A fractal approach to breaking waves

Abstract

Fractal models of breaking waves in a random surface should preferably describe dynamical as well as geometrical properties. This becomes feasible if there is a wide separation between the length scales of component waves. Using this idea, a simple model of breaking waves is constructed, which shows that whereas the downward acceleration of particles at a wave crest is limited to g, the upward accelerations in a wave trough are unbounded. Owing to tangential stretching or contraction, certain phases of a progressive or standing wave can be identified as being stable or unstable. The most striking instabilities are expected on the forward slopes of progressive waves, and in the troughs of steep waves meeting a vertical wall. -Author