The Dynamics of Disaster by Susan W. Kieffer

Author:Susan W. Kieffer
Language: eng
Format: epub
Publisher: W. W. Norton & Company
Published: 2013-09-03T16:00:00+00:00

AN ASIDE ABOUT WIND-DRIVEN WAVES

Wind-driven waves are the “deep-water waves” George Stokes mentioned in the previous chapter and illustrated in Figure 6.5. In these waves the water depth is much greater than half the wavelength. What effect do such waves have on the water through which they pass?

I figured this out when, in the 1950s, it was a big deal to take the annual vacation from landlocked northwestern Pennsylvania to the New Jersey shore. Swimming out into the ocean, I would turn around and face the shore, treading water as the waves took me up and down, toward and away from the beach. I imagined that I had pencils sticking out of my ears, and discovered that the imaginary pencils traced a circle—the top of the circle when a crest came and lifted me up and toward the shore, and the bottom when the next trough came past and pulled me down and back away from the shore. The diameter of the circle was about the height of the waves, trough to crest. In hindsight, I had discovered one of the fundamental characteristics of particle motion in wind-driven waves: the waves passed by and broke on shore, but I, and the water in the waves, just circled in orbit around a stationary point (see Figure 6.5).

Like surfers and others playing in the waves along the shore, I also discovered that the motion of water driven by these waves decreases dramatically with depth (strictly, it decreases exponentially with depth). If an ominously big wave came toward us, or if we were caught in the surf zone of breaking waves, we knew that if we simply dove down a few feet into quieter water under the surface and let the wave pass over us, we would be safe. We were playing with waves typical of a normal shoreline. Their spacing (wavelength) was a few tens to, at most, a few hundred feet. The wavelengths of wind-driven waves on the ocean are rarely greater than 500 feet, and thus, at depths of a few hundred feet, water is calm even when waves in wild and violent seas surge back and forth at the surface.

The dynamics of wind-driven waves are fundamentally different from those of tsunamis. Whereas tsunamis, as shallow-water waves, travel with a speed that depends on ocean depth, deep-water waves travel with a velocity that depends, instead, on their wavelength (or period). One way to understand this is to recognize that since deep-water waves do not affect ocean waters below about half their wavelength, they are unaffected by the ocean bottom, no matter how deep it is. Their velocity, therefore, cannot depend on the water depth.

Deep-water waves that have a long wavelength travel faster than those that have shorter wavelengths. This dependence of wave speed on wavelength has enormous implications for the ocean response to storm systems. Storms at sea generate waves with many different wavelengths. Those with the longest wavelengths travel fastest, so they move away from the storm area faster than do waves with shorter wavelengths.

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