The Bird in the Waterfall by Jerry Dennis and Glenn Wolff

The Steepness of a Wave
Jerry Dennis & Glenn Wolff

The steepness of a wave never exceeds a 1:7 ratio of height to length. Thus a wave seven feet from crest to crest cannot be more than one foot high. Whitecaps are formed when wind stronger than about 20 feet per second (13.6 miles per hour) pushes small steep waves to that 1:7 limit. When the limit is reached the waves become unstable and break into a froth of turbulence. In a whitecap or breaking wave, particles of water fall down the crest and make actual progress. But in ordinary waves, water particles move only in well-defined circular orbits, essentially remaining in place while the wave passes through them. This motion is one of the oddest and least understood features of a wave. Waves are energy passing through water, visible only on the surface, but they have roots extending downward a distance equal to one-half the wave's length. As the energy passes it sets particles of water spinning in circular orbits, like rollers on a conveyor that spin when a crate passes over them but remain seated in place. The orbit of the water particles is large at the surface, where the diameter is equal to the height of the wave, but diminishes quickly with depth. Beneath the final, smallest orbit at the bottom of the wave there is no motion at all.

This difficult concept can be tested by filling a plastic bottle with water so that it barely floats. Place the bottle in waves next to a stationary object and note how it moves slightly forward with every crest and slightly backward with every trough. The orbiting water particles within each wave follow the same swaying motion.

Excerpts I, II, III & IV:
  • Freak Waves and Rogues
  • Oil on the Water
  • Storm Surge
  • Waves Underwater
  • When waves enter shallow water they undergo dramatic changes.

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