Generation and sustenance of electric fields in sandstorms

Sandstorms are frequently accompanied by intense electric fields and lightning. In a very narrow region close to the ground, sand particles undergo a charge exchange during which larger-sized sand grains become positively charged and smaller-sized sand grains become negatively charged, and then all particles become suspended by the turbulent fluid motion. Although the association of intense electric fields with sandstorms has long been observed, the mechanism that causes these intense electric fields has not yet been described. Here, we hypothesize that differently sized sand particles are differentially transported by turbulence in the flow, resulting in a large-scale charge separation and a consequential large-scale electric field. To confirm our hypothesis, we combined a large-eddy simulation framework comprising a turbulent atmospheric boundary layer and movement of sand particles with an electrostatic Gauss law to investigate the physics of the electric fields in sandstorms. We varied the strength of the sandstorm from weak to strong as parametrized by the number density of the entrained sand particles. Our simulations reproduced observational measurements of both mean and root mean squared fluctuation values of the electric field. Our results allowed us to propose a law in which the electric field scales to two-thirds of the power of the concentration of the sand particles in weak to medium strength sandstorms.

Figure 1

The simulation domain (SD). The height of the atmospheric boundary layer $\delta$ is modeled as a turbulent half-channel flow with streamwise and spanwise periodic conditions. The lower boundary is modeled as a virtual wall (VW) at $\epsilon (\ll \delta )$ height.

Figure 2

Time history of the simulated instantaneous wall-normal electric field ($E_z$) at the midspan, midstream grid location (blue) along with the charge density variation (brown) at (a) $14.2\text{m}$, Case III-B, and (b) $35\text{m}$, Case III, where $\mathcal{N}=N_w/N_1$. Superimposed on the simulations are in situ measurements by Zhang et al. [2] (Observ. 1) and Zhang et al. [26] (Observ. 2).

Figure 3

Altitude variation of the wall-normal electric field (a) mean (time and streamwise/spanwise averaged) of ${\overline{E}}_z$, (b) root mean square (RMS) of fluctuations $E_z^{\prime }$, and (c) mean charge density, where $\mathcal{E}=\delta \mathrm{\Xi }/\varepsilon$ and $\mathrm{\Xi }=\mathcal{S}\mathrm{M}\left(n_{{}_1}\right|q_{{}_1}|,n_{{}_2}|q_{{}_2}\left|\right)$ are, respectively, the reference electric field value and the reference charge density value corresponding to Case I [$M(a,b)=\mathrm{mean}$ of $a$ and $b$]. The symbols are mean and RMS values synthesized from various sandstorm measurements by Zhang et al. [2] (circles) and Zhang et al. [26] (stars).

Figure 4

Altitude variation of the scaled net electric field magnitudes of (a) mean $\overline{\left|\mathbf{E}\right|}$, and (b) RMS fluctuations ${\left|\mathbf{E}\right|}^{\prime }$, both scaled by ${\mathcal{N}}^{\frac{2}{3}}$.