On the Parent Circulation Contributing to Form Dust Devils

Dust devils are small-scale vertical vortices that often occur over deserts or bare lands in fine weather conditions in which a convective mixed layer develops. Recent observational studies suggest that dust devil-like vortices, which are not visualized by dust particles, do occur in convective mixed layers. Thus formations of dust devils appear to be universal phenomena in convective mixed layers. Why such strong vortices are generated remains an attractive subject in the dynamics of the atmospheric boundary layer, and several hypotheses for the origin of strong vertical vorticity in dust devils have been proposed. Although both observational and numerical studies on dust devils have been performed, no quantitative study on the source of vertical vorticity of dust devils have been made.

In this study, a large eddy simulation model with grid spacing of 5m is used to simulate dust devils embedded in a convective mixed layer and a quantitative analysis on their source of its vertical vorticity is made. In order to investigate the origin of vertical vorticity in the simulated dust devil, the circulation, which is a conserved quantity in the absence of turbulent transport and baroclinic production of horizontal vorticity, is examined, where the circulation is calculated as a surface integral of vorticity vector on a material surface. The deformation of the material surface as it flows into the dust devil shows gives quantitative information about how stretching and tilting of vorticity contribute to the formation of the dust devil. Material surface is initially placed horizontally in the core of the simulated dust devil. It is divided into about 20000 triangular patches and vertices of the patches are tracked backward for 140 seconds.

Our analysis shows that the material surface converges, while approximately conserving circulation, toward the dust devil from a wide horizontal plane whose horizontal scale is on the order of 100 m near the surface. The material surface has a circulation of about 300 m²/s initially, and is enough for forming dust devils that have vertical vorticity of the order of 1 s^-1 through the vorticity stretching.

A standard deviation of circulations over horizontal circles of several hundred meters in radius near the surface shows that presence of circulations is an inherent property of the convective mixed layer and its magnitude is reasonably scaled by the product of the depth of convective mixed layer and the convective velocity. The standard deviation of circulations increases with the development of convective mixed layer, and reaches a sufficient magnitude to form dust devils. These circulations are shown to be caused by organized structures of the convection, since no significant circulations are realized when grid point values of simulated vertical vorticity are randomly shuffled.

The standard deviations of the circulations have the largest amplitudes at the middle level of the convective mixed layer, so that it appears to be created at the middle level due to tilting of horizontal vorticity resulted from the shear between the updrafts and downdrafts. The circulations thus produced are advected toward lower and upper levels of the mixed layer by downdrafts and updrafts, respectively, to form dust devils.