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16: Ocean Waves

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    Looking out to sea from the shore, we can see waves on the sea surface. Looking carefully, we notice the waves are undulations of the sea surface with a height of around a meter, where height is the vertical distance between the bottom of a trough and the top of a nearby crest. The wavelength, which we might take to be the distance between prominent crests, is around 50-100 meters. Watching the waves for a few minutes, we notice that wave height and wave length are not constant. The heights vary randomly in time and space, and the statistical properties of the waves, such as the mean height averaged for a few hundred waves, change from day to day. These prominent offshore waves are generated by wind. Sometimes the local wind generates the waves; other times, distant storms generate waves which ultimately reach the coast. For example, waves breaking on the Southern California coast on a summer day may come from vast storms offshore of Antarctica 10,000 km away.

    If we watch closely for a long time, we notice that sea level changes from hour to hour. Over a period of a day, sea level increases and decreases relative to a point on the shore by about a meter. The slow rise and fall of sea level is due to the tides, another type of wave on the sea surface. Tides have wavelengths of thousands of kilometers, and they are generated by the slow, very small changes in gravity due to the motion of the Sun and the Moon relative to Earth.

    In this chapter you will learn how to describe ocean-surface waves quantitatively. In the next chapter I will describe tides and waves along coasts.

    • 16.1: Linear Theory of Ocean Surface Waves
      Describing ocean surface waves under linear theory. Includes discussion of the dispersion relation, phase and group velocity, wave energy, and significant wave height.
    • 16.2: Nonlinear Waves
      Stokes waves and the conditions required for interacting free waves to produce another free wave. The concept of wave momentum.
    • 16.3: Waves and the Concept of a Wave Spectrum
      Applying the Fourier transform to express arbitrary wave functions of time as the sum of an infinite series of sinusoids. Calculating wave spectra to view the wave energy distribution on the sea surface. Considerations in sampling wave height on the sea surface.
    • 16.4: Ocean-Wave Spectra
      Wave spectra as generated by wind on the ocean. Includes discussion of the Pierson-Moskowitz Spectrum and JONSWAP Spectrum.
    • 16.5: Wave Forecasting
      Brief discussion of techniques for forecasting waves from individual wave component data.
    • 16.6: Measurement of Waves
      Some commonly used techniques for measuring wave data.
    • 16.7: Important Concepts
      Summary of important concepts covered in this chapter.

    This page titled 16: Ocean Waves is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Robert H. Stewart via source content that was edited to the style and standards of the LibreTexts platform.