Numerical Simulation of Dust Lifting within Dust Devils—Simulation of an Intense Vortex

Zhaolin Gu State Key Laboratory of Multiphase Flow in Power Engineering, Department of Environmental Science and Technology, Xi’an Jiaotong University, Xi’an, China

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Yongzhi Zhao Tsinghua University, Beijing, China

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Yun Li Xi’an Jiaotong University, Xi’an, China

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Yongzhang Yu Xi’an Jiaotong University, Xi’an, China

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Xiao Feng Xi’an Jiaotong University, Xi’an, China

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Abstract

Based on an advanced dust devil–scale large-eddy simulation (LES) model, the atmosphere flow of a modeled dust devil in a quasi–steady state was first simulated to illustrate the characteristics of the gas phase field in the mature stage, including the prediction of the lower pressure and higher temperature in the vortex core. The dust-lifting physics is examined in two aspects. Through the experimental data analysis, it is verified again that the horizontal swirling wind can only make solid particles saltate along the ground surface. Based on a Lagrangian reference frame, the tracks of dust grains with different density (material) and diameter are calculated to show the effect of dust particles entrained by the vertical swirling wind field. The movement of solid particles depends on the interactions between the aloft dust particles and the airflow field of dust devils, in which the drag and the centrifugal force component on the horizontal plane are the key force components. There is the trend of the fine dust grains rising along the inner helical tracks while the large dust grains are lifting along the outer helical tracks and then descending beyond the corner region, resulting in the impact between different-sized dust grains in the swirling atmospheric flow. This trend will make the dust stratification, developing a top small-sized grain domain and a bottom large-sized grain domain in dust devils.

Corresponding author address: Dr. Zhaolin Gu, State Key Laboratory of Multiphase Flow in Power Engineering, Dept. of Environmental Science and Technology, Xi’an 710049, China. Email: guzhaoln@mail.xjtu.edu.cn

Abstract

Based on an advanced dust devil–scale large-eddy simulation (LES) model, the atmosphere flow of a modeled dust devil in a quasi–steady state was first simulated to illustrate the characteristics of the gas phase field in the mature stage, including the prediction of the lower pressure and higher temperature in the vortex core. The dust-lifting physics is examined in two aspects. Through the experimental data analysis, it is verified again that the horizontal swirling wind can only make solid particles saltate along the ground surface. Based on a Lagrangian reference frame, the tracks of dust grains with different density (material) and diameter are calculated to show the effect of dust particles entrained by the vertical swirling wind field. The movement of solid particles depends on the interactions between the aloft dust particles and the airflow field of dust devils, in which the drag and the centrifugal force component on the horizontal plane are the key force components. There is the trend of the fine dust grains rising along the inner helical tracks while the large dust grains are lifting along the outer helical tracks and then descending beyond the corner region, resulting in the impact between different-sized dust grains in the swirling atmospheric flow. This trend will make the dust stratification, developing a top small-sized grain domain and a bottom large-sized grain domain in dust devils.

Corresponding author address: Dr. Zhaolin Gu, State Key Laboratory of Multiphase Flow in Power Engineering, Dept. of Environmental Science and Technology, Xi’an 710049, China. Email: guzhaoln@mail.xjtu.edu.cn

1. Introduction

Whether dust devils occur on Earth or Mars, the inducement of the dust devil vortex and the airflow of dust devils are widely studied on the convective boundary layer scale (Smith and Leslie 1976; Kanak et al. 2000; Rafkin et al. 2001; Toigo 2003; Michaels and Rafkin 2004) and on the dust devil scale (Zhao et al. 2004; Kanak 2005).

Although two possible mechanisms for particles entraining in dust devils—enhanced local wind speeds in the vortex creating the large wind shear forces, and a pressure deficit in the center of the vortex providing lift—are suggested (Balme et al. 2002; Ringrose et al. 2003), they do not explain dust stratification in dust devils. Dust stratification is the key process associated with the large-scale electric field of dust devils (Farrell et al. 2004). Until now, the interactions between the aloft dust particles and the airflow field of dust devils are not considered for the mechanisms of the dust particle entrained in a dust devil.

Zhao et al. (2004) presented a three-dimensional, unsteady, high-resolution model of a dust devil to investigate the airflow evolution of a modeled dust devil by numerical simulation, using fine grids: the radial grid spacing smoothly stretched from 0.1 m at the center to 4 m, and the vertical grid spacing stretched from 0.1 m on the surface to about 10 m at the top. The Smagorinsky scheme (Smagorinsky 1963) was used for the parameterization of the subgrid viscosity. It is indicated that the main forces exerted on the air parcels consist of the vertical components (the buoyancy and the vertical pressure gradient force) and the radial components (the centrifugal force and the radial pressure gradient force) if the air viscosity is neglected (giving high Reynolds numbers for dust devils). The main forces on the dust particles include the drag, the pressure gradient forces, the gravity and buoyancy, and the added mass force (Clift et al. 1978), among which the drag exerted on the particles by the updraft is the key force component. So the dust lifting in dust devils depends on the fine structure of the airflow field.

The motivation of this work is to examine the dust-lifting physics through tracking the particles in the airflow fields based on a Lagrangian reference frame, in which the interaction between the dust particles aloft and the airflow field of dust devils is investigated. This is described in section 6. Section 2 describes the dust devil–scale mathematical model and the treatment of boundary conditions. The simulation of airflow in a modeled dust devil in its mature stage is illustrated in section 3. Through the experimental data analysis, the wind-blowing sand transport on the ground surface and the vertical wind speed threshold for dust lifting are introduced in sections 4 and 5, respectively. Section 7 is a summary.

2. Mathematic model formation

The dust aloft may expedite the energy dissipation of the airflow and shorten the life of dust devils. However, the characteristics of the airflow in different stages might be slightly influenced by the dust aloft. It might be assumed that the sand dust has no effect on the atmosphere flow field in the developing stage, considering the swirl in this stage might not be strong enough to levitate the dust. On the other hand, this assumption might be made because of the limitation of the computer and thus the airflow field could be obtained first. The movement of sand dust will be studied only after the mature stage. The solid particle is assumed to be spherical.

a. Atmosphere (gas phase) flow large-eddy simulation (LES) model of dust devils

The filtered Navier–Stokes equations for an incompressible buoyancy flow are
i1520-0469-63-10-2630-e1
i1520-0469-63-10-2630-e2
i1520-0469-63-10-2630-e3
where ρc is the air density, g is the gravitational acceleration, μ is the air viscosity, β is the thermal expansion coefficient, Tc is the buoyancy reference temperature, and T is temperature. Also, is the source term of the interaction of particles to gas phase (this term is valid only when the gas carries solid particles), ϕs is the source term of the scalar quantity from the radiative contribution, H is enthalpy, Pr is the molecular Prandtl number, τij is the subgrid scale stress, and P is a modified pressure defined by P = p + ⅓τkk.
The subgrid stresses and fluxes are unknown and simulated by the Germano dynamic subgrid scheme (Germano et al. 1991):
i1520-0469-63-10-2630-e4
i1520-0469-63-10-2630-e5
where
i1520-0469-63-10-2630-e6
μSGS and PrSGS are the subgrid viscosity and the subgrid-scale Prandtl number, respectively. Also μSGS is determined by
i1520-0469-63-10-2630-e7
where |S| = (2SijSij)1/2 is the magnitude of the resolved-scale rate-of-strain tensor, Cd is the model coefficient determined by the dynamic scheme, and Δ is the grid filter width and Δ = V1/3.

A six-flux radiation model (Siegel and Howell 1992) is employed to solve the radiation of the gas and the wall.

b. Transport model of dust particles in atmosphere (gas phase) flow

The atmosphere flow of dust devils is calculated based on the Lagrangian reference frame. According to Newton’s second law,
i1520-0469-63-10-2630-e8
where F is the force activating on the particle, and m is its mass. See Clift et al. (1978) for a full description of the equations of particle transport.
The major component of these forces is the drag exerted on the particle by the continuous gas phase:
i1520-0469-63-10-2630-e9
where the drag factor is
i1520-0469-63-10-2630-e10
and the particle Reynolds number is defined by
i1520-0469-63-10-2630-e11
where d is the particle diameter, ρ and μ are the density and viscosity in the continuum, and vR is the relative velocity of the two phases.
There are additional forces on the particles included in the calculation as follows: The pressure gradient force
i1520-0469-63-10-2630-e12
The gravity and the buoyancy force
i1520-0469-63-10-2630-e13
where ρP is the density of the particle and g is the gravitational acceleration.
The added mass force is
i1520-0469-63-10-2630-e14

c. Treatment of boundary and initial conditions

Figure 1 shows the horizontal profiles of temperature (°C), pressure (mb), and the three cylindrical components of the wind velocity (m s−1) through the base of a dust devil, at 2.1, 5.2, and 9.4 m above the surface. The measurements were made by Sinclair (1966) near Tucson, Arizona, over flat terrain at 1300 mountain standard time (MST) 13 August 1962.

According to Sinclair’s observations (Sinclair 1966, 1973), the radius of the vortex region was about 50 m, the ambient temperature was about 313 K (40°C). With 720 000 grids stretched in the radial direction, from 0.1 m at the center to 5 m on the lateral boundary, and the vertical direction, from 0.1 m on the surface to about 15 m at the domain top, the computational domain is a cylindrical domain with radius R = 50 m and height H = 150 m, which is suitable to utilize a reasonable fine grid resolution to resolve the dominant turbulence in the dust devil core.

According to theories, the intensities of dust devils depend of the buoyancy and depth of the convective layer. Many observations and studies have shown that on a small scale, the shapes and the intensities of dust devils are sensitive to a large number of factors, such as soil cover, physical characteristics, composition, topography, and weather (Renno et al. 2004). The intensities are described by the swirl ratio. Generally, a constant heat flux is specified at the lower boundary (Zhao et al. 2004; Kanak 2005) in the simulation models to allow for temperature inversion near the ground surface. Since the temperature difference between the ground surface and near-surface air parcels, causing the buoyancy and thus the convection, is the main driving force of the dust devil, the surface temperature could be considered as a key parameter in determining the intensity of the updraft in our quasi-steady LES model. The airflow is driven by maintaining the lower boundary at fixed temperature profile T (K) = 313 + 0.4(Rr), where R is the radius of the computational region, r is the radius of nodes in the lower boundary, and 313 K is the ambient temperature (Sinclair 1966). The maximal temperature difference between the ground and ambient is 20 K at the center of the lower boundary, which approximately corresponds with the actual temperature difference in summer (Zhao et al. 2004).

The computational region is bounded by a no slip lower boundary and a pressure inlet side boundary. Neumann boundary conditions for the lateral pressure inlet condition boundary of dust devils (Leslie and Smith 1977; Smith and Leslie 1976) means that the air is allowed to flow in or out of the computational domain through the lateral boundary, and the direction of the airflow must be determined dynamically. Accordingly, on the lateral boundary, r = R, the pressure is specified while Neumann condition for the velocity on the lateral boundary is, ∂ui/∂n = 0.

The upper boundary is set to be an outlet, at which Neumann boundary conditions are also imposed on all transported variables, velocity, temperature, etc. This means that their gradients are specified, all transported quantities are given zero normal gradient, with the exception of velocity, which is given constant normal gradient to ensure global mass conservation. The air temperature is set to be the ambient temperature 313 K when flowing in the computational region. For the radiation scalar quantity, a simplified boundary condition qx = qy = σT4 was employed.

Many investigators have proposed or provided evidence that larger-scale convective circulations, which are not initially rotational, can provide vertical and/or tiltable horizontal vorticity; namely, dust devils might result from weak vertical vortex perturbation (Carroll and Ryan 1970; Cortese and Balachandar 1993; Shapiro and Kanak 2002). The initial vortex perturbation could be expressed in terms of the rotating speed on the domain boundary. The surface roughness is sensitive to the intensity of friction effect and thus the vertical distribution of the rotating speed near the ground (Smith and Leslie 1976; Leslie and Smith 1977).

At the lateral pressure inlet condition boundary, it is difficult to choose an appropriate swirling flow condition at r = R since there are a number of possibilities (Leslie and Smith 1977). Smith and Leslie (1976) indicated that two kinds of swirling flow conditions can be used, the swirling velocity υt or the vertical component of vorticity ζ, and the choice between them will depend on what information can be deduced from observations of the airflow in the vicinity of a dust devil. Fortunately, the tangential velocity around the dust devil, measured by Sinclair (1966), has been recorded. We can estimate the tangential velocity value at r = 50 m from Fig. 1. The value of tangential velocities at r = 50 m at different altitude, h = 5.2 m and h = 9.4 m (V7 and V31 in Fig. 1), is different. The tangential velocity at 9.4 m above the surface is obviously greater than that at 5.2 m. This result is explained that the friction of the surface (resulting from grass, sand, bushes, etc.) slows down the angular momentum. Thus a revised tangential velocity profile υt(z) = 2.0(1 − e−2z) is adopted for the swirling flow condition in our model at r = R.

In summary, the boundary conditions are as follows.

  • At z = 0: u = 0, υ = 0, w = 0, T (K) = 313 + 0.4(Rr).

  • At z = H: Neumann boundary conditions.

  • At r = R: p = 0, T = 313 K, qx = σT4 = 544.2 W m−2, qy = σT4 = 544.2 W m−2, ∂(υrr)/∂r = 0, ∂υz/∂r = 0, ∂(υtr)/∂r = 0 if υr > 0, and υt(z) = 2.0(1 − e−2z) if υr < 0.

The simulation of the airflow evolution is a transient problem and thus the initial conditions must be set. The initial radial and vertical velocities in the domain are set to zero and the initial temperature in the domain is set to 313 K. The initial tangential velocities are set as 100.0[1 − exp(0.01r2)]/r (Oseen vortex) to ensure the flow reaches the quasi–steady state in a short time. In our algorithm, the third-order quadratic upwind interpolation of convective kinematics (QUICK) scheme for discretizing the advection term, the pressure implicit split operator (PISO) pressure velocity coupling (Jang et al. 1986), and the quadratic time differencing are used. The simulation uses 720 000 grids, 80(r) × 72(θ) × 125(z). The azimuthal grid spacing is fixed, while the radial grid spacing, Δr, varies, smoothly stretched from 0.1 m at the center to 5 m on the lateral boundary; the vertical grid spacing, Δz, varies too, smoothly stretched from 0.1 m on the surface to about 15 m at the domain top. The time step, Δt, is chosen to be about 0.5 s according to the Courant–Friedrichs–Lewy (CFL) number.

As mentioned above, the velocities are written as two forms: (u, υ, w), which refers to Cartesian coordinate system and (υr, υt, υz), which refers to a cylindrical coordinate system. However, the simulation is performed using Cartesian coordinate system for the cylindrical computational domain. The simulated results will also be shown in the Cartesian coordinate system and then all the analysis is carried out. Then we examined the spatial distribution of solid particles within the vortex flow and the effect of these particles on the flow field based on Lagrangian reference frame.

3. Atmosphere flow of dust devils in the mature stage

In our LES model and algorithm, it takes about 200 s for the atmospheric flow of a dust devil to reach the quasi steady state. The quasi steady state of the airflow field of the modeled dust devil means that the time-averaged airflow field does not change; for example, the time-averaged airflow field within 30 s is similar to the time-averaged airflow field within 60 s. This quasi steady state indicates the characters of the gas phase field in the mature stage of a modeled dust devil, as shown in Fig. 2. The results were verified with Zhao et al.’s model (Zhao et al. 2004).

In Zhao et al. (2004)’s literature, the flow of a fully developed steady dust devil vortex was divided into four regions: the outer region, the core, the corner, and the near-surface layer. In the outer flow region, the airflow moves in response to the vorticity in the vortex core and the positive buoyancy force in the convective plume. The core region is the central core of the vortex. In fact, dust devils characteristically contain a funnel that may be visualized by dust and debris lifting from the surface. In the corner region, the inflow near the surface is deflected upward into the core region. The surface layer consists of the boundary layer feeding into the corner region. The inflow spirals into the center in this region. Figure 2a shows the instantaneous airflow profile of the modeled dust devil in the vertical plane. The corner region, part of core region and part of surface layer of the modeled dust devil, is displayed in this figure, with the violent and turbulent flow. There is an intense outward-leaning updraft in the dust devil corner caused by the overshooting of the rapidly influx in the surface layer, similar to the observations by Sinclair (1973). The angular momentum of the airflow in the surface layer is much lower than that of airflow fluid in the main vortex above it. The lower angular momentum causes a rapidly inward flow in the surface layer. The inward flow reflects upward to the core as it reaches the corner region. The overshooting of the inflow results in a quite rapid turn and centrifugal waves occurring in the corner. The swirling velocity at a certain level, about 2.5m, in the corner is much greater than that in the core region above the corner. The highest swirling velocity and the strongest turbulence of an actual dust devil are generally located at the corner region (Sinclair 1973; Ives 1947; Hess and Spillane 1990), showing that our simulation results are acceptable.

Figure 2b is the vertical velocity of the modeled dust devil in the vertical plane. It shows that the vertical velocity reaches over 10 m s−1 near the ground surface and 15 m s−1 in the corner region. The air is heated by the hot ground surface and concentrates into the vortex center and flows up. As shown in Fig. 2c, the higher airflow temperature in the corner region brings out the more thermal buoyancy and thus the more driving force of the updraft. On the other hand, the pressure drop in the corner region, as shown in Fig. 2d, is more than the other region, to reinforce the updraft in the corner region.

The dust devils can extend to levels of several kilometers, enabling particles to be carried aloft (Ives 1947; Hess and Spillane 1990). Dust devils typically have radii of about 1 to 150 m (Sinclair 1966; Schiewsow and Cupp 1975; Hess and Spillane 1990; Greeley et al. 2003) and display a maximum tangential velocity of 25 m s−1. The typical temperature and pressure drop observed within dust devils vary in the range of 4–8 K and 250–450 Pa (Sinclair 1973). In comparison, the radius of the modeled dust devil core is about 10 m, and the radius of the maximal swirling velocity ring, that is, the diameter of the vortex core near the surface, is about 3–4 m; the maximum tangential velocities are about 20 m s−1; the temperature and pressure perturbation in the modeled dust devil is about 8 K and 300 Pa, respectively. The above results show the modeled dust devil in this work is an intense dust devil compared with Renno et al.’s theory (Renno et al. 1998). In Renno et al.’s case, the temperature perturbation is 5 K, and the velocity and pressure perturbations are w ≈ 8–16 m s−1, υ ≈ 11–16 m s−1, and Δp ≈ 1.3–2.7 hPa.

A weaker and cooler downdraft, in nearly solid body rotation, is present in the modeled dust devil core, which was suggested by Sinclair and others (Sinclair 1973; Kaimal and Businger 1970). In addition, some other maximum velocities are obtained through the statistical analysis of the observed or the modeled dust devils. In our simulation, the maximum near-surface vertical velocity in the corner is 15 m s−1, compared to the peak value of the near-surface vertical velocity of about 15 m s−1 obtained by Sinclair (1973) and Ives (1947). The near-surface radial velocity usually does not exceed 5 m s−1. The radial velocity contours in the vertical plane are shown in Fig. 2e. The radial velocity reaches its peak value beyond the core region. The level the maximum radial velocity reaches is lower than the levels the maximum swirling velocity gets. There is no obvious radial velocity at level of the maximum swirling velocity, which also agrees with Sinclair’s observation (Sinclair 1973). As mentioned above, the characteristics of the modeled dust devil agree well with the observation, which provide a strong indication that our simulation results are acceptable.

Although with similar ambient conditions, many features of the measured dust devil by Sinclair (1966) can appear in the modeled dust devil, the modeled dust devil is stronger than the measured one. Perhaps the tangential velocity at the lateral inlet condition boundary, 2 m s−1, is greater than that of the measured dust devils. We cannot evaluate the specific tangential velocity value from Fig. 1. The other possible reason might be that all kinds of friction exist in actual dust devils; such as that caused by the solid particles, ground vegetation, etc. These kinds of friction can slow down the airflow of dust devil.

4. Wind-blowing sand transport

As shown in Fig. 2e, there is a great vertical gradient of the radial velocity of the airflow near the ground surface, which could cause the turbulent eddies to transfer the turbulent kinetic energy to the solid particles on the ground. Therefore, in the atmospheric flow of the modeled dust devil, there is a strong wind shear on the ground surface, causing dust particles to saltate and move along the ground surface.

The lifting effect of the wind shear has been studied extensively in atmospheric boundary layer wind tunnels (Dong et al. 2002; Ni et al. 2002). In the following, we will examine the levels of dust particles being carried up by the horizontal wind using Dong et al.’s experimental data.

The flux profile of a blowing sand cloud, or the variation of the blown sand flux with the height, is the reflection of the blown sand particles moving in different trajectories, and also the basis for checking drifting sand. Here we cite a series of experimental data by Dong et al. (2002), which are wind tunnel results obtained from systematic tests, including the flux profiles of different-sized sands at different free-stream wind velocities. Within the near surface layer, the decay of the blown sand flux with the height can be expressed as
i1520-0469-63-10-2630-e15
where qh is the blown sand transport rate at height h, and a and b are parameters varying with the wind velocity and sand size. The coefficient a in the function represents the transport rate in true saltation and the coefficient b implies the relative decay rate with the height of the blown sand transport rate. The true saltation fraction, the ratio of the sand transported on the surface (h = 0) to the total transport, decreases with both the sand size and the wind speed. From Dong’s experimental data, we can get the correlation between the transport rate and the height, showing that the sand grain diameters from 100 to 250 μm are easily lifted by winds. The range of the free-stream wind velocity is from 8 to 22 m s−1. The ambient wind speeds on Earth are generally in this range. The ranges of the sand grain diameter and the wind velocity agree with our study.

The flux profiles are converted to straight lines by plotting the sand transport rate, qh, on a log scale, as shown in Fig. 3. The slope of the straight lines, representing the relative decay rate with the height of the sand transport, decreases with an increase in the free-stream wind velocity, as shown in Figs. 3a,b,c. The slope of the straight lines also decreases with an increase in the sand grain size. These results imply that relatively more of the blown sand is transported to high levels as the grain size and the wind speed increase.

We employ a sand transport rate of 0.01 g cm−1 s−1 as the reference value in our study. If the sand transport rate is lower than the reference value, the airflow at this level can be regard as the clean airflow. From Fig. 3, we can see that the height where the blown sand transport rate qh reaches 0.01 g cm−1 s−1 are generally lower than 0.6 m, which means sand particles are very difficult to lift for simple boundary layer wind shear. The sand grains, blown by the horizontal wind, can only saltate and move near the surface.

Greeley et al. (1992) suggested that horizontal winds initially lift the larger sand-sized particles, but once airborne they return to the surface and impart kinetic energy to smaller lighter particles (the cascade effect). These smaller particles then get raised into suspension via the imparted momentum. Other wind systems, not simple horizontal wind, should play an important role in carrying dust grains up to high levels.

5. Vertical wind speed threshold for dust lifting

As mentioned above, the drag exerted on the particles by the continuous gas phase is the key force component. The drag is related to the updraft speed. Stronger the updraft, the more drag to lift solid particles. Thus, the updraft speed is the necessary condition for dust lifting within dust devils. Here the basic dust-lifting theory in updraft, or the updraft effect for dust lifting, will be discussed.

It is well known that the lifting velocity threshold of a particle is equal to the particle deposition velocity in the static air. For the particle depositing freely in the static air, the inertial term of the momentum equation is zero, and only the drag force and the gravity are considered. So Eq. (9) can be written as
i1520-0469-63-10-2630-e16
The lifting velocity threshold of a particle can be expressed as the following formula:
i1520-0469-63-10-2630-e17
where
i1520-0469-63-10-2630-e18
and CD = 24(1 + 0.15 Re0.687)/Re.

The lifting velocity thresholds of two kinds of different density particles are shown in Fig. 4. It indicates that the lifting velocity threshold is proportional to the density and the particle size. And with the same diameter the lifting velocity threshold of the high-density particle is higher than that of the low-density particle. The vertical wind speed of the updraft in the convective plume on Earth is usually below 10 m s−1, so the solid particles with more than 1-mm diameter are difficult to lift.

The level at which the solid particles can be lifted by the wind shear is lower than 0.6 m, while above the 0.6-m level, grains cannot be lifted by the wind shear and instead are lifted by the drag force from the updraft speed.

6. Dust-lifting patterns within the swirling airflow of dust devils

Since dust devils can carry a great amount of particulate matter into the atmosphere, it is necessary to study the dust-lifting mechanisms within dust devils through numerical modeling, laboratory simulations, and field studies (Balme et al. 2002). Each technique has unique attributes. For example, field investigations involve full-scale events, but the complexities of the natural processes often cannot identify the critical variables for analysis. Laboratory simulation is a primary approach to study dust devils under controlled conditions, in which the critical variables can be isolated for analysis. Balme et al. (2002) have performed a series of laboratory simulations to explore the lifting process within dust devils. Nevertheless, the small scale of the laboratory model does not correspond to actual events, so that some parameters cannot be measured; not only that, the experiments are expensive and time-consuming. In the following, numerical simulation of the dust-lifting mechanism will be carried out.

The maximum wind speed near the ground surface is about 20 m s−1 in the modeled dust devil, enough to make the solid particles “hop” on the ground surface. The saltating particles are easily lifted by the updraft in the corner region because of the high vertical velocity. The maximal wind speed of the updraft (below the 0.6-m level) in the corner of the modeled dust devil is about 5 m s−1 (Fig. 2b). This updraft speed may lift solid grains with a diameter of up to 600 μm.

The trajectories of the particles entrained in the swirling flow are generally determined by Newton’s second law. In the airflow in the mature stage of the modeled dust devil, the tracks of three kinds of grain diameters, 100, 200, and 300 μm, are respectively simulated, in a Lagrangian reference frame (Figs. 5 –7). Owing to the limitation of our computer, only 20 000 particles with the same size are tracked in each case, and we ignored the interaction between different-sized particles. Still, the airborne particle tracks of different sizes could be composed in vertical plane for the qualitative demonstration of the movement and interplay among different size particles, as shown in Fig. 8. To compare the lifting patterns of different density particles, the spatial distribution of low-density particles (wood) with the diameter, 300 μm, is simulated too (Fig. 9). Note that the tangential component of the particles movement is not plotted in Figs. 5 –9. If the tangential component of the particles movement is composed with the vertical component, all the track lines should be spiral.

In our simulation, solid grains with the same size are injected into the mainstream of dust devils with different initial velocity in three cases, and we make sure that these grains are sprayed under the 0.3-, 0.5-, and 0.7-m levels, respectively. In each case, 20 000 particles are injected into the simulation region from the center field of lower boundary within about 50 m2. The injection rate is 400 particles per time step (in this two-phase flow simulations, a constant time step of 0.1 s is used instead of the CFL condition). In other words, the mass flow rate is 10 kg s−1; that is, each particle in the simulation represents a group of particles weighing 25 g. The simulation in each case continues for t = 5 s.

If the average dust flux, the airborne dust rate per horizontal unit area, in the computational region is evaluated by dividing the injection mass flow rate by the area, the dust flux at 1-m level in the computational region is about 1.27 g m−2 s−1, which is of order 1 g m−2 s−1, as in Renno et al.’s study (Renno et al. 2004). In Renno et al.’s study, the dust flux is obtained by multiplying the dust concentration by the vertical velocity. However, the dust flux changes in radial direction and vertical direction and needs to be further investigated. Obviously, the vertical dust flux reduces with height due to the large-sized particles descending.

Figures 5, 6 and 7 show the spatial distribution of dust particles with diameters 100, 200, and 300 μm, respectively, at t = 5 s within the modeled dust devil. These figures demonstrate that the spatial distributions of different-sized grains are different. The small particles move along with the main streamline of the updraft while the large ones deflect outward from the main streamline.

In addition to the drag in the updraft, the centrifugal force exerted on the solid particles in the swirling airflow of dust devils is another key force component on the horizontal plane. It is easily understood that centrifugal force exerted on large particles is greater than that exerted on small ones. The centrifugal force exerted on an individual particle is
i1520-0469-63-10-2630-e19
The large particles deflect outward from the updraft main streamline and deposit beyond the updraft mainstream. These descending particles may be entrained in the rapid near-surface inflow to the vortex center again, illustrated in Fig. 7. Therefore, these particles will move circularly in the dust devil corner until the updraft decay and the drag is not enough to lift them. Because large particles are thrown beyond the vortex, the spatial distribution of them draws the outer profile of the dust devil corner. On the contrary, the centrifugal force exerted on small-sized particles is rather smaller, so they spiral up within the updraft and would not deposit in the vortex, as shown in Fig. 5. For the medium size particles, the centrifugal force exerted on them is not so great, so they can be carried to a higher altitude and then deflect from the updraft main streamline. The medium-sized particles descend from the higher level, compared to the large-sized particles. They may also be entrained in the near-surface inflow to the vortex center too, like the large ones illustrated in Fig. 6.

Figure 8 shows the composite of the airborne grain tracks of different sizes in vertical plane according to the results in three cases. In the lhs of Fig. 8, the arrowed curve 1 indicates the track of the small-sized grains, according to the spatial grain distribution in Fig. 5. Similarly, the arrowed curve 2 denotes the track of the medium-sized grains, in the light of the spatial grain distribution in Fig. 6. And the arrowed curve 3 illustrates the track of the large-sized grains, with regard to the spatial grain distribution in Fig. 7. Although the above track simulations of different-sized particles within the modeled dust devil are separately carried out and thus the interaction of different-sized grains cannot be revealed, the composite grain-lifting patterns in Fig. 8 could qualitatively demonstrate the interplay among different-sized particles. Only the small-sized particle could be helically raised very high with the atmosphere flow (arrowed curve 1). The medium-sized dust particles are spirally lifted to some height owing to the strong updraft in the corner, deflect outward from the updraft main streamline owing to the more centrifugal force on them and then they descend beyond the corner region (arrowed curve 2). They will come into impact with the helically rising large-sized particles (arrowed curve 3), resulting in a series of small vortices (arrowed curve 4). So the movements of the solid particles seem in chaos (rhs of Fig. 8).

In natural dust devils, all dust grains are different in size and shape; the interactions between medium and large particles are more complex. The airflow with dust grains is more complex and turbulent than the modeled dust devils. Like the typical case in Greeley et al.’s (2003) literature, the vortex in the core and upper part of dust devils is composed of loose fine dust, whereas a skirt of dense larger particles surrounds the base. The medium and large dust grains move circularly in the corner region and play an important role in the vanishing of dust devils.

The above mode of grain moving, mixing, and collision could develop a top small-sized (lighter) grain domain and a bottom large-sized (heavier) grain domain, or grain mass stratification, and thus tribo-electrically produce strong electric fields within dust devils. The dust cloud has a macroscopic electric dipole moment oriented in the nadir (downward) direction, which might play a significant role in dust sourcing (Farrell et al. 2004).

Field studies indicate that dust devils usually occur on many places, such as smooth playa and rocky alluvial fans (Metzger et al. 1999). The composition of the particles on different surfaces is various. In the desert, the particle is mainly quartz. In the barren farm or the dry riverbed, the particles are primarily soil dust. When dust devils occur on different surfaces, all kinds of particles, such as sands (quartz particles), soil dust, or wood particles, etc., can be lifted by dust devils. It is significant to study the tracks of different density particle with the same size, as shown in Fig. 9. The spatial distributions of low-density grains, for example, wood, with a diameter of 300 μm were simulated in the modeled dust devil. Comparing to the spatial distributions of large density grains with the same size in Fig. 7, the low-density particles are easier to be carried up to high levels relative to dust particles.

7. Summary

The dust-lifting mechanisms are carefully examined in this paper. The effect of horizontal and vertical wind on dust lifting is specified that the horizontal wind can only make solid grain saltate and move along the ground surface and the updraft plays an important role in dust lifting. In the atmosphere flow of the modeled dust devil, there is a strong wind shear to make dust particles saltate due to the high gradient of the radial velocity of the airflow near the ground surface.

Once dust grains entrained in the swirling updraft, the movement of solid particles in the airflow of dust devils depends on the interactions between the aloft dust particles and the airflow field of dust devils. The drag and the centrifugal force component on the horizontal plane are the most important components, exerted on the solid particles. The airflow field in the mature stage of the modeled dust devil was simulated based on the advanced dust devil–scale large-eddy simulation (LES) model, using the dynamic subgrid-scale scheme. The tracking of different sized grains in the gas phase field of the modeled dust devil was carried out based on Lagrangian reference frame.

There is the trend of the fine dust grains rising along the inner helical tracks while the large dust grains lifting along the outer helical tracks and then descending beyond the corner region, resulting in the impact between different-sized dust grains in the swirling atmospheric flow. This trend will make the dust stratification in dust devils, developing a top small-sized (lighter) grain domain and a bottom large-sized (heavier) grain domain. In comparison with high density particles of the same size, the low-density particles are easier to be carried up to high levels by the airflow of dust devils.

Acknowledgments

This research is financially supported by National Basic Research Program of China (2004CB720200) and Trans-century Training Program Foundation for Talents by State Education Ministry, China. The authors would like to express their sincere appreciation to the reviewers for their constructive comments.

REFERENCES

  • Balme, M., R. Greeley, B. Mickelson, J. Iversen, G. Beardmore, D. Branson, and S. Metzger, 2002: Dust devils on Mars: Results from threshold test using a vortex generator. Extended Abstracts, 33d Annual Lunar and Planetary Science Conf., Houston, TX, Lunar and Planetary Institute, CD-ROM, 1048.

  • Carroll, J. J., and J. A. Ryan, 1970: Atmospheric vorticity and dust devil rotation. J. Geophys. Res., 75 , 51795184.

  • Clift, R., J. R. Grace, and M. E. Weber, 1978: Bubbles, Drops, and Particles. Academic Press, 380 pp.

  • Cortese, T., and S. Balachandar, 1993: Vortical nature of thermal plumes in turbulent convection. Phys. Fluids, A5 , 32263232.

  • Dong, Z. B., X. P. Liu, and H. T. Wang, 2002: The flux profile of a blowing sand cloud—A wind tunnel investigation. Geomorphology, 49 , 219230.

    • Search Google Scholar
    • Export Citation
  • Farrell, W. M., and Coauthors, 2004: Electric and magnetic signatures of dust devils from the 2000-2001 MATADOR desert tests. J. Geophys. Res., 109 .E03004, doi: 10.1029/2003JA009965.

    • Search Google Scholar
    • Export Citation
  • Germano, M., U. Piomelli, P. Moin, and W. H. Cabot, 1991: A dynamic subgrid-scale eddy viscosity model. Phys. Fluids, A3 , 17601765.

  • Greeley, R., N. Lancaster, S. Lee, and P. Thomas, 1992: Martian eolian processes, sediments and features. Mars, H. H. Kieffer et al., Eds., University of Arizona Press, 730–766.

    • Search Google Scholar
    • Export Citation
  • Greeley, R., M. R. Balme, J. D. Iversen, S. Metzger, R. Mickelson, J. Phoreman, and B. White, 2003: Martian dust devil: Laboratory simulations of particle threshold. J. Geophys. Res., 108 .5041, doi: 10.1029/2002JE001987.

    • Search Google Scholar
    • Export Citation
  • Hess, G. D., and K. T. Spillane, 1990: Characteristics of dust devils in Australia. J. Appl. Meteor., 29 , 498507.

  • Ives, R. L., 1947: Behavior of dust devils. Bull. Amer. Meteor. Soc., 28 , 168174.

  • Jang, D. S., R. Jetil, and S. Acharya, 1986: Comparison of the PISO, SIMPLER, AND SIMPLEC algorithms for the treatment of the pressure-velocity coupling in steady flow problems. Numer. Heat Transfer, 10 , 3. 209228.

    • Search Google Scholar
    • Export Citation
  • Kaimal, J. C., and J. A. Businger, 1970: Case studies of a convective plume and a dust devil. J. Appl. Meteor., 9 , 612620.

  • Kanak, K. M., 2005: Numerical simulation of dust devil-scale vortices. Quart. J. Roy. Meteor. Soc., 131 , 12711292.

  • Kanak, K. M., D. K. Lilly, and J. T. Snow, 2000: The formation of vertical vortices in the convective boundary layer. Quart. J. Roy. Meteor. Soc., 126 , 27892810.

    • Search Google Scholar
    • Export Citation
  • Leslie, L. M., and R. K. Smith, 1977: On the choice of radial boundary conditions for numerical models of sub-synoptic vortex flows in the atmosphere, with application to dust devils. Quart. J. Roy. Meteor. Soc., 103 , 499510.

    • Search Google Scholar
    • Export Citation
  • Metzger, S. M., J. R. Carr, J. R. Johnson, T. J. Parker, and M. T. Lemmon, 1999: Dust devil vortices seen by the Mars Pathfinder camera. Geophys. Res. Lett., 26 , 27812784.

    • Search Google Scholar
    • Export Citation
  • Michaels, T. I., and S. C. R. Rafkin, 2004: Large eddy simulation of atmospheric convection on Mars. Quart. J. Roy. Meteor. Soc., 130B , 12511274.

    • Search Google Scholar
    • Export Citation
  • Ni, J. R., Z. S. Liu, and C. Mendoza, 2002: Vertical profiles of aeolian sand mass flux. Geomorphology, 49 , 205218.

  • Rafkin, S. C. R., R. M. Haberle, and T. I. Michael, 2001: The Mars Regional Atmospheric Modeling System—Model description and selected simulations. Icarus, 151 , 2. 228256.

    • Search Google Scholar
    • Export Citation
  • Renno, N. O., M. L. Burkett, and M. P. Larkin, 1998: A simple theory for dust devils. J. Atmos. Sci., 55 , 32443252.

  • Renno, N. O., and Coauthors, 2004: MATADOR 2002: A field experiment on convective plumes and dust devils. J. Geophys. Res, 109 .E07001, doi:10.1029/2003JE002219.

    • Search Google Scholar
    • Export Citation
  • Ringrose, T. J., M. C. Towner, and J. C. Zarnecki, 2003: Convective vortices on Mars: A reanalysis of Viking Lander 2 meteorological data, sols 1-60. Icarus, 163 , 7887.

    • Search Google Scholar
    • Export Citation
  • Schiewsow, R. L., and R. E. Cupp, 1975: Remote Doppler velocity measurements of atmospheric dust devil vortices. J. Appl. Opt., 15 , 12.

    • Search Google Scholar
    • Export Citation
  • Shapiro, A., and K. M. Kanak, 2002: Vortex formation in ellipsoidal thermal bubbles. J. Atmos. Sci., 59 , 22532269.

  • Siegel, R., and J. R. Howell, 1992: Thermal Radiation Heat Transfer. Hemisphere Publishing Corporation, 1072 pp.

  • Sinclair, P. C., 1966: A quantitative analysis of the dust devil. Ph.D. thesis, The University of Arizona, 292 pp.

  • Sinclair, P. C., 1973: The lower structure of dust devils. J. Atmos. Sci., 30 , 15991619.

  • Smagorinsky, J., 1963: General circulation experiments with the primitive equations. I. The basic experiment. Mon. Wea. Rev., 91 , 99164.

    • Search Google Scholar
    • Export Citation
  • Smith, R. K., and L. M. Leslie, 1976: Thermally driven vortices: A numerical study with application to dust-devil dynamics. Quart. J. Roy. Meteor. Soc., 102 , 791804.

    • Search Google Scholar
    • Export Citation
  • Toigo, A. D., 2003: Numerical simulation of Martian dust devils. J. Geophys. Res, 108 .5047, doi:10.1029/2002JE002002.

  • Zhao, Y. Z., Z. L. Gu, Y. Z. Yu, Y. Ge, Y. Li, and X. Feng, 2004: Mechanism and large eddy simulation of dust devils. Atmos.–Ocean, 42 , 6184.

    • Search Google Scholar
    • Export Citation

Fig. 1.
Fig. 1.

Horizontal profile of temperature (°C), pressure (mb), and three cylindrical components of the wind velocity (m s−1) through the base of a dust devil, at 2.1-, 5.2-, and 9.4-m height above the surface (Sinclair 1966).

Citation: Journal of the Atmospheric Sciences 63, 10; 10.1175/JAS3748.1

Fig. 2.
Fig. 2.

Simulation of the gas phase field in the mature stage of a modeled dust devil. (a) The airflow profile of the modeled dust devil in the vertical plane. (b) The vertical velocity of the modeled dust devil in the vertical plane (m s−1). (c) The temperature of the modeled dust devil in the vertical plane (K). (d) The pressure drop of the modeled dust devil in the vertical plane (Pa). (e) The radial velocity of the modeled dust devil in the vertical plane (m s−1).

Citation: Journal of the Atmospheric Sciences 63, 10; 10.1175/JAS3748.1

Fig. 3.
Fig. 3.

The flux profiles of the blowing sand cloud with the blown heights.

Citation: Journal of the Atmospheric Sciences 63, 10; 10.1175/JAS3748.1

Fig. 4.
Fig. 4.

The lifting velocity threshold of two different density particles.

Citation: Journal of the Atmospheric Sciences 63, 10; 10.1175/JAS3748.1

Fig. 5.
Fig. 5.

The spatial distribution of the dust particles with diameter 100 μm in the modeled dust devil at Δt = 5 s.

Citation: Journal of the Atmospheric Sciences 63, 10; 10.1175/JAS3748.1

Fig. 6.
Fig. 6.

The spatial distribution of the dust particles with diameter 200 μm in the modeled dust devil at Δt = 5 s.

Citation: Journal of the Atmospheric Sciences 63, 10; 10.1175/JAS3748.1

Fig. 7.
Fig. 7.

The spatial distribution of the dust particles with diameter 300 μm in the modeled dust devil at Δt = 5 s.

Citation: Journal of the Atmospheric Sciences 63, 10; 10.1175/JAS3748.1

Fig. 8.
Fig. 8.

The dust-lifting patterns in a dust devil.

Citation: Journal of the Atmospheric Sciences 63, 10; 10.1175/JAS3748.1

Fig. 9.
Fig. 9.

The spatial distribution of the low density particles, e.g. wood particles, with diameter 300 μm in the modeled dust devil at Δt = 5 s. The grains with low density could reach higher levels than those with heavier density.

Citation: Journal of the Atmospheric Sciences 63, 10; 10.1175/JAS3748.1

Save
  • Balme, M., R. Greeley, B. Mickelson, J. Iversen, G. Beardmore, D. Branson, and S. Metzger, 2002: Dust devils on Mars: Results from threshold test using a vortex generator. Extended Abstracts, 33d Annual Lunar and Planetary Science Conf., Houston, TX, Lunar and Planetary Institute, CD-ROM, 1048.

  • Carroll, J. J., and J. A. Ryan, 1970: Atmospheric vorticity and dust devil rotation. J. Geophys. Res., 75 , 51795184.

  • Clift, R., J. R. Grace, and M. E. Weber, 1978: Bubbles, Drops, and Particles. Academic Press, 380 pp.

  • Cortese, T., and S. Balachandar, 1993: Vortical nature of thermal plumes in turbulent convection. Phys. Fluids, A5 , 32263232.

  • Dong, Z. B., X. P. Liu, and H. T. Wang, 2002: The flux profile of a blowing sand cloud—A wind tunnel investigation. Geomorphology, 49 , 219230.

    • Search Google Scholar
    • Export Citation
  • Farrell, W. M., and Coauthors, 2004: Electric and magnetic signatures of dust devils from the 2000-2001 MATADOR desert tests. J. Geophys. Res., 109 .E03004, doi: 10.1029/2003JA009965.

    • Search Google Scholar
    • Export Citation
  • Germano, M., U. Piomelli, P. Moin, and W. H. Cabot, 1991: A dynamic subgrid-scale eddy viscosity model. Phys. Fluids, A3 , 17601765.

  • Greeley, R., N. Lancaster, S. Lee, and P. Thomas, 1992: Martian eolian processes, sediments and features. Mars, H. H. Kieffer et al., Eds., University of Arizona Press, 730–766.

    • Search Google Scholar
    • Export Citation
  • Greeley, R., M. R. Balme, J. D. Iversen, S. Metzger, R. Mickelson, J. Phoreman, and B. White, 2003: Martian dust devil: Laboratory simulations of particle threshold. J. Geophys. Res., 108 .5041, doi: 10.1029/2002JE001987.

    • Search Google Scholar
    • Export Citation
  • Hess, G. D., and K. T. Spillane, 1990: Characteristics of dust devils in Australia. J. Appl. Meteor., 29 , 498507.

  • Ives, R. L., 1947: Behavior of dust devils. Bull. Amer. Meteor. Soc., 28 , 168174.

  • Jang, D. S., R. Jetil, and S. Acharya, 1986: Comparison of the PISO, SIMPLER, AND SIMPLEC algorithms for the treatment of the pressure-velocity coupling in steady flow problems. Numer. Heat Transfer, 10 , 3. 209228.

    • Search Google Scholar
    • Export Citation
  • Kaimal, J. C., and J. A. Businger, 1970: Case studies of a convective plume and a dust devil. J. Appl. Meteor., 9 , 612620.

  • Kanak, K. M., 2005: Numerical simulation of dust devil-scale vortices. Quart. J. Roy. Meteor. Soc., 131 , 12711292.

  • Kanak, K. M., D. K. Lilly, and J. T. Snow, 2000: The formation of vertical vortices in the convective boundary layer. Quart. J. Roy. Meteor. Soc., 126 , 27892810.

    • Search Google Scholar
    • Export Citation
  • Leslie, L. M., and R. K. Smith, 1977: On the choice of radial boundary conditions for numerical models of sub-synoptic vortex flows in the atmosphere, with application to dust devils. Quart. J. Roy. Meteor. Soc., 103 , 499510.

    • Search Google Scholar
    • Export Citation
  • Metzger, S. M., J. R. Carr, J. R. Johnson, T. J. Parker, and M. T. Lemmon, 1999: Dust devil vortices seen by the Mars Pathfinder camera. Geophys. Res. Lett., 26 , 27812784.

    • Search Google Scholar
    • Export Citation
  • Michaels, T. I., and S. C. R. Rafkin, 2004: Large eddy simulation of atmospheric convection on Mars. Quart. J. Roy. Meteor. Soc., 130B , 12511274.

    • Search Google Scholar
    • Export Citation
  • Ni, J. R., Z. S. Liu, and C. Mendoza, 2002: Vertical profiles of aeolian sand mass flux. Geomorphology, 49 , 205218.

  • Rafkin, S. C. R., R. M. Haberle, and T. I. Michael, 2001: The Mars Regional Atmospheric Modeling System—Model description and selected simulations. Icarus, 151 , 2. 228256.

    • Search Google Scholar
    • Export Citation
  • Renno, N. O., M. L. Burkett, and M. P. Larkin, 1998: A simple theory for dust devils. J. Atmos. Sci., 55 , 32443252.

  • Renno, N. O., and Coauthors, 2004: MATADOR 2002: A field experiment on convective plumes and dust devils. J. Geophys. Res, 109 .E07001, doi:10.1029/2003JE002219.

    • Search Google Scholar
    • Export Citation
  • Ringrose, T. J., M. C. Towner, and J. C. Zarnecki, 2003: Convective vortices on Mars: A reanalysis of Viking Lander 2 meteorological data, sols 1-60. Icarus, 163 , 7887.

    • Search Google Scholar
    • Export Citation
  • Schiewsow, R. L., and R. E. Cupp, 1975: Remote Doppler velocity measurements of atmospheric dust devil vortices. J. Appl. Opt., 15 , 12.

    • Search Google Scholar
    • Export Citation
  • Shapiro, A., and K. M. Kanak, 2002: Vortex formation in ellipsoidal thermal bubbles. J. Atmos. Sci., 59 , 22532269.

  • Siegel, R., and J. R. Howell, 1992: Thermal Radiation Heat Transfer. Hemisphere Publishing Corporation, 1072 pp.

  • Sinclair, P. C., 1966: A quantitative analysis of the dust devil. Ph.D. thesis, The University of Arizona, 292 pp.

  • Sinclair, P. C., 1973: The lower structure of dust devils. J. Atmos. Sci., 30 , 15991619.

  • Smagorinsky, J., 1963: General circulation experiments with the primitive equations. I. The basic experiment. Mon. Wea. Rev., 91 , 99164.

    • Search Google Scholar
    • Export Citation
  • Smith, R. K., and L. M. Leslie, 1976: Thermally driven vortices: A numerical study with application to dust-devil dynamics. Quart. J. Roy. Meteor. Soc., 102 , 791804.

    • Search Google Scholar
    • Export Citation
  • Toigo, A. D., 2003: Numerical simulation of Martian dust devils. J. Geophys. Res, 108 .5047, doi:10.1029/2002JE002002.

  • Zhao, Y. Z., Z. L. Gu, Y. Z. Yu, Y. Ge, Y. Li, and X. Feng, 2004: Mechanism and large eddy simulation of dust devils. Atmos.–Ocean, 42 , 6184.

    • Search Google Scholar
    • Export Citation
  • Fig. 1.

    Horizontal profile of temperature (°C), pressure (mb), and three cylindrical components of the wind velocity (m s−1) through the base of a dust devil, at 2.1-, 5.2-, and 9.4-m height above the surface (Sinclair 1966).

  • Fig. 2.

    Simulation of the gas phase field in the mature stage of a modeled dust devil. (a) The airflow profile of the modeled dust devil in the vertical plane. (b) The vertical velocity of the modeled dust devil in the vertical plane (m s−1). (c) The temperature of the modeled dust devil in the vertical plane (K). (d) The pressure drop of the modeled dust devil in the vertical plane (Pa). (e) The radial velocity of the modeled dust devil in the vertical plane (m s−1).

  • Fig. 3.

    The flux profiles of the blowing sand cloud with the blown heights.

  • Fig. 4.

    The lifting velocity threshold of two different density particles.

  • Fig. 5.

    The spatial distribution of the dust particles with diameter 100 μm in the modeled dust devil at Δt = 5 s.

  • Fig. 6.

    The spatial distribution of the dust particles with diameter 200 μm in the modeled dust devil at Δt = 5 s.

  • Fig. 7.

    The spatial distribution of the dust particles with diameter 300 μm in the modeled dust devil at Δt = 5 s.

  • Fig. 8.

    The dust-lifting patterns in a dust devil.

  • Fig. 9.

    The spatial distribution of the low density particles, e.g. wood particles, with diameter 300 μm in the modeled dust devil at Δt = 5 s. The grains with low density could reach higher levels than those with heavier density.

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