## Gustave Coriolis, and the Coriolis effect

 E. Linacre and B. Geerts 1/'99

Gustave Gaspard Coriolis was born in 1792 in Paris of an aristocratic family impoverished by the French Revolution. He studied mathematics, became an academic and published a book ‘Calculation of the Effect of Machines’ in 1829. In 1835 he published his famous paper ‘On the equations of relative motion of a system of bodies’. The explanation of the effect sprang from problems of early 19th-century industry, i.e. rotating machines like water-wheels. Coriolis died in 1843 while working on a revision of his book, and he never applied his theory to ocean or atmospheric circulations, nor to its implication on the firing of ballistic missiles. It was William Ferrel who deduced in 1856 that the direction of winds tends towards a direction along the isobars, leading to C.H.D. Buys Ballot publishing his rule (Section 11.4) in 1857.

Coriolis regarded the effect he had discovered as the result of a complementary centrifugal force due to the rotation of the frame of reference. For him this force was no more fictitious than the usual centrifugal force. This way of thinking has some advantages in explaining meteorological processes. It is based on the two principles, of the conservation of angular momentum and conservation of rotational kinetic energy. These principles differ from that of the conservation of linear momentum, i.e. of absolute velocity, applied by George Hadley in 1735 to explain Trade winds.

A fascinating consideration is the case of the rotating skater who folds her arms inwards, and thereby spins faster because her angular momentum (I x W) remains constant. (I is the moment of inertia, which increases with radius from the axis of rotation, and W the angular velocity). However, her rotational kinetic energy is (I x W2 / 2), and this increases with the rate of spin. Where has the additional energy come from? It comes from the (negative) work done in drawing one’s arms to the body, against the centrifugal force (1).

Reference

1. Persson, A. 1998. How do we understand the Coriolis Force? Bull. Amer. Meteor. Soc., 79, 1373-85.