Water waves have many applications in geophysics.
Here is a list of important points.
- Wavelength and frequency of waves are related through the dispersion relation.
- The velocity of a wave phase can differ from the velocity at which wave energy propagates.
- Waves in deep water are dispersive, longer wavelengths travel faster than shorter wavelengths. Waves in shallow water are not dispersive.
- The dispersion of ocean waves has been accurately measured, and observations of dispersed waves can be used to track distant storms.
- The shape of the sea surface results from a linear superposition of waves of all possible wavelengths or frequencies traveling in all possible directions.
- The spectrum gives the contributions by wavelength or frequency to the variance of surface displacement.
- Wave energy is proportional to variance of surface displacement.
- Digital spectra are band limited, and they contain no information about waves with frequencies higher than the Nyquist frequency.
- Waves are generated by wind. Strong winds of long duration generate the largest waves.
- Various idealized forms of the wave spectrum generated by steady, homogeneous winds have been proposed. Two important ones are the Pierson-Moskowitz and JONSWAP spectra.
- Observations by mariners on ships and by satellite altimeters have been used to make global maps of wave-height. Wave gauges are used on platforms in shallow water and on the continental shelf to measure waves. Bottom-mounted pressure gauges are used to measure waves just offshore of beaches. And synthetic-aperture radars are used to obtain information about wave directions.
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