17.1 Waves
Waves form on the ocean and on lakes because energy from the wind is transferred to the water. The stronger the wind, the longer it blows, and the larger the area of water over which it blows (the fetch), the larger the waves are likely to be.
The important parameters of a wave are its wavelength (the horizontal distance between two crests or two troughs), its amplitude (the vertical distance between a trough and a crest), and its velocity (the speed at which wave crests move across the water) (Figure 17.2).
The typical sizes and speeds of waves in situations where they have had long enough to develop fully are summarized in Table 17.1. In a situation where the fetch is short (say 19 km on a lake) and the wind is only moderate (19 km/h), the waves will develop fully within 2 hours, but they will remain quite small (average amplitude about 27 cm, wavelength 8.5 m). On a large body of water (the ocean or a very large lake) with a fetch of 139 km and winds of 37 km/h, the waves will develop fully in 10 hours; the average amplitude will be around 1.5 m and average wavelength around 34 m. In the open ocean, with strong winds (92 km/h) that blow for at least 69 hours, the waves will average nearly 15 m high and their wavelengths will be over 200 m. Small waves (amplitudes under a metre) tend to have relatively shallow slopes (amplitude is 3% to 4% of wavelength), while larger waves (amplitudes over 10 m) have much steeper slopes (amplitude is 6% to 7% of wavelength). In other words, not only are large waves bigger than small ones, they are also generally more than twice as steep, and therefore many times more impressive. It is important to recognize, however, that amplitudes decrease with distance from the area where the waves were generated. Waves on our coast that are generated by a storm near Japan will have similar wavelengths but lower amplitudes than those generated by a comparable storm offshore from Vancouver Island.
| Wind Speed | Fetch | Duration | Amplitude | Wavelength | Wave Period | Wave Velocity | |
| km/h | km | h | m | m | s | m/s | km/h |
| 19 | 19 | 2 | 0.27 | 8.5 | 3.0 | 2.8 | 10.2 |
| 37 | 139 | 10 | 1.5 | 33.8 | 5.7 | 5.9 | 19.5 |
| 56 | 518 | 23 | 4.1 | 76.5 | 8.6 | 8.9 | 32.0 |
| 74 | 1,313 | 42 | 8.5 | 136 | 11.4 | 11.9 | 42.9 |
| 92 | 2,627 | 69 | 14.8 | 212 | 14.3 | 14.8 | 53.4 |
Table 17.1 The parameters of wind waves in situations where the wind blows in roughly the same direction for long enough for the waves to develop fully. The duration times listed are the minimum required for the waves to develop fully. [SE from data at: http://en.wikipedia.org/wiki/Wind_wave]
Exercises
Exercise 17.1 Wave Height Versus Length
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This table shows the typical amplitudes and wavelengths of waves generated under different wind conditions. The steepness of a wave can be determined from these numbers and is related to the ratio: amplitude/wavelength. 1. Calculate these ratios for the waves shown. The first one is done for you. 2.