E4 Ocean Waves - Surface

Topic

Ocean surface waves are disturbances at the air-water interface in which gravity acts as the restoring force. In deep water—where the depth exceeds approximately one-quarter of the wavelength—the speed at which each wave travels depends solely on its own wavelength rather than the water depth; long waves travel faster than short ones, a behavior known as dispersion. In shallow water—where the depth is much less than the wavelength—the exact opposite occurs: all waves, whether long or short, travel at the same speed. This speed depends solely on the water depth and increases with the square root of that depth; it is this uniformity of speed that causes shallow-water waves to cease dispersing relative to one another.

Wind generates ocean waves, and as they form, they evolve into a spectrum of frequencies and directions that can take one of two typical forms, depending on the stage of wave generation. The spectrum of a wind sea that is still actively forming features an energy peak concentrated at a well-defined peak frequency; its peak enhancement factor is approximately 3.3 times that of a fully developed sea, meaning the spectrum's energy is much more sharply concentrated around the peak frequency than in a developed sea. In contrast, the Pierson-Moskowitz spectrum describes a fully developed sea—one where the wind no longer adds energy to the waves—and has a peak enhancement factor of exactly one. Significant wave height quantifies the average amplitude of the highest third of all waves making up the spectrum and is directly related to that spectrum's variance: the more energy the wave spectrum contains, the higher its variance—and consequently, the greater the significant wave height it produces—meaning that knowing the spectrum's variance is sufficient to predict the average height of the sea's largest waves.

When the amplitude of a specific wave exceeds approximately one-seventh of its own wavelength—a threshold known as the Stokes criterion—that wave breaks, creating whitecaps on the surface. This wave breaking is the primary source of energy dissipation across the entire wave spectrum, and it is this very process that causes the waves to transfer momentum and dissolved gases to the ocean beneath them.

In addition to dissipating energy upon breaking, waves also generate Stokes drift currents: a net flow of water mass in the direction of wave propagation, arising because water is transported differently at the crest than in the trough of each wave. These Stokes currents are responsible for transporting surface drifter buoys and floating pollutants, while within the wave spectrum itself, nonlinear interactions between waves constantly redistribute energy from one frequency to another, causing the spectrum to continually reorganize internally—even long after the wind has ceased blowing. The expected behavior is that, far from the region where the wind generated them, the waves propagate as an increasingly organized swell; it is precisely the dispersion described earlier that causes this swell to separate by frequency as it travels thousands of kilometers: the longer, faster waves reach a distant shore first, while the shorter ones arrive later—much later. Thus, from the dispersion that distinguishes deep water from shallow water to the frequency separation a swell undergoes after traveling thousands of kilometers, ocean surface waves carry within the very structure of their spectrum the complete history of the wind that generated them and the ocean they subsequently traversed.

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