Cyclostrophic balance in surface gravity waves

Abstract

The cyclostrophic balance (pressure forcevs. force centrifugal force) is shown to be satisfied for all fluid particles in surface gravity waves with sinusoidal form and circular particle orbits. Consequences of the cyclostrophic balance are 1) that the normal dispersion relation for deep water hold and 2) that the orbital radius decrease with increasing depth at the usual exponential rate, from which it follows that the wave pressure and particle speed also decrease with depth exponentially. In addition, the cyclostrophic and hydrostatic balances together predict wave breaking at the crests for amplitudes exceeding one divided by the wave number. In contrast to the traditional perturbation method, based on irrotational flow, the cyclostrophic method does not demand that the amplitude be much less than a wave length and does not require an infinite wave train.