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The Coriolis effect

Air and fluids · level 8, lesson 4 of 6

A question to start

On a weather map, the wind does not blow straight from high to low pressure. It swirls round the lows instead. What turns it?

The idea

A planet spins. Seen from the spinning ground, anything moving across it seems to be pushed sideways: to the right in the northern hemisphere, to the left in the southern. This is the Coriolis effect. Its size is set by the Coriolis parameter

\[f = 2\Omega \sin\varphi,\]

where \(\Omega\) is the planet's spin rate in radians per second and \(\varphi\) the latitude. A wind of speed \(v\) feels a sideways acceleration \(f v\).

Away from the ground, the wind settles where the Coriolis push balances the pressure push. Then it blows along the lines of equal pressure, at the geostrophic speed:

\[v_g = \frac{1}{\rho f}\,\frac{\Delta p}{\Delta x}.\]
Spin Mars Earth
Sidereal day 24.6229 h 23.9345 h
\(\Omega = 2\pi/\text{day}\) \(7.09\times10^{-5}\) rad/s \(7.29\times10^{-5}\) rad/s
\(f\) at 45° \(1.00\times10^{-4}\) s⁻¹ \(1.03\times10^{-4}\) s⁻¹

Mars and Earth spin at almost the same rate, so the Coriolis effect is almost the same on both.

lownorthernhemisphere

Worked examples

1. Mars's spin. \(\Omega = 2\pi/(24.6229 \times 3600) = 7.09\times10^{-5}\) rad/s. At 45°: \(f = 2 \times 7.09\times10^{-5} \times 0.707 = 1.00\times10^{-4}\) s⁻¹.

2. A Mars geostrophic wind. A 1% pressure difference over 1,000 km gives \(\frac{1}{\rho}\frac{\Delta p}{\Delta x} = 4.0\times10^{-4}\) m/s². So \(v_g = 4.0\times10^{-4}/1.00\times10^{-4} = 4.0\) m/s.

3. On Earth, the same 1% over 1,000 km: \(8.3\times10^{-4}/1.03\times10^{-4} = 8.1\) m/s.

Try it

  1. Which way does the Coriolis effect turn a wind in the southern hemisphere?
  2. Find \(f\) on Mars at 20° latitude.
  3. Why is the Coriolis effect almost the same on Mars as on Earth?
  4. Why is there no geostrophic wind at the equator?
Answers
  1. To the left.
  2. \(2 \times 7.09\times10^{-5} \times \sin 20° = 4.85\times10^{-5}\) s⁻¹.
  3. Both planets spin once in about 24 hours.
  4. \(\sin 0° = 0\), so \(f = 0\) and there is no sideways push to balance the pressure push.

Common mistake

"The Coriolis effect makes bathwater swirl one way." In a bath, it is far too weak to matter. It matters for winds that travel hundreds of kilometres over many hours.

Where it leads