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October, 1953
MOULT : WATER EFFECTS
91
pressure on the sheltered side is, however, reduced. There is thus a net pressure tending to drive the wave before the wind. In this way, the wind maintains the wave-motion and generates a wave train from a local disturbance. It is clear from this explanation that the waves must travel slower than the wind, for otherwise their relative velocity would drop and the net pressure maintaining them also drop. Hence for any given wind there is a maximum velocity which can be imparted to the waves and at which they can travel. This is approximately 80 per cent of the wind velocity. Likewise there is a maximum wavelength which can be maintained (since A a V2), and a maximum height (d = \/l). The tendency is, therefore, that as the wind drops, the waves become shorter as well as lower.
crested and short-crested waves. A shortcrested wave can be formed by the crossing of two convergent long-crested wave-trains. This is frequently seen in a pond when two trains of waves from stone-casts cross. Conversely, a short-crested wave generated by an impulse may resolve itself into two divergent long-crested waves. Thus the waves emanating from a storm centre may be long-crested although originating in a small confined area. Long-crested waves tend to predominate in a strong wind. In shallow water, greater power is required to maintain a given wave than in deep water.
This production of short-crested waves explains the formation of a mackerel sky, where two divergent wave-trains generated in the interface between a cloud layer and a thin layer of the adjacent air in motion break
wind
Fig. 10. Generation of water-waves by wind.
Moreover, when the wind is strong, it may tend to supply power to short waves to the extent of increasing their height above the limit (A/7). The crests then break, giving " white horses." These are then seen on the shorter waves before the longer waves, which can absorb more power owing to their size and their greater rate of loss of energy by friction.
A further consequence is that, since there is a minimum velocity beneath which waves cannot travel, so there is a minimum wind velocity below which waves cannot be maintained. This minimum wind velocity is approximately 110 cm. /sec, at which velocity a wavelength of approximately 88 cm. is maintained.
The length of the crest of a wave (measured at right-angles to its direction of motion) may vary considerably. There are both long
up the cloud layer into a regular pattern of small patches.
In like manner waves are produced on the surface of wet sand which behaves as a fluid in contact with the moving sea.
Waves generated and maintained as described do not retain their regular pattern for long. Apart from the interference of other waves, any one wave tends to develop a train of waves which travel away from it forwards and backwards. The original wave also tends to change in length as it advances, thus also changing its velocity.
There is a property of wave-motion which must be considered, if we are to account for the existence of " swell " and the existence of waves in water over which the wind is not blowing, heralding as they may do, a storm. This is the property of group-velocity and its relation to phase-velocity.