Steady‐state properties and statistical distribution of atmospheric dust devils

Abstract

[1] A steady Rankine-like vortex model of a dust devil is reported, which takes into account the sunlight absorption by airborne dust particles and the diabatic heating of a rotating dust column. For the maximum swirl velocity being a few times larger than the mean updraft velocity, the model admits significant simplifications allowing for its complete analytical treatment. The competitive effects of (i) the surface heat fluxes and (ii) the suspended-dust-caused diabatic heating on the vortex constitution (strength, height and shape) are examined. The second factor is found to be more influential for the strongest vortices. A reference exponential distribution of dust devils over their radius (visible diameter), which was introduced based on general arguments of mathematical information theory, is shown to fit satisfactory well the observational data on dust devils in Arizona and southern California and, in a preliminary way, on Mars. Citation: Kurgansky, M. V.(2006), Steady-state properties and statistical distribution of atmospheric dust devils, Geophys. Res. Lett., 33, L19S06,

On the statistical distribution of dust devil diameters

“…The height of the dust devil will likely be confined to the height of the atmospheric boundary layer, and the observed aspect ratios (height:diameter) of dust devils suggests this should translate into an upper diameter limit that is a factor of a few smaller than this. Similarly, the minimum size to the distribution may be the Obhukov length, as suggested by Kurgansky (2006).…”

“…While many workers have noted the minimum, maximum and mean in their respective surveys, these numbers have only modest utility for describing skewed and incompletely-sampled populations. The first useful analytic description of a dust devil size distribution appears to be that of Kurgansky (2006) Contents lists available at ScienceDirect Icarus j o u r n a l h o m e p a g e : w w w . e l s e v i e r .…”

“…The function (upper case) P(x) is the cumulative probability that a dust devil of size x or larger: the Weibull function, used widely in terrestrial wind energy studies, was advanced by Lorenz (1996) as a convenient description of Viking measurements of Mars surface windspeeds -the shape parameter which leads to a Rayleigh distribution for k = 2. Kurgansky (2006) then goes onto compare the shape of this distribution, via linear histograms without discussion of statistical errors, with a few surveys and finds the function to be a satisfactory fit. Lorenz (2009), noting the coarse binning of those surveys, examined the more finely-histogrammed data of Greeley et al (2006) of dust devil diameters on Mars (Gusev) recorded in MER images, plotting the data with counting errors on a doublelogarithmic plot (apparently the first time dust devil sizes were presented this way).…”

“…First, we note that the real dust devil population is likely to be bounded by two finite values -a maximum and a minimum. This is significant, because the principal theoretical justification offered for an exponential distribution by Kurgansky (2006) is that this function is the maximum-entropy (most probable) distribution. This maximum-entropy argument is only true if the distribution is allowed to span the range of zero to infinity.…”

History and Applications of Dust Devil Studies

“…Lorenz 2011; Kurgansky 2006). There exists an association of power law statistics with self-organized criticality and other forced physical systems.…”