Dust devils — concentrated vertical vortices in dry daytime convective boundary layers on Earth and Mars — pose a long-standing question: what is the source of their rotation? Tracking a material surface backward from a simulated dust-devil-like vortex, Ito, Niino, and Nakanishi (2013) showed that the feeding air originates in downdrafts that already carry circulation generated at midlevels of the convective mixed layer, chiefly by tilting of baroclinically produced horizontal vorticity, with circulation statistics scaling as the product hw∗h w_* of the mixed-layer depth and the convective velocity scale. They left open how the organized structure of convection produces the spatial correlation of tilting terms required for a significant area-integrated circulation, how to characterize the true three-dimensional convergence pathways that fixed-radius circular estimates only crudely approximate, and how the mechanism operates in real dust devils under surface friction, externally forced horizontal shear, ambient rotation, and realistic near-surface boundary conditions — processes that shape the observed frequency, lifetime, and structure of dust devils. The problem therefore remains open: no study to date has extended the circulation-budget analysis to realistic conditions or characterized the actual convergence pathways.

Background

Dust devils are small, concentrated vortices with vertical axes that form over deserts and other dry, bare surfaces on sunny afternoons; on Mars they are among the most common meteorological phenomena, and they contribute a still poorly quantified fraction of atmospheric dust loading on both planets (Balme and Greeley 2006). They arise in the convective mixed layer — the lowest part of the atmosphere, well mixed by dry convection driven by strong surface heating — where buoyant updrafts and compensating downdrafts organize into cellular convection. Large-eddy simulation (LES, a numerical method that resolves the energy-containing turbulent eddies and parameterizes the smaller subgrid-scale (SGS) motions) showed early on that dust-devil-like vortices spontaneously appear in idealized, shear-free convective mixed layers (Kanak, Lilly, and Snow 2000; Kanak 2005; Ito et al. 2010; Raasch and Franke 2011). This posed a puzzle: with no background wind, no environmental horizontal vorticity, and no topography, where does the rotation come from?

The candidate mechanisms (near-surface tilting by convergence, cell-edge tilting, topographic or background-shear forcing) could not be cleanly discriminated with vorticity budgets, because vorticity itself is not conserved: tilting and stretching continually convert horizontal vorticity into vertical vorticity and amplify it. Ito, Niino, and Nakanishi (2013) therefore analyzed circulation, Γ=∮u⋅dl\Gamma=\oint \mathbf{u}\cdot d\mathbf{l}, the velocity integrated around a closed material contour, which is conserved except for identifiable source terms (baroclinic generation from horizontal buoyancy gradients and SGS turbulent transport). Tracking a material surface (a surface advected with the flow, so that it always encloses the same air) backward from a strong simulated dust devil in a large-eddy simulation with 5-m grid spacing, they found that the air feeding the vortex descends from downdraft regions already carrying circulation of roughly 400–500 m²/s; the surface contracts by about two orders of magnitude while its circulation changes by less than about 25%, so the roughly hundred-fold amplification of vertical vorticity in the vortex core is mainly stretching of pre-existing circulation. At the population scale, the standard deviation of vertical circulation σ(Γz)\sigma(\Gamma_z) over horizontal circles scales with the product hw∗h w_* of the mixed-layer depth hh and the convective velocity scale

w∗=(gQh/θ0)1/3,w_*=(gQh/\theta_0)^{1/3},

where gg is gravity, QQ the surface kinematic heat flux, and θ0\theta_0 a reference potential temperature; randomly shuffling the vorticity field destroys this circulation, so it is coherently produced by convection rather than being an aggregate of random fluctuations. Both σ(Γz)\sigma(\Gamma_z) and the area-integrated tilting term peak at midlevels (z≈0.5hz≈0.5h), indicating that the circulation is generated mainly by tilting of baroclinically produced horizontal vorticity (horizontal vorticity created by horizontal buoyancy gradients at the edges of updrafts and downdrafts) and is then advected downward by downdrafts to feed low-level vortices.

What the study did not establish — the open problem — is (i) how the organized structure of convection produces the spatial correlation of tilting terms needed for a significant area-integrated midlevel circulation; (ii) how well the true, three-dimensional convergence pathways of circulation-bearing air are represented by the fixed-radius horizontal circles used to estimate them, which the authors themselves called a crude approximation; and (iii) how this formation pathway operates in real dust devils, in which surface friction, externally forced horizontal shear, ambient rotation, and realistic near-surface boundary conditions are all present and are expected to matter for the frequency, lifetime, and structure of the observed vortices.

Problem Statement

Complete the circulation-based account of dust devil formation left open by Ito, Niino, and Nakanishi (2013). The problem has three linked components serving one common objective — a quantitative mechanism traceable from vorticity generation by convection, through circulation transport, to observed vortex statistics:

  1. Midlevel circulation generation. Explain quantitatively how the organized structure of convection in the mixed layer produces the observed spatial correlation of the tilting terms that yields a significant area-integrated circulation at midlevels (near z≈0.5hz≈0.5h) — the circulation that is subsequently advected downward by downdrafts and stretched in low-level updrafts to form dust-devil-like vortices. This includes identifying which structural properties of the convective cells (for example, the geometry and nonaxisymmetry of their updraft and downdraft branches) are necessary and sufficient for that correlation, and whether the circulation statistics continue to scale with hw∗h w_* when conditions change.

  2. Convergence pathways. Characterize the actual three-dimensional, time-dependent material pathways by which circulation-bearing air converges into the vortex core, replacing the crude approximation of fixed-radius horizontal circles as source areas, and quantify how circulation is modified along those pathways (for example, by subgrid-scale turbulent transport).

  3. Realistic dust devils. Determine how the formation mechanism operates in the presence of surface friction, externally forced horizontal shear, ambient rotation, and more realistic near-surface boundary conditions, and quantify the role of these processes in setting the frequency, lifetime, and structure of real dust devils.

An answer resolves the problem only if it connects all three components — for instance, by extending the material-surface circulation-budget analysis to simulations that include friction, shear, and rotation, and validating the resulting mechanism against observed dust devil statistics. The three components are jointly mandatory, and the cell-structure properties, realistic processes, and vortex properties named within them — together with the illustrative examples — describe the scope of the required account rather than independent sub-questions each to be settled on their own. Progress confined to the shear-free, frictionless idealized limit, or to vortex intensity statistics without a circulation-budget diagnosis, leaves the source question unanswered.

References

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