Dust devil vortex generation from convective cells

Abstract

Abstract.We have developed a hydrodynamic theory of the nonlinear stage of dust devil generation in a convectively unstable atmosphere with large-scale seed vertical vorticity. It is shown that convective motion in such an atmosphere transforms into dust devils extremely fast. The strong vortical structure of the dust devils can be formed in a few minutes or even in a fraction of a minute. The formation process strongly depends on the convective instability growth rate and horizontal vorticity.

“Explosively growing” vortices of unstably stratified atmosphere

“…Equation can also be obtained from the system of two equations originally derived by Stenflo [] and has been discussed recently by Shukla and Stenflo [] and Onishchenko et al []. This equation describes the dynamics of convective motion in an unstable atmosphere, when [ Onishchenko et al , , ]. Using the approximation ∂ ω z / ∂ z = 0, where , the interaction of the growing convective motion with vertical vorticity ω z is described by the equation …”

“…According to observations reported by Balme and Greeley [] and Sinclair [], the lower part of the “typical” dust devil can be described as an “inverted cone whose apex is touching or near to the ground,” which tends to a cylindrical shape at a higher altitude. Onishchenko et al [] studied the lower V‐shaped vertical vorticity of dust devils and developed a reduced nonlinear model of vortex generation for a narrow central region when r / r 0 <<1 or r / r 0 >>1, where r 0 is the vortex radius.…”

Dust Devils: Structural Features, Dynamics and Climate Impact

“…In this section, which describes the generation of convective jets (plumes) and vortices in a convectively unstable atmosphere, we will focus on the results obtained in the works [95][96][97][98]. Similar to these models we will consider only the axisymmetric case assuming that ∂/∂φ = 0 in the cylindrical coordinate system (r, φ, z) with the flow velocity denoted as…”

“…Given that sand grains in DDs move at subsonic speeds, the incompressible fluid approximation is valid. According to [95][96][97] the radial and vertical velocities of convective incompressible motion in plums of an unstable stratified atmosphere are equal to…”

“…Using the expressions for the radial and vertical velocities of convective motion (2) and (3), one can obtain an initial large scale vertical vorticity ( × v) z = 4v φ0 /r, where v φ0 = (1/4) Ωa (r/a) 3 is the initial toroidal velocity. Taking into account the interaction of the vertical vorticity with an exponentially increasing poloidal motion, one can obtain [95][96][97][98] expression for jet toroidal (or azimuthal) velocity,…”