Structure and formation of dust devil like vortices in the atmospheric boundary layer: A high resolution numerical study

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 116,, doi: /2011jd016010, 2011 Structure and formation of dust devil like vortices in the atmospheric boundary layer: A high resolution numerical study S. Raasch 1 and T. Franke 1 Received 29 March 2011; revised 6 May 2011; accepted 20 May 2011; published 26 August [1] The development of dust devil like vortices in the atmospheric convective boundary layer (CBL) is studied using large eddy simulation (LES). Special focus is placed on the analysis of the spatial structure of the vortices, the vorticity generating mechanisms, and how the vortices depend on the larger scale coherent near surface flow pattern of the CBL. Vortex centers are automatically detected during the simulation, and a tracking method is developed, which allows us to determine the temporally averaged structures of selected vortices. Also, various vorticity budget terms are calculated. A reference study with high resolution (2 m) and large model domain ( grid points) is carried out to account for the dependency of vortex generation on the larger scale CBL flow pattern, i.e., the near surface hexagonal cells. Vortices predominantly appear within the vertices of the cells. Their vorticity is maintained by a combination of divergence and twisting effects. Flow visualizations by tracers show that the vortices have an inverted cone like shape, similar to observed dust devils. Simulated vortex characteristics like tangential velocity or vorticity are at the lower limit of observed values. Strength and number of vortices heavily depend on the background wind. A small background wind enhances vortices, but for a mean wind speed of 4.4 m s 1, vortex generation is significantly reduced, mainly because the near surface flow changes from a cellular to a more band like pattern. A new mechanism is suggested, which relates the initial vortex generation to the cellular flow pattern. Citation: Raasch, S., and T. Franke (2011), Structure and formation of dust devil like vortices in the atmospheric boundary layer: A high resolution numerical study, J. Geophys. Res., 116,, doi: /2011jd Introduction [2] Dust devils are small scale convective vortices with vertical axes which are made visible by entrained dust or other particles. They are mainly characterized by high wind speeds, significant electrostatic fields, and by reduced pressure and enhanced temperature at their centers [Balme and Greeley, 2006]. Dust devils develop in the convective boundary layer of the Earth and Mars, especially in environments with low ambient wind speeds and strong superadiabatic lapse rates [Sinclair, 1969]. [3] Although the wind speeds of terrestrial dust devils are in general not high enough to present serious danger to humans they are of significant interest. One reason is the particle transport within dust devils. Renno et al. [2004] showed that dust devils significantly increase the vertical transport of dust. Since mineral dust and aerosols play an important role in terrestrial weather and climate, e.g., by changing the atmospheric radiation budget and by affecting 1 Institut für Meteorologie und Klimatologie, Leibniz Universität Hannover, Hannover, Germany. Copyright 2011 by the American Geophysical Union /11/2011JD cloud microphysics, it is necessary to understand and quantify the particle transport within dust devils [Renno et al., 2004]. Furthermore previous studies showed that dust devil like vortices seem to appear even in the absence of visible tracers suggesting that they are much more common than thought and thus may be of broader significance for boundary layer transports, e.g., for pollution dispersion [Kanak, 2006]. Another reason is that the study of terrestrial dust devils may help to understand Martian dust devils. They are of special interest because they can be an order of magnitude larger than terrestrial ones and thus might endanger future exploration [Balme and Greeley, 2006]. In addition Martian dust devils appear to support the persistent background atmospheric haze and influence the surface albedo through the formation of tracks on the surface [Balme and Greeley, 2006]. Accordingly they play an important role for studies of the climate, surface atmosphere interaction and the dust cycle on Mars [Toigo et al., 2003; Greeley et al., 2003]. 2. State of the Art [4] The investigations of dust devils started in 1860 with the first description by Baddeley [1860]. The following studies were mostly in form of measurements/observations [e.g., Sinclair, 1969, 1973; Renno et al., 2004; Bluestein et al., 1of16

2 Table 1. Observed and/or Measured Characteristics of Terrestrial and Martian Dust Devils a Diameter (m) Height (m) Tangential Velocity (m s 1 ) Vertical Velocity (m s 1 ) Rotation Sense D (K) Dp* (Pa) Earth (50) ( ) 5 20 or greater 3 15 (4) Random 2 8 (3 4) Mars (250) 8000 ( ) 2 93 n/a Random 0, 5 6 1, 1 4, 6 (2 3) a Taken from Kanak [2006]. The estimates of mean or typical values are given in parentheses. 2004], laboratory simulations [e.g., Mullen and Maxworthy, 1997; Greeley et al., 2003] and theoretical vortex models [e.g., Renno et al., 1998; Kurgansky, 2005]. These investigations focused mainly on the structure and characteristics of dust devils. A comprehensive summary of their results was given by Balme and Greeley [2006] and some measured and/ or observed quantities of dust devils are shown in Table 1. Amongst others the previous studies showed that the center of a dust devil is marked by a local maximum of the temperature, a minimum of the pressure and the change of direction of the horizontal wind speed components [e.g., Sinclair, 1973]. The structure of a typical dust devil is dominated by radial inflow near the surface, upward flow within the dust column (right outside the center) and possible down flow at the center [Balme and Greeley, 2006].The wind speeds reach their peak values outside the dust devil center: the tangential and vertical velocities within the dust column and the radial velocity outside the dust column [Sinclair, 1973]. [5] Additionally the dust devil formation and in particular the vorticity source in areas without terrain features were investigated. Observations found thermal plumes several kilometers above large dust devils [e.g., Sinclair, 1966] suggesting that a dust devil is the near surface expression of a convective plume [Balme and Greeley, 2006]. In this case the source of vorticity would be concentration of ambient vorticity. But also other sources were suggested; for example, Renno et al. [2004] proposed the twisting of horizontal atmospheric vortices developed from opponent cold and warm air currents into the vertical by convection. Up to now this issue is still disputed, which points out, that even though there has been more than one century of dust devil investigations, the knowledge is still limited and open questions remain. Another problem is, that measurements can only provide instantaneous values/pictures and thus averaged flow patterns of dust devils are unknown. Furthermore it is uncertain what governs the characteristics of dust devils, e.g., the size, wind speed, pressure and temperature excursions [Balme and Greeley, 2006]. Especially the impact of the background wind speed seems to be interesting since dust devils have been reported to be favored in environments with weak winds of less than 5 m s 1 [Sinclair, 1969; Ives, 1947]. [6] An essential tool for the analysis of dust devils are turbulence resolving numerical simulations, but due to the high computational efforts large eddy simulations (LES) of dust devils were not possible until a couple of years. Mason [1989] was probably the first one discovering small scale vertical vortices within the LES of the turbulent convective boundary layer but paid no attention to them. Later on several numerical simulation studies concentrating on dust devil like vortices followed and Kanak [2005] likely produced the first high resolution LES of dust devil scale vortices on Earth that had physical characteristics in reasonable agreement with observations. Some of these previous LES studies of turbulent convective boundary layers of the Earth and Mars are documented in the work of Kanak [2006]. One of their most important results is that dust devils form at the intersections and branches of the developing, near surface cellular convective pattern, which are characterized by local maxima of the vertical velocity [Kanak et al., 2000; Kanak, 2005]. Additionally it was shown that dust devils can form in the absence of mean winds or surface inhomogeneities [Kanak, 2005]. Nevertheless there are still some problems and deficits concerning the LES of dust devils, e.g., the simulated dust devil features are at the lower limit or even below the range of the observed values and there is still no generally accepted theory regarding the formation mechanism and source of vorticity. The main challenge for simulations is that dust devils are not an isolated phenomenon, but rather a part of the local convective system and thus it is necessary to resolve the typical scales of the convective boundary layer and the small scale dust devils simultaneously. Up to now only investigations with high resolution and small model domains [Kanak, 2005; Zhao et al., 2004; Gu et al., 2008; Gheynani and Taylor, 2010] or large model domains but coarse resolution were performed [Kanak et al., 2000; Gheynani and Taylor, 2010; Ito et al., 2010]. Furthermore, previous LES studies analyzed dust devil features only from instantaneous snapshots, except for the study of Gheynani and Taylor [2011] who recently developed an algorithm for the detection of Martian dust devil like vortices and performed statistical analysis. So far, mean dust devil features (e.g., from temporal averaging over the lifetime of dust devils) have not been determined for dust devils on Earth. Gu et al. [2008] derived the mean three dimensional structure of terrestrial dust devils from very high resolution LES with grid spacing down to 0.1 m in the dust devil center, but with a cylinder shaped model domain of only 200 m diameter where the background vorticity has been prescribed, so this study can not explain where and why naturally formed vortices are generated in a flow without mean background vorticity. [7] Up to now nearly all LES of dust devil like vortices have been carried out either with or without background wind. Only Toigo et al. [2003] and Ito et al. [2010] performed simulations with background wind of different wind speeds, Toigo et al. [2003] for Mars and Ito et al. [2010] for Earth. However their results were different. Toigo et al. [2003] proposed that the dust devil development is not really affected by background wind speed or shear, since during their simulations dust devils developed in the case with no initial wind and in the case with relatively intense initial wind and shear. In contrast Ito et al. [2010] showed 2of16

3 Table 2. Summary of Main Simulation Parameters Number of Grid Points Domain Size L x L y L z (m) Grid Spacing (m) Background Wind (m s 1 ) R2L R R B B that the formation of strong vertical vortices is more frequent for weaker general wind. [8] During the last years the dust devil investigations additionally focused on two other questions: the particle transport and the electrical fields within dust devils. Approaches concerning these topics were made, e.g., by Farrell et al. [2004], Balme and Hagermann [2006], Gu et al. [2006], Huang et al. [2008] and Neakrase and Greeley [2010]. [9] The aim of our present study is to resolve some of the deficits of previous studies by carrying out an LES for the dry atmospheric convective boundary layer with both a large domain size of 4 4 km 2, where the large scale nearsurface cellular like flow pattern can freely develop, and a very high spatial resolution of 2 m, which allows us to resolve the developing dust devil like vortices sufficiently. It should be emphasized that this resolution is still insufficient to resolve the dynamics of the inner vortex core, like it was realized in the very high resolution simulations of Gu et al. [2008]. In contrast to Gu et al. [2008], our main focus is on the larger vortex features and on how the vortices are embedded in and generated by the larger scale flow patterns of the convective boundary layer. Vortex tracks for different ambient wind speeds are analyzed and the mean threedimensional structure of vortices is derived from tracking selected vortices throughout their lifespan. Additionally, all major terms of the vorticity budget equation are calculated for these selected vortices in order to determine how their vorticity is maintained. 3. Numerical Setup and Analysis Methods [10] The study has been carried out with PALM (PArallelized LES Model) which has been designed for optimal performance on massively parallel computer architectures [Raasch and Schröter, 2001]. It has been successfully applied in many previous convective boundary layer studies [see, e.g., Letzel and Raasch, 2003; Kanda et al., 2004] and it has demonstrated its ability to handle large numerical grids with up to 10 9 grid points [Schröter et al., 2005; Gryschka and Raasch, 2005; Gryschka et al., 2008]. [11] One reference simulation and several sensitivity runs for the dry convective boundary layer have been carried out. Initial and boundary conditions of all simulations closely follow those used by Kanak [2005], i.e., cyclic lateral boundary conditions, no slip conditions at the lower and free slip conditions at the upper boundary, a constant surface sensible heat flux of 0.24 K m s 1 is applied and, in the reference simulation, no mean background wind is imposed. The initial potential temperature is constant at 300 K up to 700 m and increases at 0.02 K m 1 above that. Small initial random disturbances are imposed to the horizontal velocity field in order to trigger convection. The grid spacing is uniform with D = 2 m for the reference simulation, while Kanak [2005] used a horizontal spacing of 2 m and a vertical spacing of 4.12 m at the surface which was smoothly stretched to 24 m at the top of the domain. In the present study, Dz is uniform (2 m) up to 800 m, smoothly stretched by a factor of 1.08 above and reaches a maximum value of 68 m at the top (1704 m). The study of Kanak [2005] showed that dust devil like vortices are linked to the convergence lines of the near surface hexagonal cell pattern. This pattern is typical for free convection and has a length scale tied to the depth of the boundary layer. Therefore, a total horizontal domain size of about 4 km 4 km is chosen for the reference simulation (about five times the boundary layer depth) in order to allow for a free development of this pattern and the related vortices. This size is the main difference to Kanak [2005], where it has been only 740 m 740 m, which was even less than the initial boundary layer height of 900 m used in her study. The total number of grid points in the reference simulation is which is about and hence requires to run it on a larger number of processors. The simulated time was 5400 s (1.5 h) with an average time step of about 0.25 s and needed about two weeks CPU time on 256 processors of an IBM Regatta system equipped with Power4 processors. This reference simulation is referred to as run R2L from now on. [12] The sensitivity runs have been carried out to study the dependence of vortex evolution on the grid resolution and on the magnitude of the background wind. Due to limited computational resources they used a smaller domain size and various grid spacings. The main simulation parameters of all runs are summarized in Table 2. [13] The average features of vortices are analyzed by proceeding the following steps: [14] 1. Vortex centers were automatically detected during a run after each time step and the respective grid point indices were written to disk. The criterion used here for a grid point to be a vortex center is to have both a local pressure minimum p* 4.0 Pa, where p* is the perturbation pressure used in the LES, and a local vorticity maximum z 1.0 s 1, where local minimum/maximum means that values are smaller/larger than those of the eight horizontally adjacent grid points (together forming a 3 3 grid block). Vorticity is defined as the vertical component of the rotation of the velocity where x and y represent Cartesian coordinates and u and v the corresponding horizontal components of the velocity. This analysis is done at the first computational level above the surface, i.e., at 1 m for the reference run (because a staggered grid is used, all scalar quantities are defined at ð1þ 3of16

4 middle and the lowest grid point at the bottom boundary of the model. This grid has the same grid spacing as used in the simulation. The center position of the grid at each time step is determined from the vortex track information derived from the first simulation. [17] The very large number of grid points used in this simulation did not allow the usual postprocessing of the data. Record of the domain data at every time step and the postprocessing analysis would have required about 350 TByte of storage space. [18] On the other hand, sampling of the data during the run (online) required additional memory. Due to the horizontal, two dimensional domain decomposition used in PALM, the complete sampling grid was allocated on each processor (for each subdomain), but only those processors having grid points in the respective vicinity of the vortex center were contributing their data at respective time steps to this sampling grid. After the vortex has disappeared the sum over the sampling grids of all subdomains was calculated and grid point values were normalized with the number of time steps. One sampling grid for each analyzed quantity (velocity components, potential temperature, perturbation pressure, vorticity, vorticity budget terms) was required. The limited memory size (about 1.6 GByte per processor) allowed a maximum size of the sampling grid of grid points. Only one vortex at a time could be sampled, i.e., the two analyzed vortices had to be chosen from different nonoverlapping time intervals of the simulation. Figure 1. Mean profiles of (a) potential temperature and (b) total sensible heat flux (resolved scale plus subgridscale) for run R2L. intermediate grid levels). The threshold values have been determined empirically in order to eliminate the random noise of noncoherent turbulence as much as possible. However, due to these threshold values, the very initial and very last period of the vortex life cycle could not be recorded. The pressure and vorticity signals have been selected because other variables like temperature or vertical velocity do not show a clear extremum at the center or have their extremum outside of the center (e.g., the horizontal velocities). [15] 2. In a postprocessing step, the respective centers were combined to vortex tracks. This was done by comparing centers of respective two adjacent time levels t and t + Dt. Those centers which were not more than two grid spacings apart were assumed to belong to the same vortex. [16] 3. Two vortices with the longest lifetime were selected from all detected tracks. The simulation was rerun and at each respective time step within the lifetime of the two vortices various variables are sampled on a points (x/y/z) moving grid with the vortex center in its 4. Results [19] Sections 4.1 to 4.5 describe results of the reference simulation, run R2L, with a domain size of 4096 m 4096 m 1704 m and grid spacing of D = 2 m. The results of the sensitivity studies are presented in section General Boundary Layer Structure [20] Figure 1 displays the temporal development of mean vertical profiles of potential temperature and total sensible heat flux w until the end of the simulation (5400 s), horizontally averaged over the total domain and time averaged over the respective last 900 s. The vertical profiles clearly represent a typical convective boundary layer condition, well known from observations and many previous LES studies. A well mixed nearly neutral stratified layer is capped by an inversion with a height of about 850 m at the end of the simulation. After about 45 min, the flow has reached a quasi stationary state where the heat flux is almost linearly decreasing with height with negative values in the entrainment zone, where warm air is mixed from the inversion into the boundary layer. [21] Figures 2 and 3 show instantaneous cross sections (xy and xz) of vertical velocity at t = 4378 s. Time and position of the vertical cross section has been chosen in order to match the position of one of the selected vortices (named vortex B), which will be analyzed and discussed in detail later. The horizontal cross section at z = 40 m reveals the typical hexagonal or spoke like pattern, which has been found by many previous LES studies [see, e.g., Schmidt and Schumann, 1989; Mason, 1989]. The updrafts are concentrated along narrow lines which seem to form the spokes of a wheel. Only at the center of the wheels (or, in other 4of16

5 Figure 2. Horizontal cross section of vertical velocity w at z = 40 m and t = 4378 s. The white dashed line shows the position of the vertical cross section displayed in Figure 3. The position of vortex B is marked by a black dot. words, at the cell vertices), where several spokes are merging, large updrafts develop which extend throughout the whole depth of the boundary layer [Schmidt and Schumann, 1989]. The vertical cross section in Figure 3 at x = 2991 m shows such large updrafts for y < 1000 m and at about y = 3000 m. Near the surface, the horizontal wind field converges toward the narrow updrafts, and broad areas of relatively weak downdrafts are forming between these updrafts. Maximum values of vertical velocity are about +5 m s 1 in the updrafts and 3ms 1 in the downdrafts. The maximum updraft velocity observed during the simulation has been about 9 m s 1. The temporal development of the near surface horizontal flow becomes very apparent from an animation of particles passively advected by the flow, which is provided in the auxiliary material (Animation S1) Vortex Tracks and Statistics [22] All vortex centers satisfying the extrema conditions z 1s 1 and p 4 Pa are identified for each time step following the method described in section 3. Figure 4a shows the position of all identified centers. The color displays the simulated time, at which the respective centers were detected. In total, about 1.6 million centers have been identified within the about time steps that the simulation required. Figure 5 shows the time series of the number of vortices per square kilometer, which levels off to a mean value of about 2.5 after the simulation has reached the quasi stationary state (for t > 2700 s). At this stage, there are slightly more cyclonic than anticyclonic vortices, but the time series of positive and negative vorticity extrema (not shown) does not support that Coriolis force creates any difference in the strength of rotation between cyclonic and anticyclonic vortices. The minimum perturbation pressure found in the centers was about 72.4 Pa, while the extreme value of vorticity was about 6.8 s 1, which is quite near to observed values of 7 s 1 < z <14s 1 from Sinclair [1973]. 1 Auxiliary materials are available in the HTML. doi: / 2011JD The maximum tangential velocities within the vortices were about 9 m s 1 and in good agreement to the values measured by Bluestein et al. [2004]. [23] The vortex centers could be connected to about tracks, although most of the tracks were quite short in space and in time. Tracks for those vortices with a lifetime of more than 450 s (about 1800 time steps) are shown in Figure 4c. The lifespan of the longest track exceeds 660 s (2800 time steps). [24] It is obvious from Figure 4a that the centers are not uniformly distributed but that all centers together are forming a hexagonal pattern very similar to that of the nearsurface vertical velocity, which strongly supports previous findings from single observations [Kanak et al., 2000; Kanak, 2005; Willis and Deardorff, 1979], that dust devil like vortices preferably occur close to the near surface convergence lines. Moreover Figure 4b, where the detected centers at t = 5400 s are plotted together with the corresponding instantaneous vertical velocity field, shows that the vortices mainly appear in those areas where several convergence lines are merging, i.e., at the vertices of the hexagonal cells, as observed in the water tank experiment of Willis and Deardorff [1979]. All the strong and persistent vortices displayed in Figure 4c are found within the vertex areas. As in the work of Kanak [2005] bookend vortex patterns are found along the convergence lines, but they only persist for short times and are probably no candidates for the longer living dust devils. [25] A typical vortex pattern sequence is displayed in an animation of the near surface horizontal flow, provided in the auxiliary material (Animation S2). Animation S2 shows a m 2 zoom into the total domain, in order to resolve the small scale vortex features. None of the displayed vortices belong to the long living vortices displayed in Figure 4c Average Features of Selected Vortices [26] Those two vortices with the longest lifetime were selected in order to determine their mean, time averaged, three dimensional structure and other features from a second, identical simulation, following the method described in section 3. These vortices are named A and B and their respective tracks are marked in Figures 4a and 4c. A appeared during the interval s < t < s, while B was tracked during s < t < s. [27] Although vortices A and B had a slightly different intensity, their spatial structure was found to be very similar. Therefore, mainly results for A will be shown and discussed here. Figure 6 gives the time series of perturbation pressure p* and vorticity z for both A and B. It shows that they have the same sense of rotation with maximum vorticity of about 5s 1, while the minimum pressure for both is about 44 Pa. As should be expected, vorticity and pressure are strongly correlated, because the pressure gradient always has to balance the centrifugal forces. Both vortices intensify during the first s and keep almost constant in strength, with some fluctuations, during the rest of their lifetime. Due to the threshold criteria used for the detection of vortex centers, no statements can be made about the very initial stage of the vortices. The lifetime of A and B, following these criteria, has been 490 s and 670 s, respectively. All results given below are temporal averages over these inter- 5of16

6 Figure 3. Vertical cross section of vertical velocity w at x = 2991 m and t = 4378 s. The position of vortex B is marked by a white line. vals. Observations showed that most of the dust devils (approx. 90%) have a lifetime of only a few minutes (less than 3 4 min [e.g., Sinclair, 1969; Ives, 1947]) but it was also stated that the lifetimes from visual observations might be underestimated since the dust devils can exist without a source of visible debris [Sinclair, 1969]. Furthermore larger dust devils tend to have longer lifetimes than smaller ones (up to 20 min) and also rare dust devils with durations up to several hours were reported [Sinclair, 1969; Ives, 1947]. The lifetimes of our simulated vortices are falling well within the range of these observed values. [28] Figure 7 shows horizontal transects at 1 m height through the vortex centers along x of the radial, tangential, and vertical velocity component u r, u t, and w, the potential temperature, vorticity z, and perturbation pressure p*. Both vortices have very similar features. The shape of the tangential velocity lines indicates cyclonic vortices in both cases with maximum vorticity of 3 s 1 in their centers, and maximum absolute values of the tangential velocity of about 3.5 4ms 1 at a distance of 2 4 m from the center, while the radial velocity shows a convergent flow toward the center with a maximum absolute value of about m s 1 at about 8 m distance from the center. The vertical velocity has a maximum value of about 1.7 m s 1 at about 2 m distance to the left and right of the center and shows a significant drop in the center. The temperature difference between the center and the surrounding air is about 1 K, the minimum perturbation pressure is around 24 Pa. This quite small magnitude of pressure is due to the relatively weak tangential velocity (the pressure minimum deepens with the square of the tangential velocity). From the shape of the transect lines, the vortices diameter is roughly estimated to about 30 m. [29] All values are at the lower limit of dust devil data given by Sinclair [1973] (see Table 1), but it should be kept in mind that Figure 7 shows temporal averages, which might be much smaller than instantaneous values (as those from Sinclair [1973]). Kanak [2005] also reported larger magnitudes from her LES (which used the same initial and boundary conditions as in our study) in general, but these were also taken from instantaneous horizontal transects. Due to these snapshots, her profiles also showed more scatter. The vertical velocity from the transect in the work of Kanak [2005] was almost zero, which she attributed to numerical deficits from resolution and/or the subgrid scale model. In contrast, both of our vortices show maximum updrafts of 1.7 m s 1, which is smaller than the 3 to 15 m s 1 reported by Sinclair [1973], but still in the observed order of magnitude. [30] The cross sections in Figure 8 provide a more comprehensive view on the mean spatial structure of vortex A. Figures 8a and 8b show horizontal cross sections of potential temperature at 1 m height and vertical velocity at 2 m height, respectively. Both cross sections include isolines of perturbation pressure. In the temperature cross section also vectors of horizontal velocity have been added. The origin of the coordinate system is set to the vortex center. Most quantities reveal a quite symmetric vortex structure. Two tongues of warmer air are advected from southwest and east into the vortex center. The vertical velocity has a clear maximum northwest of the center. The vectors of horizontal velocity clearly confirm the near surface convergent flow spiraling into the vortex center, which has been already identified from the horizontal transect (Figure 7). [31] Figures 8c and 8d present corresponding vertical xz cross sections of potential temperature and vertical velocity, respectively, through the vortex center. Isolines of perturbation pressure have been also added here. From the pressure field, as well as from the vorticity field (not shown), the vortex height can be roughly estimated to about 150 m, based on the thresholds also used for the detection of the vortex centers. Its vertical axis is almost upright. Both, temperature and pressure have their respective maximum/ minimum in the vortex center. The vertical section of w (Figure 8d) shows that, like already seen in the horizontal transect (Figure 7), the strongest near surface updrafts can be found adjacent to the vortex core, while there is a, still positive, minimum in the core. These conditions continue up to a height of about 25 m. Further above, only one updraft remains, which significantly broadens and gets stronger with height. At the estimated top of the vortex, this updraft is already much broader than the sampling grid (60 m) and even becomes stronger. Although this grid only extends up to 200 m, Figure 8d suggests that the updraft further broadens and gets stronger beyond that height. This is supported by the instantaneous cross section of vertical velocity at t = 4378 s (Figure 3), which is about at the beginning of the last third of the vortex s lifetime. At the vortex position, marked by a white line, a big updraft extends toward the top of the mixed layer. [32] Such broad and strong updrafts are found to be characteristic for all analyzed vortices (vortex B as well as 6of16

7 mixed layer, mainly form above these vertices, it is evident that Figure 8d just shows one of these updrafts. It is also obvious, that these strong and broad updrafts seem to be an essential component, or better to say an essential requirement for the formation of strong near surface vortices, which has been already stated by Willis and Deardorff [1979] and Sinclair [1966]. The role of these updrafts will be further discussed in section 4.4, where the vorticity budget terms are analyzed. [33] It should be noted that the near surface structure of the vortex vertical velocity field is similar to the inverted cone like structure found by Gu et al. [2008], while there is a disagreement at larger heights, probably because Gu et al. [2008] could not capture the large convective cells with their small model domain Vorticity Budget [34] In this section various terms of the vorticity budget equation are analyzed in order to determine the source of the vortex rotation. The respective budget ¼ ~v h ~r h fflfflfflfflffl{zfflfflfflfflffl} adv þ other ffl{zffl} vad ð þ f Þ ~r h ~v fflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflffl} @z fflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflffl} twi ð2þ Figure 4. (a) Identified vortex centers, matching the extrema conditions z 1s 1 and p 4Pa, for run R2L. Color displays the simulated time at which the respective center was detected. (b) Vortex centers, marked by black dots, and vertical velocity at z =20mandt =5400s.(c) Tracks of vortices with lifetimes of more than 450 s. Vortices analyzed in detail are labeled A and B. The arrows display the starting point of the vortices as well as their rotational sense. other vortices analyzed in the sensitivity studies). Since Figure 4b already showed that vortices preferably appear within the vertices of the near surface hexagonal cells, and since the strong updrafts, which extend up to the top of the where the first term represents the advection of vorticity with the horizontal velocity v h, followed by vertical advection, the change of vorticity by divergence of the horizontal velocity field, representing conservation of angular momentum, and the twisting term, which describes the influence of a horizontal gradient of vertical velocity in transforming vorticity about a horizontal axis to that about a vertical axis. The Coriolis and solenoidal terms have been neglected here, because they are found to be more than one order of magnitude smaller than the first four terms. All terms have been calculated for the center of the grid boxes using central finite differences. Due to the staggered grid, this required additional linear interpolation of the calculated derivatives, which reduced the amplitude of the signals, especially in case of the twisting term. Also, because of the central finite differences, the lowest height for which values could be calculated was z =3m. [35] Figure 9 displays the time series for the four budget terms at 3 m height. In order to reduce scatter, all quantities have been averaged over a square of grid points with the vortex center in the middle. Figure 9 shows that both divergence and twisting term contribute to vorticity generation throughout the whole lifetime of the vortex. The twisting term is smaller in magnitude, but this is probably caused by the interpolation mentioned above, because in the sensitivity study with higher grid resolution, where spatial gradients are better resolved so that interpolation has smaller effects, both have the same magnitude. Both advection terms reduce the vorticity: the vertical advection term because of the positive vertical velocity within the vortex which transports vorticity generated near the surface toward the upper parts of the vortex, the horizontal advection because we used velocities defined in the nonmoving LES grid, instead of transforming them into the moving sample grid which followed the vortex track. Therefore, the vortex 7of16

8 Figure 5. Time series of the number of detected cyclonic/ anticyclonic vortices per km 2 during run R2L. Figure 7. Horizontal transects at 1 m height through the centers of the time averaged vortices (a) A and (b) B. Lines show radial (u r ), tangential (u t ), and vertical velocity (w) as well as potential temperature (), vorticity (z), and perturbation pressure (p*) divided by has a permanent tendency to move out of the sample grid, thereby reducing vorticity. [36] The time averaged horizontal cross sections of the divergence and twisting term at 3 m height for vortex A are displayed in Figures 10a and 10b. They generally support the findings from the time series, that both terms contribute to the vorticity generation. However, the divergence term has positive values in the direct center of the vortex, which is because the near surface vertical velocity field (Figure 8b) has its maximum outside the inner vortex core and hence generating a divergent flow in the direct center. [37] The fields of vertical velocity and vorticity budget terms suggest that the strong near surface vortices are maintained by a combination of divergence and twisting effects. The strong updraft, typically located above the vertices of the near surface hexagonal cells, creates a strong near surface horizontal flow which converges toward the center of the updraft. Vertical shear of the strong nearsurface horizontal velocities creates horizontal vorticity, which is then turned into vertical vorticity within the updraft. The convergent flow additionally concentrates the vorticity into an intense vortex. The vertical advection of Figure 6. Time series of vorticity z (black) and perturbation pressure p* (gray) in the vortex center for vortices (a) A and (b) B. 8of16

9 Figure 8. Time averaged (a and b) horizontal and (c and d) vertical cross sections of potential temperature (Figures 8a and 8c) and vertical velocity w (Figures 8b and 8d) for vortex A from run R2L. Isolines display contours of perturbation pressure p*. The horizontal cross section of temperature additionally includes vectors of horizontal velocity. Horizontal cross sections are at 1 m height; the vertical cross sections are through the center of the vortex. vorticity then expands and stretches the vortex in vertical direction. [38] Certainly, the results from the vortex analysis only explain how a vortex maintains its vorticity once it is generated. Horizontal vorticity from an initially nonrotating flow field, which symmetrically converges to one point, can not create vertical vorticity by twisting, because the contributions from the opposing flow directions cancel out each other. Only horizontal vorticity of an already rotating flow, twisted by the central updraft, will generate vertical vorticity always of the same sign. Further conclusions about the initial vortex conditions are difficult to obtain from our vortex track method, because it only considers vortices after their vorticity has exceeded a threshold value of 1 s 1, i.e., their initial phase is not captured. A possible explanation for the onset of vortex rotation will be given in section 5 and contrasts with earlier theories of dust devil generation Three Dimensional Instantaneous Structure [39] The instantaneous 3 D flow structure of dust devil like vortices can be properly visualized by using particles as passive tracers which appear as the real dust in nature. For this purpose, at z =1ms 1 one particle per horizontal grid point has been released within the simulation at 2 m height and at every 7.5 s, but only in those areas where the perturbation pressure was below 8 Pa. These particles were 9of16

10 Figure 9. Time series of vorticity budget terms, averaged over grid points, for (a) vortex A and (b) vortex B. advected with the resolved scale velocity field. For even better visualization, every particle pulled a tail behind it representing the particle trajectory. The tail color displays the magnitude of horizontal velocity at the respective tail position (red: high velocity, blue: low velocity). Figure 11 shows an instantaneous tail snapshot for a vortex up to a height of about 100 m from run R2 with reduced model domain of km 2 (this visualization method could not be applied for the full 4 4 km 2 domain because of limited computer resources). Figure 11 reveals the strong near surface inward spiraling flow and a tube like flow pattern which extends even above 100 m, which has many similarities with pictures from real dust devils. [40] An animated sequence of such instantaneous snapshots gives an even better impression of the flow dynamics. It is given in the auxiliary material (Animation S3). Details of the passive tracer methodology are described by Steinfeld et al. [2008] Sensitivity Studies [41] Two sensitivity studies have been carried out in order to determine possible effects of grid resolution and of the background wind. Due to the extreme CPU time demands, the sensitivity runs used only a reduced horizontal domain size of m 2. Therefore, the reference for these runs is a simulation with 2 m grid spacing and zero mean wind (like in run R2L discussed in sections ), but with this reduced domain size. It is referred to as run R2. See Table 2 for an overview of simulation features. [42] Since many of the vortex features observed in the sensitivity studies are very similar to those discussed in sections , we will mainly present figures which highlight the differences Effects of Grid Resolution [43] In order to proof if a 2 m grid spacing resolves the small scale vortices sufficiently, we carried out an additional simulation with 1 m grid size (run R1). Figure 10. Horizontal cross sections at z = 3 m of vorticity production by (a) divergence term z div and (b) twisting term z twi for vortex A. The black line represents the zero isoline. 10 of 16

11 Figure 11. Flow visualization of a vortex from run R2. Flow direction is indicated by trajectories of particles moving passively with the resolved scale flow. Particles were released at 2 m height and at fixed time intervals of 7.5 s in those areas where the perturbation pressure was below 8 Pa. Color shows the magnitude of horizontal velocity (red, high; blue, low). The displayed vortex has a diameter of about 30 m and is plotted up to about 100 m height. [44] Figure 12 show all vortex centers identified during the 2 m run R2 in Figure 12a and the horizontal cross section of vertical velocity at the end of run R2 in Figure 12b, as well as the corresponding plots for the 1 m run R1, in Figures 12c and 12d. The vertical velocity fields at the end of both runs indicate that the cellular flow structure is not developed as well as for run R2L. At that time, cells would have grown to a size of approximately 800 m (see Figure 4b from run R2L), which is about the domain size of R2 and R1. Due to this limited domain size, the cell structure and the corresponding spoke pattern is much less pronounced than in run R2L (see Figure 2). As a result, the identified vortex centers of both runs (Figures 12a and 12c) also do not show a pronounced pattern. The number of identified centers in the 1 m resolution run R1 was about twice as large as in the 2 m run R2. The minimum pressure and maximum vorticity found in the centers are p* = 60 Pa and z = s 1 in run R1 while in R2 p* = 40 Pa and z = +5.0 s 1 (see Table 3 for a comparison of vortex center characteristics). Maximum vertical velocities in the vortex centers have been 6.9 m s 1 (R1) and 3.4 m s 1 (R2), the maximum tangential velocities were about 9.0 m s 1 (R1) and 7.0 m s 1 (R2). Despite possible statistical fluctuations from run to run, vortices appeared more frequently in the higher resolution run and have been stronger than in the 2 m run. However, our analysis of selected vortices revealed that diameter and height of the vortices have been the same for both runs. As a conclusion, a 1 m resolution (at least) should have been used for the large domain run in order to give more realistic magnitudes of vortex velocities, but the large computational resources required for such a run have not been available. Anyhow, a 2 m grid spacing seems to be sufficient to simulate the typical spatial structure of the vortices (height, diameter) Effects of Background Velocity [45] The effects of background wind on the frequency of occurrence of dust devils and on the vortex strength are still under debate [Toigo et al., 2003; Ito et al., 2010]. In order to study how the vortices depend on the mean boundary layer wind, we carried out two simulations with an implied geostrophic wind ug of 2.5 and 5.0 m s 1, which results in a mean boundary layer wind of 2.2 m s 1 and 4.4 m s 1, respectively. For both runs, named run B25 and B50, a grid spacing of 2 m was used. [46] Figure 13a 13d show the vortex centers identified during these runs, and horizontal cross sections of vertical velocity at their end (t = 5400 s). Most evidently, for run B25 the vortex tracks are now roughly aligned with the mean wind direction and tracks are much longer than in the run without background wind (R2), because the vortices are moving with the background wind. Tracks in run B50 show the same alignment, but this run displays significantly less centers and well developed tracks than all other runs. This is likely caused by the more shear dominated conditions, which inhibit a cellular pattern of the near surface flow. Figure 13d shows that the near surface updrafts are generally aligned with the background wind, as typical under these conditions [Moeng and Sullivan, 1994]. For a mean boundary layer wind of 2.2 m s 1, the cellular pattern is still maintained, apart from the limiting effects of the small domain size (Figure 13b). The vortices in run B25 are even stronger than in run R2 without background wind. The minimum pressure found in the vortex centers for B25 (R2) is p* = 57.2 Pa (p* = 40.0 Pa), while vorticity and vertical velocity have maximum values of z = 6.4 s 1 (z = 5.0 s 1) and w = 4.4 m s 1 (w = 3.4 m s 1). It could be argued, that the background wind somehow increases the near surface horizontal vorticity, which then contributes to stronger vortices by the twisting effect. The analysis of the vorticity budget terms for selected vortices of run B25 indeed showed, that the mean contribution from the twisting term is about twice as large than for selected vortices of run R2. However, this increase could also be contrary explained by the fact that vortices in B25 are stronger rotating than in R2 due to some other unknown reason. A stronger vortex creates stronger near surface vertical shear which in turn may increase the magnitude of the twisting term. Currently, this problem remains an open question and requires further analysis. It will be addressed in a follow up study. [47] Generally, this sensitivity study relates the significant decrease of vortices for stronger background wind to a 11 of 16

12 Figure 12. Identified vortex centers for (a) run R2 and (c) run R1 as well as instantaneous horizontal cross sections of vertical velocity at z = 2 m and t = 5400 s for (b) run R2 and (d) run R1. The vortex centers are marked by black dots. switch from a cellular to a band like near surface flow pattern. [48] The mean spatial structure of a selected vortex from run B25 is presented in Figures 14a 14d, which includes the same quantities as Figure 8 (run R2L). This vortex, named C, had a lifetime of about 600 s and appeared during the interval s < t < s. Compared to vortex A from run R2L, C has an anticyclonic rotation. The mean minimum vorticity and pressure were 3.3 s 1 and 26.8 Pa, respectively. The main difference between C and A is that the vertical axis of C is tilted by the background wind toward the moving direction of the vortex, which is from west to east, while the axis of A is almost oriented perpendicular to the surface. The tilted axis of C is best visualized in the vertical cross section of potential temperature and pressure (Figure 14c). Observations show that dust devil cores are often tilted toward the direction of motion [Balme and Greeley, 2006; Sinclair, 1969], but the tilting has never been related to the magnitude of the background wind. It should be noted that also the axis of vortex A shows a small tilt toward the north because the vortex is slowly moving to the north (see Figure 5c), but this tilt is not displayed in Figure 9 because it only shows an xz cross section. [49] The horizontal cross sections of temperature (Figure 14a) and vertical velocity (Figure 14b) as well as the included isolines of pressure show that these quantities are not symmetrically aligned around the vortex center. A high temperature area extends upstream of the vortex center, which is probably responsible for, that the area with maximum vertical velocity is located upstream of the direct core as well. Similar but much weaker tongues of warm air have been found for vortex A (Figure 8a). Other features of C like height and diameter, and especially the strong updraft above the vortex, displayed in Figure 14d, are very similar to vortex A. [50] These sensitivity runs have clearly shown, that the strength and the frequency of occurrence of vortices heavily depend on the magnitude of the background wind. Under more shear dominated regimes, the near surface coherent flow structures switch from hexagonal to band like patterns, which seem to be significantly less favorable for vortex generation. Our results are in agreement with the study of Gheynani and Taylor [2011] but they are contrary to Toigo et al. [2003], who proposed that vortex generation is not strongly sensitive to mean wind. 5. Discussion and Summary [51] In this large eddy simulation study of the atmospheric convective boundary layer, a systematic analysis of near surface dust devil like vortices with vertical axes has been made for the first time by identifying all vortices above a certain vorticity threshold level. Detected vortex centers Table 3. Vortex Center Characteristics p min (Pa) p avg (Pa) z min (s 1 ) z max (s 1 ) z mean (s 1 ) R2L R R B B of 16

13 Figure 13. Identified vortex centers for (a) run B25 and (c) run B50 as well as instantaneous horizontal cross sections of vertical velocity at z = 20 m and t = 5400 s for (b) run B25 and (d) run B50. The vortex centers are marked by black dots. The vortex which was analyzed in detail is labeled with C. The arrow in the top left corner of each part shows schematically the direction and velocity of the mean boundary layer wind. were combined to vortex tracks which have been used to derive the temporally averaged three dimensional structure of selected vortices. For these selected vortices, also vorticity budget terms have been calculated and analyzed in order to clarify the source of the vortex rotation. The domain size of 4 4 km2 for the reference run was chosen big enough to capture the large coherent near surface flow patterns, which turned out to be closely connected with the occurrence of vortices. An isotropic grid spacing of 2 m makes this reference run one of the most expensive simulations of the CBL ever carried out so far. A sensitivity study has shown that with an even higher resolution of 1 m vortices become more intense, but it has also shown that with 2 m resolution the vortices height and diameter are simulated sufficiently well. In a further sensitivity study, the effect of background wind on the vortex generation has been clarified. The study goes beyond previous LES studies of atmospheric dust devil like vortices, where much smaller domain sizes were used, and where limited vortex features have been derived only from instantaneous snapshots. [52] Mean vortex features like maximum horizontal and vertical velocities near the vortex center, temperature difference between the center and its environment, or height and diameter are in good correspondence with previous LES results from Kanak [2005], but are, except for the diameter, at the lower limit of observed dust devils [e.g., Sinclair, 1969, 1973; Kanak, 2006]. In general, the simulated vortices are weaker but broader (more diffuse) than the observed dust devils which is mainly due to the finite grid resolution and the model s weaknesses in resolving in detail the vortex core dynamics and the vortex flow ground interaction within the thin surface adjacent boundary layer. A realistic simulation of the intense circulation of the inner vortex core would have required a much higher resolution, e.g., as used by Gu et al. [2008]. Although the vortex core region was not in the focus of our study, a sensitivity test with increased resolution of 1 m in fact created stronger vortices. Besides this resolution effect, another reason for the comparably weak vortices is that because of limited computational resources the boundary layer height in the simulations has been much smaller (zi m) than, e.g., typically observed with dust devils. In desert areas, zi can easily reach 3000 m. Under such conditions, vertical velocities in the big thermals as well as the corresponding near surface convergent flows, which are essential for the vortex development, can be much more vigorous than in the simulated cases. Results from a second sensitivity test show that vortices intensify in case of a light background wind. [53] It should also be pointed out, that strong dust devils are relatively rare events and that their strength probably follows a statistical distribution. Even if all initial and boundary conditions, required for creating very strong vortices, are given in the simulation, the strongest possible vortices (under given grid resolution) will not necessarily appear within a run of only 1.5 hours. On the other hand, the fact that several, although relatively weak vortices appeared in all the simulations let assume, that these weaker vortices are also very frequent in nature. However, they can not be 13 of 16

14 Figure 14. Time averaged (a and b) horizontal and (c and d) vertical cross sections of potential temperature (Figures 14a and 14c) and (Figures 14b and 14d) vertical velocity w for vortex C from run B25. Isolines display contours of perturbation pressure p*. The horizontal cross section of temperature additionally includes vectors of horizontal velocity. Horizontal cross sections are at 1 m height; the vertical cross sections are through the center of the vortex. observed easily, because they are not strong enough to lift any dust. Only the very strong ones appear as dust devils. It should also be pointed out that there is some evidence that the frequency of dust devils depend on certain surface characteristics. Sinclair [1969] and Balme and Greeley [2006] have reported that a heterogeneous or gently sloping terrain enhances the generation of dust devils. The simple homogeneous surface boundary conditions used in our model does not study these effects. [54] The three dimensional structure of atmospheric vortices embedded in the larger scale convective cell pattern has been derived for the first time from LES by temporally averaging all respective quantities on a moving grid which follows the vortex track over most of its lifetime. Selected vortices of the reference run without background wind are more or less axially symmetric. Especially under background wind, the axes are tilted toward the moving direction of the vortices as given by the background wind. Diameter (near surface) and height of all analyzed vortices are about 30 m and 150 m, respectively. Their shape corresponds to an inverted cone with a relative minimum of vertical velocity in the vortices center. This shape is similar to that found by Gu et al. [2008] for artificially generated atmospheric vortices. [55] One of the most important results of this study is that all selected vortices are coupled to a strong updraft which extends far beyond the top of the existing vortex. Such 14 of 16

15 Figure 15. (a) Sketch of a near surface horizontal flow pattern around a vertex center, which may lead to intense vortex generation. In this case, the flow would create a clockwise rotation. (b) Vorticity conservation of an existing vortex by twisting of horizontal vorticity. strong plumes, extending throughout the whole depth of the CBL typically form above the vertex regions of the nearsurface hexagonal cells. [56] The analysis of all detected vortex centers showed that the vortex tracks are strongly related to the larger scale coherent cellular flow pattern and confirmed that vortices generally appear in the vertex regions. The number and strength of vortices significantly decreases in a more shear dominated CBL, where the hexagonal pattern changes to a band like pattern. [57] The analysis of the vorticity budget terms shows that during the lifetime of the vortices, their rotation is maintained by a combination of divergence and twisting effects. Due to vertical shear, the near surface rotating flow itself generates horizontal vorticity, which is converted to vertical vorticity when the flow enters the updraft region of the vortex. A simply sketch of this mechanism is given in Figure 15b. The near surface flow convergence caused by the strong plume above the vortex further concentrates vorticity in the vortex core. [58] Although this mechanism does explain, how the vortex maintains its vorticity in a nonrotating environment, it already assumes an initially rotating vortex and hence can not explain where and why vortices are forming at all. [59] One of the most favored theories for dust devil generation so far is based on the so called hairpin mechanism [Renno et al., 2004; Kanak, 2005]. Opposing warm and cold winds along a convergence line are creating a horizontal vortex because the cold and dense air moves under the warm air. The updraft due to the rising of the warm air lifts this horizontal vortex forming a loop. Then the apex of the vortex thins and finally the vortex breaks into two vortices of opposite rotation. One vortex often decays leaving a single dust devil. The related bookend vortex patterns were reported by Kanak [2005] and we also found them along the near surface convergence lines, but the temporal analysis showed that these vortices were only short living. Moreover, the hairpin mechanism cannot explain, why vortices preferably form and appear at the vertices. [60] For this reason, we suggest a new mechanism, which can directly create an initial vertical vorticity within the vertices. When air is moving uniformly from all directions to the vertex center, the overall flow has no vertical vorticity. However, the flow normally does not converge directly to the vertex center, but has velocity components toward the convergence lines, which are merging in the vertex center. Sometimes, by chance, the flow may have a pattern like in the sketch given by Figure 15a, which displays a case where the overall vertical vorticity of the flow is nonzero. This direct initial vertical vorticity is then further concentrated by the general flow convergence. Once the vortex is established, it maintains its vorticity by twisting of horizontal vorticity due to the vertical shear of the already rotating near surface flow, as shown by the analysis of the vorticity budget terms. [61] As a future next step, we will focus on the onset phase of vortex development in order to verify this mechanism. Further goals are simulations with 1 m resolution and model domains of 4 4 km 2 for longer times in order to get more realistic magnitudes of vortices and to allow for better statistics. The effects of surface heterogeneities, which are known to enhance dust devil formation, will also be studied. [62] New generations of parallel computers with tens of thousands of cores and even more will allow for such simulations, where processes on different scales closely interact. [63] Acknowledgments. The authors would like to thank three anonymous reviewers for their useful comments. All simulations have been carried out on IBM Regatta and SGI ICE systems of the North German Supercomputing Alliance (HLRN). This work was partly funded from grant RA 617/19 1 of the German Research Foundation (DFG). The first draft of this paper was written during a stay of the first author as a Visiting Researcher at the Research Institute for Applied Mechanics, Kyushu University, Fukuoka, Japan. References Baddeley, P. F. H. (1860), Whirlwinds and Dust Storms of India, 137 pp., Bell and Daldy, London. Balme, M., and R. Greeley (2006), Dust devils on Earth and Mars, Rev. Geophys., 44, RG3003, doi: /2005rg of 16