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Formation Mechanism of Dust Devil–Like Vortices in Idealized Convective Mixed Layers

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Formation Mechanism of Dust Devil–Like Vortices in Idealized Convective Mixed Layers APRIL 2013 I T O E T A L . 1173 Formation Mechanism of Dust Devil–Like Vortices in Idealized Convective Mixed Layers JUNSHI ITO AND HIROSHI NIINO Atmosphere and Ocean Research Institute, The University of Tokyo, Kashiwa, Japan MIKIO NAKANISHI National Defense Academy, Yokosuka, Japan (Manuscript received 5 March 2012, in final form 9 November 2012) ABSTRACT Dust devils are small-scale vertical vortices often observed over deserts or bare land during the daytime under fair weather conditions. Previous numerical studies have demonstrated that dust devil–like vertical vortices can be simulated in idealized convective mixed layers in the absence of background winds or envi- ronmental shear. Their formation mechanism, however, has not been completely clarified. In this paper, the authors attempt to clarify the vorticity source of a dust devil–like vortex by means of a large-eddy simulation, in which a material surface initially placed in the vortex is tracked backward and the circulation on the material surface is examined. The material surface is found to originate from downdrafts, which already have sufficient circulation. As the material surface converges toward the vortex, the vorticity is increased because of conservation of circulation. It is shown that a convective mixed layer is inherently accompanied by cir- culation, which is scaled by a product of the convective velocity scale and the depth of the convective mixed layer. This circulation is considered to be originally generated by tilting of baroclinically generated horizontal vorticity principally at middepths of the convective mixed layer. 1. Introduction Taylor 2010b). Indeed, Fujiwara et al. (2011, 2012) de- tected a number of invisible vertical vortices in con- Dust devils are small-scale vertical vortices often ob- vective mixed layers by a Doppler lidar. Experimental served over deserts and bare land in the early afternoon (e.g., Willis and Deardorff 1974) and numerical (e.g., under fair weather conditions. Previous studies (e.g., Kanak et al. 2000; Toigo et al. 2003; Kanak 2005, 2006; Williams 1948; Sinclair 1965; Snow and McClelland Ito et al. 2010; Gheynani and Taylor 2010a; Raasch and 1990; Greeley et al. 2006; Oke et al. 2007; Kurgansky Franke 2011) studies have succeeded in simulating dust et al. 2011) have shown that dust devils are ubiquitous devil–like vortices (DDVs) in convective mixed layers. in convective mixed layers. In fact, we know that dust A natural question to be raised then is how such strong devils also occur in Mars’s atmosphere during the day- vortices are formed in convective mixed layers. The time (e.g., Cantor et al. 2006; Greeley et al. 2006; Balme preceding numerical studies, which have demonstrated and Greeley 2006) and that they may contribute to formation of DDVs in convective mixed layers in the global warming on Mars (Fenton et al. 2007). These absence of background winds, shed some light on this vortices are believed to occur even when dust particles question (Kanak et al. 2000; Toigo et al. 2003; Kanak to be picked up from the bottom surface of the vortices 2005; Ohno and Takemi 2010; Raasch and Franke 2011). are not available: a feedback of the dust particles is not However, the source of the vertical vorticity and the essential for the vortices (Sinclair 1969; Gheynani and formation mechanism of the vortices remain contro- versial, and no quantitative study on the source of the vertical vorticity has been performed. Corresponding author address: Junshi Ito, Atmosphere and Ocean Research Institute, The University of Tokyo, 5-1-5 Ka- For DDVs to form, there must be a source of vertical shiwanoha, Kashiwa, Chiba 277-8564, Japan. vorticity that is stretched by an updraft caused by air E-mail: [email protected] with a large buoyancy originating from the surface layer DOI: 10.1175/JAS-D-12-085.1 Ó 2013 American Meteorological Society Unauthenticated | Downloaded 09/30/21 09:10 AM UTC 1174 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 70 TABLE 1. Summary of the experimental design. Domain (km) 1.8 3 1.8 3 1.6 Grid points 362 3 362 3 320 Grid spacing (m) 5 2 Surface heat flux Q (K m s 1) 0.24 3 sin[p(t 2 7)/11] subject to a superadiabatic lapse rate. Several hypothe- ses have been proposed for the source of the vertical vorticity in DDVs: 1) mechanism A (mech. A): effects of topography or even a small animal (Williams 1948; Barcilon and Drazin 1972); 2) mechanism B (mech. B): tilting of horizontal vorticity, associated with vertical shear of a background wind, by the updraft of the DDV (Maxworthy 1973); 3) mechanism C (mech. C): tilting of horizontal vorticity, associated with a convective cell within the convective mixed layer, by the updraft of the convective cell (Willis and Deardorff 1979; Hess et al. 1988; Cortese and Balachandar 1993); and 4) mechanism FIG. 1. Vertical profiles of horizontally averaged potential D (mech. D): nonuniform convergence in convection temperatures at 1-h time increments from 0700 to 1200 LST. cells and associated horizontal shear near the ground (Carroll and Ryan 1970; Cortese and Balachandar 1993). circulation using an area integral of vorticity over a ma- Recently, numerical studies have started to provide im- terial surface (MS), which has an advantage of giving portant suggestions for the generation mechanism of additional information about how tilting and stretching DDVs. Kanak et al. (2000) mentioned that mech. C oc- of vorticity take place. curred in their large-eddy simulation (LES) while mech. The next section describes a numerical simulation A and mech. B did not. Kanak (2005) later suggested of DDVs in a convective mixed layer, performed at that mech. D occurs in low-level convergence zones a very fine resolution. Section 3 describes results of the associated with convective cells, while mech. C occurs backward-trajectory analysis on the circulation. The at convective cell vertices. Raasch and Franke (2011) results are discussed in section 4, and conclusions are performed an LES with an extraordinarily fine mesh, given in section 5. and suggested that mech. C is significant for the forma- tion of DDVs while mech. D can operate only in short- 2. Numerical methodology lived vertical vortices. This paper attempts to quantitatively examine the a. Model description ways in which vertical vorticity of DDVs is generated in The LES model used in the present study is the same the convective mixed layer without background wind. as that described by Nakanishi (2000) and Ito et al. For this purpose, a backward-trajectory analysis may (2010), except that the bottom boundary condition is provide a useful approach. Using a backward-trajectory changed to free slip. A brief description of the model is analysis, Markowski and Hannon (2006) examined the given in this subsection. vorticity budgets of miso-scale vortices that occur in The resolved-scale momentum equation, the ther- convective mixed layers and have a horizontal scale modynamic equation, and the continuity equation un- larger than that of dust devils. However, a disadvantage der the Boussinesq approximation are, respectively, of the vorticity analysis is that vorticity is not conserved, expressed as even in the absence of turbulent mixing or baroclinic production, when stretching and compression are pres- ›u ›u u 1 ›p ›t g i 1 j i 52 2 ij 1 (u 2 u )d , (1) ent. Thus, we will instead examine a circulation, which is ›t ›x r ›x ›x u 0 i3 defined as an area integral of vorticity or a line integral j 0 i j 0 of velocity along a closed curve and is a conserved ›u ›u u ›t quantity in the absence of turbulent mixing and baro- 1 j 52 uj › › › , and (2) clinic production. A similar analysis using a circulation t xj xj was performed by Mashiko et al. (2009), who studied the ›u mechanism of a tornadogenesis. While they calculated i 5 › 0, (3) the circulation using a line integral, we calculated the xi Unauthenticated | Downloaded 09/30/21 09:10 AM UTC APRIL 2013 I T O E T A L . 1175 21 FIG. 2. Iso-surface of vertical vorticity of 0.25 (red) and 20.25 s (green) at 1210 LST. The lower part of the calculation domain at heights , 100 m is displayed. The color shading shows 2 the vertical velocity at the lowest model level (m s 1). The DDV to be examined in detail in this study is indicated by the white arrow. where the overbars denote resolved-scale variables; scale (SGS) motions; dij is the Kronecker delta; g is the ui (i 5 1, 2, 3) the velocity components (u, y, and w)in gravitational acceleration; u is the potential tempera- the x, y, and z directions, respectively; p is the pertur- ture; u0 is the basic potential temperature; r0 is the air bation pressure; tij is the stress tensor due to subgrid- density; and tuj is the SGS heat flux. The Coriolis force is FIG. 3. Horizontal distribution of vertical velocity (gray scale) and the horizontal component of wind vectors (arrows) at 1210 LST at the lowest layer around the DDV for which backward trajectories were obtained. Unauthenticated | Downloaded 09/30/21 09:10 AM UTC 1176 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 70 FIG. 5. Example of a backward trajectory of an air parcel initially located in the core region of a DDV. is set to 5 m. The surface heat flux Q is prescribed by FIG. 4. Vertical profile of maximum vertical vorticity in the domain 5 3 p 2 at 1210 LST. a sinusoidal function, Q Qmax sin[ (t 7)/11], where t is the local standard time (LST) in hours and 21 Qmax is set to 0.24 K m s .
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