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Dust devils

Air and fluids · level 7, lesson 6 of 6

A question to start

On 27 September 2021, a dust devil passed right over Perseverance, and its microphone recorded the wind and the patter of dust grains. What makes a dust devil spin, and what is it like inside?

The idea

On a sunny day, the ground heats the air just above it. The warm air rises (convection), and air rushes in along the ground to replace it. If that air has even a little spin, it spins faster as it moves inward, like a skater pulling in their arms. For a ring of air with no twisting forces on it, speed times radius stays fixed:

\[v r = \text{constant}.\]

Spinning air needs a force towards the centre to keep it going round, and the only force available is a pressure difference. So the core of a dust devil has low pressure. A simple model gives a drop of about

\[\Delta p \approx \rho v_\text{max}^2,\]

where \(v_\text{max}\) is the fastest wind in the vortex.

air flows inand spins fasterlow-pressure corewarm air rises
A dust devil with a 10.7 m/s top wind Mars Earth
Air density 0.016 kg/m³ 1.217 kg/m³
Pressure drop in the core, about \(\rho v^2\) 1.8 Pa 139 Pa
As a share of the air pressure 0.3% 0.14%

The dust devil over Perseverance was about 25 m wide, at least 118 m tall, and moved at about 5 m/s. The rover's weather station measured a top wind of 10.7 m/s. On Mars, dust devils usually show up as pressure dips of 0.3 Pa to a few pascals. Perseverance spotted 91 of them in its first 216 sols.

Worked examples

1. Spinning up. Air 50 m from the centre circles at 1 m/s. At 5 m from the centre: \(v = 1 \times 50/5 = 10\) m/s.

2. The core pressure on Mars. \(0.016 \times 10.7^2 = 1.8\) Pa, inside the measured range of a few pascals.

3. Share of the pressure. \(1.8/636 = 0.3\%\). Small in pascals, but a bigger share of Mars's air pressure than the same storm would be on Earth.

Try it

  1. Why does air spin faster as it moves towards the centre of a dust devil?
  2. Air circling at 2 m/s, 30 m from the centre, moves in to 6 m. How fast does it go now?
  3. Why must the core of a dust devil have low pressure?
  4. Find the core pressure drop for a 20 m/s Mars dust devil.
Answers
  1. Speed times radius stays fixed, so a smaller radius means a higher speed.
  2. \(2 \times 30/6 = 10\) m/s.
  3. The spinning air needs a force towards the centre, which only a pressure difference can give.
  4. \(0.016 \times 400 = 6.4\) Pa.

Common mistake

"Dust devils are tornadoes." Tornadoes hang from storm clouds. Dust devils grow from the ground up, on sunny days, from air heated by the ground.

Where it leads