }}$, the entrainment rates for the WP runs are substantially larger than those for the NP runs. This result suggests that in addition to the mean surface shear stress $\stackrel{\mathrm{‾}}{\mathit{\tau }}$, the surface shear stress perturbations $\mathit{\tau }{}^{\prime }$ significantly influence the entrainment rate. It shows that the slight increase of $\stackrel{\mathrm{‾}}{\mathit{\tau }}$ in quasi-convective conditions is not sufficient alone to explain the measured differences in the entrainment rates of the four soils. It implies that the perturbations of the shear stress $\mathit{\tau }{}^{\prime }$ are also responsible for a part of the differences in the entrainment rates. As $\mathit{\tau }{}^{\prime }$ is related to the structure of boundary-layer turbulence, it can be said that the structure of boundary-layer turbulence also influences the entrainment rate: for a given mean surface shear stress, convective turbulence is more efficient in lifting particles from the surface into the air. This finding is consistent with the observations of the Japan-Australian Dust Experiment (JADE; , 2020); i.e., aeolian sand transport and dust emission are much more intensive in convective ABLs than in stable ABLs.

Figure 4

Entrainment rate of four different soils observed in the NP and WP runs. Open symbols represent the NP runs and solid symbols the WP runs.

[Figure omitted. See PDF]

Using the $\mathit{\tau }$ measurements of the Irwin sensor, we estimate the PDF of $\mathit{\tau }$, $p$($\mathit{\tau }$). and suggested that $p$($\mathit{\tau }$) is approximately Weibull-distributed and positively skewed: 11$$p\left(\mathit{\tau }\right)={\displaystyle \frac{K}{\mathit{\lambda }}}{\left({\displaystyle \frac{\mathit{\tau }}{\mathit{\lambda }}}\right)}^{K-\mathrm{1}}\exp \left[-{\left({\displaystyle \frac{\mathit{\tau }}{\mathit{\lambda }}}\right)}^K\right],$$ where $K$ is the shape parameter, and $\mathit{\lambda }$ is the scaling parameter.

Figure  shows as an example $p$($\mathit{\tau }$) for the NP and WP runs for a fan speed of 7000, 9000 and 12 000 rpm. As seen, the forced perturbation results in significantly different PDF of $\mathit{\tau }$ by slightly increasing $\stackrel{\mathrm{‾}}{\mathit{\tau }}$ and clearly increasing the probability of large $\mathit{\tau }$. It is this increase in the probability of large $\mathit{\tau }$ that explains the differences in the $F\sim \stackrel{\mathrm{‾}}{\mathit{\tau }}$ dependency between the NP and WP runs seen in Fig. .

Figure 5

(a) Probability density function of surface shear stress $\mathit{\tau }$ for NP and WP runs with a fan speed of 7000, 9000 and 12 000 rpm. The dashed gray line marks the threshold shear stress for S1 (${\mathit{\tau }}_{\mathrm{t}\mathrm{\_}\mathrm{S}\mathrm{1}}$). The symbols are the results from the Irwin sensors and curves the Weibull distributions. By fitting Eq. (11) to the respective data of the various runs, the corresponding shape parameter $K$ and scaling parameter $\mathit{\lambda }$ are estimated and plotted against the mean shear stress $\stackrel{\mathrm{‾}}{\mathit{\tau }}$ in (b) and (c), respectively. The curves are polynomial fits. In (b), the solid black line shows $K=-\mathrm{15.10}{\mathit{\tau }}^{\mathrm{2}}+\mathrm{12.28}\mathit{\tau }+\mathrm{0.85}$ and the dashed black line $K=-\mathrm{21.15}{\mathit{\tau }}^{\mathrm{2}}+\mathrm{15.65}\mathit{\tau }+\mathrm{0.79}$. In (c), the solid red line shows $\mathit{\lambda }=\mathrm{1.01}\mathit{\tau }+\mathrm{0.02}$ and the dashed red line $\mathit{\lambda }=\mathrm{0.97}\mathit{\tau }+\mathrm{0.02}$.

[Figure omitted. See PDF]

The structure of ABL turbulence, reflected here in $p$($\mathit{\tau }$), significantly influences the sand and dust entrainment and saltation fluxes because this depends non-linearly on $\mathit{\tau }$. As explained in Sect. 6.12.4, for a given particle size, the entrainment rate can be expressed as 12$$F=\mathit{\gamma }\sqrt{\mathit{\tau }/\mathit{\rho }}\left(\mathit{\tau }-{\mathit{\tau }}_{\mathrm{t}}\right),$$ with $\mathit{\gamma }$ being an empirical efficiency parameter for particle entrainment, and ${\mathit{\tau }}_{\mathrm{t}}$ is the threshold shear stress for particle entrainment. The threshold is in general a stochastic variable , but for simplicity, we assume it is constant for given particle size. To account for the fluctuations of $\mathit{\tau }$, we estimate 13$$F=\underset{{\mathit{\tau }}_{\mathrm{t}}}{\overset{\mathrm{\infty }}{\int }}\mathit{\gamma }\sqrt{\mathit{\tau }/\mathit{\rho }}\left(\mathit{\tau }-{\mathit{\tau }}_{\mathrm{t}}\right)p\left(\mathit{\tau }\right)\mathrm{d}\mathit{\tau }.$$ For the four soils tested, S1, S2, S3 and S4, ${\mathit{\tau }}_{\mathrm{t}}$ is estimated to be 0.13, 0.27, 0.31 and 0.37 N m${}^{-\mathrm{2}}$, respectively. Figure  shows that Eq. (12) fits well to the measurements for all runs. Equation (12) reveals that convective turbulence may influence both the efficiency parameter, $\mathit{\gamma }$, and the statistical behavior of the term, ${\int }_{{\mathit{\tau }}_{\mathrm{t}}}^{\mathrm{\infty }}\mathit{\gamma }\sqrt{\mathit{\tau }/\mathit{\rho }}(\mathit{\tau }-{\mathit{\tau }}_{\mathrm{t}})p\left(\mathit{\tau }\right)\mathrm{d}\mathit{\tau }$. To facilitate discussion, we rewrite Eq. (12) as 14$$F=\stackrel{\mathrm{‾}}{\mathit{\gamma }}\underset{{\mathit{\tau }}_{\mathrm{t}}}{\overset{\mathrm{\infty }}{\int }}\sqrt{\mathit{\tau }/\mathit{\rho }}\left(\mathit{\tau }-{\mathit{\tau }}_{\mathrm{t}}\right)p\left(\mathit{\tau }\right)\mathrm{d}\mathit{\tau }.$$

A comparison of $\stackrel{\mathrm{‾}}{\mathit{\gamma }}$ for NP and WP runs is shown in Table . It is seen that $\stackrel{\mathrm{‾}}{\mathit{\gamma }}$ is significantly increased for the WP runs. The low value of $\stackrel{\mathrm{‾}}{\mathit{\gamma }}$ for S1 is supposed to be caused by the wide distributed particle size, leading to an increased mean threshold friction velocity when wind speed increases, which means a constant threshold is not suitable in this situation. However, this is beyond the scope of this work, which mainly focuses on the comparison of the WP and NP conditions. Thus, we estimate the ratio ${\mathit{\sigma }}_F$ defined as 15$${\mathit{\sigma }}_F={\displaystyle \frac{{\int }_{{\mathit{\tau }}_{\mathrm{t}}}^{\mathrm{\infty }}\sqrt{\mathit{\tau }/\mathit{\rho }}\left(\mathit{\tau }-{\mathit{\tau }}_{\mathrm{t}}\right)p_{\mathrm{WP}}\left(\mathit{\tau }\right)\mathrm{d}\mathit{\tau }}{{\int }_{{\mathit{\tau }}_{\mathrm{t}}}^{\mathrm{\infty }}\sqrt{\mathit{\tau }/\mathit{\rho }}\left(\mathit{\tau }-{\mathit{\tau }}_{\mathrm{t}}\right)p_{\mathrm{NP}}\left(\mathit{\tau }\right)\mathrm{d}\mathit{\tau }.}}$$

Figure 6

Estimated entrainment rates with and without forced perturbation. The dots are experimental data, and lines derive from Eq. (12).

[Figure omitted. See PDF]

Table 3

Threshold shear stress ${\mathit{\tau }}_{\mathrm{t}}$ and empirical parameter $\mathit{\gamma }$ for test surfaces.

Soil type	${\mathit{\tau }}_{\mathrm{t}}$ (N m${}^{-\mathrm{2}}$)	WP		NP		$\frac{\stackrel{\mathrm{‾}}{{\mathit{\gamma }}_{\mathrm{NP}}}}{\stackrel{\mathrm{‾}}{{\mathit{\gamma }}_{\mathrm{WP}}}}$
		$\stackrel{\mathrm{‾}}{{\mathit{\gamma }}_{\mathrm{WP}}}$(m${}^{-\mathrm{2}}$ s${}^{\mathrm{2}}$)	$R_{\mathrm{WP}}^{\mathrm{2}}$	$\stackrel{\mathrm{‾}}{{\mathit{\gamma }}_{\mathrm{NP}}}$(m${}^{-\mathrm{2}}$ s${}^{\mathrm{2}}$)	$R_{\mathrm{NP}}^{\mathrm{2}}$
S1	0.13	7.12	0.89	3.30	0.86	1.96
S2	0.27	4919.84	0.95	3605.29	0.99	1.29
S3	0.31	4675.62	0.97	2521.74	0.98	1.97
S4	0.37	1996.39	0.95	1713.19	0.95	1.34

Figure  shows the relationship between ${\mathit{\sigma }}_F$ and excess surface shear stress ($\stackrel{\mathrm{‾}}{\mathit{\tau }}-{\mathit{\tau }}_{\mathrm{t}}$). A negative exponential law appears to exist. For the conditions with $\stackrel{\mathrm{‾}}{\mathit{\tau }}>{\mathit{\tau }}_{\mathrm{t}}$ (corresponding to the continuous entrainment defined by ), ${\mathit{\sigma }}_F$ is close to 1, indicating relatively small influence from the quasi-convective turbulence. But for the conditions with $\stackrel{\mathrm{‾}}{\mathit{\tau }}<{\mathit{\tau }}_{\mathrm{t}}$, ${\mathit{\sigma }}_F$ significantly increase with decreasing $\stackrel{\mathrm{‾}}{\mathit{\tau }}-{\mathit{\tau }}_{\mathrm{t}}$, reaching up to 6 at $\stackrel{\mathrm{‾}}{\mathit{\tau }}-{\mathit{\tau }}_{\mathrm{t}}=-\mathrm{0.25}$ N m${}^{-\mathrm{2}}$, indicating that the influence of convective turbulence is significant (corresponding to the intermittent entrainment defined by ). We can thus conclude that convective turbulence may significantly enhance dust entrainment by altering how shear stress acts on the surface, especially for the cases of intermittent entrainment when the mean shear stress is below the threshold. Considering that the lower-than-threshold wind conditions may have a high temporal weight in natural conditions, we believe that this effect deserves particular attention in dust emission schemes.

Figure 7

Relationship between ${\mathit{\sigma }}_F$ and excess surface shear stress ($\stackrel{\mathrm{‾}}{\mathit{\tau }}-{\mathit{\tau }}_{\mathrm{t}}$).

[Figure omitted. See PDF]

4 Conclusions

We carried out wind-tunnel experiments and studied the influences of turbulence structure on aerodynamic entrainment of sand and dust particles. We considered $\mathit{\tau }$ to be a stochastic variable and showed that the probability distribution of $\mathit{\tau }$ (i.e., $p$($\mathit{\tau }$)), in addition to the mean surface shear stress $\stackrel{\mathrm{‾}}{\mathit{\tau }}$, has a significant impact on aeolian fluxes, as the entrainment rate of sand and dust particles depends non-linearly on surface shear stress, $\mathit{\tau }$. Because the fluctuations of $\mathit{\tau }$ are closely related to the structure of ABL turbulence, aeolian fluxes in ABLs of different stabilities can be substantially different even if $\stackrel{\mathrm{‾}}{\mathit{\tau }}$ is the same. The wind-tunnel experiments provided direct data which show that ABL convective large eddies are of particular importance to the entrainment of sand and dust particle, as they not only increase the mean shear stress on the surface, but also increase the probability for instantaneous shear stress to exceed the threshold, leading to intermittent entrainment.

Wind-tunnel flows are normally neutrally stratified and do not contain large eddies similar to those in convective ABLs. By examining the power spectra of turbulence for the NP runs, we showed that wind-tunnel turbulence lacks energy-containing eddies, even compared with ABL flows in neutral conditions. Although advanced techniques for measuring turbulence structure and intensity associated with sediment entrainment and transport have been developed in the past few decades, some focusing on the effects of gusting wind e.g.,, few studies have been done focusing on the effects of ABL convective turbulence. Also, means for generating large-scale eddies (not necessarily convective large eddies) in wind-tunnel simulations for wind engineering applications have not been widely used in aeolian studies due to their complexity and high operational cost. We showed that the deployment of a piece of fluttering cloth is both simple and effective in generating quasi-convective turbulence. By comparing the power spectra of turbulence for the WP runs and NP runs, we found that the energy density in the eddy-energy-containing range is substantially increased. The energy spectrum of quasi-convective eddies agrees reasonably well with that of turbulence in unstable ABL, with $z/L=-\mathrm{2}$. Although the employment of the forced-perturbation technique did not fully reproduce the energy spectra of convective turbulence, this simple technique can be further developed and optimized to obtain the desired turbulent features and overcome a vital limitation to aeolian wind-tunnel experiments.

By comparing the WP runs and NP runs, we found that quasi-convective turbulence increases the mean value (just as in convective ABLs) as well as the variance and skewness of the surface shear stress, all contributing to the entrainment of sand and dust particles. For a given mean shear stress, the entrainment rate for the WP runs is substantially higher than for the NP runs; i.e., convective turbulence is more effective than neutral turbulence in entraining particles into the atmosphere. The enhancing effect is greatest at low wind speeds around threshold and when transport is intermittent and becomes relatively weaker when the mean wind speed is strong enough and dominates over the fluctuations.

The findings of this study obtained through wind-tunnel observations are consistent with the results of . The latter authors showed based on field observations that the PDF of $u_{*}$ can influence the magnitude of saltation flux, $Q$. With a fixed $u_{*}$ mean, a larger $u_{*}$ variance corresponds to a larger $Q$. Unstable ABL has in general larger $u_{*}$ variances, which generate stronger saltation bombardment for dust emission and produce the emission of finer dust particles, and saltation in unstable ABLs is generally more fully developed, leading to stronger saltation bombardment. In a more recent study, demonstrated using large-eddy simulations that dust deposition is also strongly affected by the structure of turbulence. Together with the earlier studies of , , , , , and , we have shown the critical importance of taking turbulence structure into consideration in aeolian studies and have partly quantified the impact of turbulence on sand and dust entrainment, dust emission, saltation fluxes and dust deposition.

Data availability

Data are available from Jie Zhang ([email protected]) or Guang Li ([email protected]) upon request.

Author contributions

YS and JZ conceived and designed the wind-tunnel experiment; JZ, GL and LS carried out the experiment, performed the data analyses, and prepared the first draft; and YS and NH organized this study and contributed to its conceptualization, discussions and finalization of the paper.

Competing interests

The contact author has declared that none of the authors has any competing interests.

Disclaimer

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Acknowledgements

The authors wish to show their great appreciation to Gilles Bergametti, Xueling Cheng and Cheryl McKenna Neuman for their affirmation of this work and constructive suggestions. They are also grateful to Armin Sigmund, who shared his thoughts after reading this manuscript.

Financial support

This research has been supported by the National Natural Science Foundation of China (grant nos. 41931179 and 42006187), the Major Science and Technology Project of Gansu Province (grant no. 21ZD4FA010), the Second Tibetan Plateau Scientific Expedition and Research Program (grant no. 2019QZKK020611), and the Fundamental Research Funds for the Central Universities (grant no. lzujbky-2020-cd06).

Review statement

This paper was edited by Guangjie Zheng and reviewed by Gilles Bergametti, Xueling Cheng, and Cheryl McKenna Neuman.