Mechanisms for intensification and maintenance of numerically simulated dust devils

ATMOSPHERIC SCIENCE LETTERSAtmos. Sci. Let. 11: 27–32 (2010)Published online 12 January 2010 in Wiley InterScience(www.interscience.wiley.com) DOI: 10.1002/asl.249

Mechanisms for intensification and maintenanceof numerically simulated dust devilsHiroshi Ohno* and Tetsuya TakemiDisaster Prevention Research Institute, Kyoto University, Gokasho, Uji, Kyoto, Japan

*Correspondence to:Hiroshi Ohno, DisasterPrevention Research Institute,Kyoto University, Gokasho, Uji,Kyoto, Japan.E-mail:[email protected]

Received: 29 August 2009Accepted: 29 October 2009

AbstractA large eddy simulation (LES) of a well-developed convective boundary layer (CBL) underno mean wind condition was performed with the Weather Research and Forecasting modelin order to investigate the mechanisms for the intensification and maintenance of dust devils.By examining intense vortices from high temporal-frequency outputs, it was found that mostof the intense vortices are intensified through the merger of multiple vortices. Moreover,such a significantly intense vortex was maintained and more enhanced by additionallymerging small-scale vortices and tilting horizontal vortices at boundaries of convective cells.Copyright 2010 Royal Meteorological Society

Keywords: dust devils; LES; merger; horizontal vorticity; convective boundary layer

1. Introduction

Dust devils are microscale, intense vorticaldisturbances. They often occur over arid and semi-arid regions in summer. The vortices reported aremostly those in the United States (Sinclair 1969,1973; Bluestein et al. 2004) and in Australia (Hesset al., 1988; Hess and Spillane, 1990). From the pre-vious observational studies, it was found that thereare conditions under which dust devils prefer tooccur: (1) over a fairly flat plain; (2) with an intenseheat flux at the surface; and (3) under weak ambi-ent winds. These conditions are easily satisfied inarid-climate regions in which a well-developed con-vective boundary layer (hereafter CBL) is frequentlyseen.

Recently, some studies have tried to simulate dustdevils on Earth and Mars with numerical models(Michaels and Rafkin, 2004; Kanak, 2006). Kanaket al. (2000) and Fiedler and Kanak (2001) showedthat vertical vortices are generated at the vertex ofthe convective cells which are forced with a constantheat flux at the flat surface under no mean windcondition.

Although the grid spacing in the large eddy sim-ulation (LES) of Kanak et al. (2000) was too coarse(35 m in the horizontal direction and 10 m in the ver-tical) to simulate realistic dust devils, the simulatedvertical vortex reproduced the basic structure of a dustdevil even though its diameter (300 m) was signifi-cantly larger than that of a realistic dust devil (tensto a hundred meter). Kanak (2005) increased the reso-lution both horizontally (2 m) and vertically (4 m) tosimulate more realistic dust devils. The high-resolutionLES showed that dust devils also form not only atthe vertex but also at the branches of the convec-tive cells. Both studies showed that vertical vortices

are generated by tilting horizontal vorticity into thevertical, and thus a pair of vortices with opposite signsof vorticity is produced.

Toigo et al. (2003) performed numerical experi-ments of dust devils on Mars and investigated theeffects of mean wind on vortex generation. Theyshowed that vortices are significantly intensified underno-shear and high-shear conditions but not undermedium-shear conditions. Although it seems to bewidely known from the previous observational studiesthat dust devils are preferably generated when meanwind is weak, the result of Toigo et al. (2003) partlydisagrees with them. Therefore, the generation andeven the intensification processes of dust devils arestill unclear.

From high-resolution Doppler radar observations innorthwestern Texas, Bluestein et al. (2004) examineddetailed structures within dust devils, and indicatedthat there exists sometimes a pair of vortices withthe same sign rotating with each other. Does suchan interaction with two vortices play a role in theintensification of dust devils?

Although there have been many studies on the gen-eration processes of dust devils and the relevant envi-ronmental conditions, there are relatively few stud-ies on the intensification processes of dust-devil-like,strong vortices. In addition, the maintenance processesfor intensified vortices should also be of interest. Inthis study, we investigate the processes for the inten-sification and maintenance of strong vertical vorticeson realistic dust devil-scales within CBL by perform-ing an LES with a non-hydrostatic atmospheric modelunder idealized settings. We examine the character-istics of intensified vortices from a large numberof the simulated vortices and propose the mecha-nisms for the intensification and maintenance of dustdevils.

Copyright 2010 Royal Meteorological Society

28 H. Ohno and T. Takemi

2. Model settings and experimental design

The Weather Research and Forecasting (WRF) model -Advanced Research WRF (ARW) version 3.0 (Ska-marock et al., 2009), a fully compressive and non-hydrostatic model developed by The National Centerfor Atmospheric Research (NCAR), is used for thepresent LES. An LES version of the WRF model isextended to include the nesting capability for simu-lating multiscale boundary-layer flow (Moeng et al.,2007). The model is configured with an idealized modewhere minimum physics processes are included, i.e.only sub-grid-scale turbulence and surface momentumand heat transfer are parameterized. No other physicsprocesses such as cloud microphysics and radiationsare included.

Turbulent diffusion is computed with the Smagorin-sky–Lilly model (Lilly, 1962), while a bulk methodis used for the surface transfer parameterization. Peri-odic condition is imposed at the lateral boundaries,and free slip at the upper boundary. Model domainhas a horizontal area of 1 km × 1 km with the verti-cal depth of 1.5 km. The horizontal resolution is 3 m,while the vertical grid spacing is stretched graduallyfrom 3 m at the surface up to 60 m at the top of thedomain, with 185 levels. Although the ratio of verti-cal grid-scale to horizontal is quite high at the top, theeffects of this grid ratio does not affect the represen-tation of dust devils in the lower part of the domain,where the grid aspect ratio is nearly unity. Rayleighdamping is imposed above the 1200-m level to min-imize the effects of the reflection of gravity wave atthe upper boundary. A constant heat flux H0 = 0.24 Km s−1 ≈ 290 W m−2 is given at the surface, assumingrelatively intense solar heating. The vertical structureof the initial state is characterized by no mean windand by constant potential temperature (θ0) of 300 K(which represents CBL) capped by a strongly stablelayer above the height of 800 m with the increasingrate of 0.01 K m−1. The initial perturbation is pre-scribed as small and random temperature perturbationsat the five lowest model-levels.

3. Results

In the following analyses, some representative param-eters of CBL are used. h ≈ 1 km is the depth ofCBL, g the gravitational acceleration, w∗ ≡ (g H0

h θ−10 )

13 ≈ 2 m s−1 the convective velocity scale and

t∗ = h∗/w−1∗ ≈ 500 s the convective turnover time.We here examine the model outputs at 10-s interval.

3.1. Convective boundary layer

Shortly after the start of the time integration, updraftsand downdrafts were generated in a form of theRayleigh–Benard convection. At about 5 t∗, the simu-lated field became completely turbulent and consistedof organized convective cells. The depth of the CBL

was 800 m initially, and then developed to 1 km atthat time.

The horizontal means of potential temperature, ver-tical heat flux, and the variance and skewness of ver-tical velocity at each height were calculated at eachoutput time during 7 t∗ –11 t∗ and then temporallyaveraged. The vertical profiles of these turbulent statis-tics showed CBL features typically seen in previousobservational and numerical studies (e.g. LeMone andPennell, 1976; Kanak et al., 2000). The temperaturelapse rate in the highly unstable layer near the sur-face was 0.47 K m−1, which was reasonable since theobserved lapse rate was as high as 1 K m−1 in aridareas (Sinclair, 1973). With these properties, a well-developed CBL and convective cells are considered tobe properly reproduced in the present simulation.

3.2. Structure and evolution of intense vortices

In order to elucidate the common features of intensevortices, we choose vortices with an intensity over acertain threshold from a large number of vortices gen-erated in the lower part of the convective-cell bound-aries. It may not be easy to identify and separate avortex from its background flow, since the simulatedflow field is quite turbulent and unsteady. Therefore,we employ an analytical vortex model (i.e. the Rank-ine vortex) to identify a vortical structure within aturbulent, unsteady flow field by examining the spa-tial distribution of pressure at the height of 10 m. InKanak (2005), it is seen that the Rankine vortex is agood approximation for the simulated vertical vorticesat least within the radius of maximum wind (here-after RMW). Local maxima of vorticity are chosen bythe following three procedures. (1) Set thresholds ofpressure deficit from horizontal mean being 10 Pa andof vertical vorticity magnitude being 0.15 s−1, choosegrid points which have higher values than the twothresholds, and identify the grid location having thelocal maximum among the surrounding eight grids andthemselves. The grid chosen is assumed to be a tem-poral center. (2) Divide a 3 × 3 grids region centeredat the temporal center with 40 × 40 meshes, and finda function which is the best fit for the pressure pro-file of the Rankine vortex by least-square method onthe 40 × 40 meshes. The location having the minimumpressure on the 40 × 40 meshes from the best-fit forthe Rankine vortex is set to be a real center. (3) Dividewinds on the 3 × 3 grids with radial and azimuthalcomponents, and then find the maximum azimuthalwind and the RMW. Totally 225 vortices are selectedfrom these procedures during 7–11 t∗ (an identicalvortex may be counted more than once.) Note thatwe exclude vortices whose RMWs are smaller thanone grid-scale.

Figure 1(a) shows the radial profiles of pressuredeficits for each chosen vortex. The pressure deficitsat the center of the vortices are mostly 10–25 Pa;however, some intense vortices have the pressuredeficits of 40 Pa and the maximum wind speeds of

Copyright 2010 Royal Meteorological Society Atmos. Sci. Let. 11: 27–32 (2010)

Intensification and maintenance of dust devils 29

Figure 1. (a) Pressure deviations of all chosen vortices at the height of 10 m during 7–11 t∗ as a function of the distance from thecenter of each vortex. A single line represents each vortex. (b) Frequency distribution of the vortices against RMW normalizedby the horizontal grid spacing.

about 6 m s−1 (wind speed is not shown). Examiningthe temporal evolution of each intense vortex at the10-s interval, it was found that the intense vortices arefurther strengthened by the merger of multiple vortices(described in Section 3.3).

The frequency distribution of RMW was exhibitedin Figure 1(b). This indicates that most of the RMWsare within 1–2 grid-scales, but some of them are morethan 3 grid-scales. These large vortices have moreincreased pressure deficits and enhanced vorticities onthe order of 1 s−1. It is noted that the RMWs ofless than 1–2 grid size mostly reflect the vorticityextrema, which are marginally resolved and may notalways appear to be vortical flows. Some of thesesmall vorticity extrema will eventually become well-defined vortices through the increase in size. In thisstudy, we mainly focus on the intensification andmaintenance processes of strong vortices developedfrom those vorticity extrema.

3.3. Intensification and maintenance of verticalvortices

By examining the temporal evolutions of pressureand vertical vorticity fields at all output times forthe intense vortices that are shown in Figure 1, weidentified each vortex and its life-cycle, which isshown in Figure 2. It indicates that pressure deficitfor each vortex generally increases and sustains itsintensity with time and that vortices with both negativeand positive signs are equally found. The examinationof the temporal evolution of these vortices at 10-sinterval indicated that in many cases the merger ofmultiple vortices with the same vorticity sign furtherenhances and sustains the intensity of vertical vortices.The merger of opposite-sign vortices, on the otherhand, was found to result in diminishing their intensity(not shown).

Figure 2 also shows that there are two intensi-fied vortices without the merger (denoted by red andgreen lines during 3500–3950 s) and a weakeningvortex after the merger (denoted by blue line dur-ing 5300–5350 s). The former two were intensified

Figure 2. Time series of (a) pressure deviation (Pa) and(b) vertical vorticity (s−1) at the center of each vortex at a heightof 10 m. Each vortex is denoted as a single line distinguishedby different colors. Arrows mark the time when a merger ofvortices is seen.

by low-level convergence and by tilting of horizontalvortices at the boundaries of the convective cells,which are similar to the mechanisms described shortly,while the latter was weakened in spite of the mergerbecause of the absence of appropriate low-level con-vergence and the tilting mechanisms. However, it isindicated that the merger of multiple vortices takesplace for most of the intense vortices to be furtherenhanced at some times (mostly initial stage) duringtheir lifetimes. Therefore, the merger is considered tobe one of the important mechanisms for the intensifi-cation of vertical vortices.

We here focus on the merger processes for the vor-tex denoted by red line shown in Figure 2 duringt = 5050–5080 s (Figure 3). Significant updrafts indi-cated in Figure 3 occurred at the boundaries of theconvective cells. At 5050 s, there is an intense vor-tex at (x , y) = (540, 288) and a region with somepositive vorticity at around (x , y) = (545, 315). At



Figure 3. Horizontal sections of wind vectors, vertical velocity (shaded) and vertical vorticity (contoured at 0.3 s−1 interval from0.15 s−1) at the 1.5 m height during 5050–5080 s.

5060 s, the merger of the vortices with positive signleads to the development of another intense vortexat (x , y) = (535, 320). At 5070 s, these two intensevortices merge to become a more intensified vortex.At 5080 s, this vortex becomes sufficiently intense tohave a two-cell structure that has downdraft at thecenter and strong updraft and vertical vorticity at theperiphery. The existence of such a two-cell structurewas found in observed dust devils (Bluestein et al.,2004). The simulation seems to capture a feature ofwell-intensified dust devils.

After 5080 s the merged vortex is maintained foranother 300 s, with the vorticity of 1–2 s−1 and thepressure deficit of 40 Pa at its maximum (Figure 2).The processes for the maintenance of this well-developed vortex are diagnosed with the use of thevertical component of the equation of vorticity asfollows:

(1)

where (u, v , w ) and (ξ, η, ζ ) are the velocity andvorticity components in the x , y , and z direc-tion, respectively. Figure 4(a) shows the verticalvelocity and the tilting term in Equation (1). Thevalue of the tilting term is high across (x , y) =(515, 310)–(540, 345) near updraft regions that cor-respond to the the boundaries of the convective cells.This means that horizontal vortices generated at theboundaries of the cells due to convection and verticalshear were transported into the periphery of the vortex(the maximum value of the tilting term is 0.10 s−2),and therefore vertical vorticity is further enhanced bytilting of horizontal vorticity into the vertical directionin the presence of the horizontal gradient of verticalvelocity. This tilting mechanism seems to be differ-ent from the theory proposed by Maxworthy (1973)who suggested that the vertical vorticity of dust dev-ils is maintained by tilting horizontal vortices inherentin mean wind shear. The present study indicates thatthe tilting mechanism plays a role in maintaining theintensity of mature vortices even under no mean windcondition.

There are also some remarkable features in the ver-tical structure of the vortex (Figure 4(b)). It can beseen that convergence is very large (the maximum


Intensification and maintenance of dust devils 31

Figure 4. (a) Horizontal section of vertical velocity (shaded) and tilting term (contoured at 0.03 s−2 interval from 0.01 s−2)at z = 1.5 m and t = 5080 s. (b) Vertical section of vertical vorticity (shaded) and horizontal divergence (contoured at 0.1 s−1

interval, with the zero-line being omitted).

convergence is 0.5 s−1 and the corresponding stretch-ing term is 0.35 s−2) at the periphery of the lowerpart of the intense vortex at x = 520 and 540 m. Thehorizontal vortices concentrated due to the conver-gence are tilted vertically by horizontal gradient ofvertical velocity, and the tilted vorticities are stretchedvertically due to the third term on the right-handside in Equation (1). Divergent regions which locatethrough (x , z ) = (525, 10)–(540, 10) should also benoted, since this couple of the convergence and thedivergence is a common pattern for a well-developedvortex (Zhao et al., 2004). Furthermore, this vortexis elongated vertically up to the height of 300 m byupdrafts (not shown). The merger of multiple vorticesand the tilting of horizontal vorticity produce such awell-developed, strong vortex in CBL.

4. Conclusions and remarks

In this study, an LES of a well-developed CBL with aconstant heat flux at the surface under no mean windcondition was conducted. In the simulated turbulentfield, there are many vortices with both negative andpositive vorticity: when vortices with the same signof vorticity approach with each other they mergeto become a more intensified vortex. It was foundthat the merger of multiple vortices with the samesign is an important mechanism for strengtheningand maintaining intense vortices. It is noted thatthe merger of multiple vortices does not frequentlyoccur, since both cyclonic and anti-cyclonic vorticesequally exist and vortices with the same sign donot frequently approach with each other within theturbulent CBL. However, if vortices with the samesign happen to get closer with each other, the mergertakes place to become a single intensified vortex. In

maintaining or further intensifying the vortices, thetilting of horizontal vorticity and the stretching ofvertical vorticity also play an important role.

Although the maximum wind speeds and pressuredeviations of observed dust devils are greater than10 m s−1 and 2.5 hPa respectively (Kanak, 2006),those of the simulated vortices were not so intense. Itis expected that the maximum wind speed and pressuredeficit will be enhanced in a much finer-resolution LESowing to the extended range of explicitly resolvedflow field. By simulating the lower part of CBL inmore detail, a vortex with an observed intensity willbe generated.

Acknowledgements

This study was supported by JSPS Scientific Research20403008. We would like to thank Drs. K. Kai, H. Ishikawa,Y. Oku, and Mr. M. Horiguchi for their useful comments.

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Mechanisms for intensification and maintenance of numerically simulated dust devils

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