*Journal of Oceanography,* Vol. 53 (No. 3), pp. 311-315, 1997

*Short Contribution*

## Cyclostrophic Balance in Surface Gravity Waves: Essay on Coriolis Effects

Kern E. Kenyon

4632 North Lane Del Mar, CA 92014-4134, U.S.A.

(Received 11 July 1996; in revised form 12 December 1996; accepted 18 December 1996)

**Abstract: **
When gravity waves of small amplitude progress over the surface of deep water, the particle orbits are observed to be closed circles; therefore the waves possess orbital angular momentum. The particles experience a balance of two equal and opposite forces, called the cyclostrophic balance: the outward centrifugal force and an inward pressure force. On the Earth's surface the Coriolis force causes a minor disruption of the normal cyclostrophic balance. For plane waves it is possible that the Coriolis force can be balanced at all times, and the cyclostrophic balance can be maintained as well, by a slight change in the orientation and the shape of the particle orbits. In order to balance all three forces simultaneously in either hemisphere, the shape of the orbits should be oval (perhaps elliptical) in general, where the shorter axis of the oval is parallel to the mean surface, and the plane of the orbits should be tilted to the left of the direction of wave propagation. In the northern hemisphere the orbital planes should also be tilted to the left of the vertical and in the southern hemisphere to the right of the vertical, facing in the direction of wave propagation. For ocean swell the order of magnitude of the sine of both tilt angles, as well as the eccentricity of the orbits, is comparable to the ratio of the Coriolis parameter to wave frequency, or one in ten thousand, which is probably too small to be observed. If in some particular circumstance (perhaps transient conditions) the Coriolis force is not balanced, then a Coriolis torque exists that will try to change the direction, but not the magnitude, of the orbital angular momentum of the waves. The general form of the Coriolis torque is worked out in Appendix.

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