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BRITISH KINEMATOGRAPHY
Vol. 23, No. 4
" When an isolated group (train) of waves of sensibly the same length is advancing over relatively deep water, the velocity of the group as a whole is less than that of the individual waves composing it. If attention be fixed on a particular wave, it is seen to advance through the group, gradually dying out as it approaches the front, whilst its former place in the group is occupied in succession by other waves which have come forward from the rear."
Henceforth, we will refer to the velocity of a single wave as V\ and the velocity of the group as Vg. Then KA is known as the Phase Velocity and Vg as the Group Velocity. The significance of this distinction is that the wave-form travels with velocity KA and its energy content travels with velocity Vg. Phase velocity is double group velocity for gravity waves in deep water but as the depth is decreased, phase velocity approaches group velocity, thus :
the limit 3/2 times phase velocity, thus :
If KA
{Vk
(6)
If d > A, KA = 2 Vg
If | -> O, KA
■(4) (5)
For capillary waves, group velocity is greater than phase velocity, approaching in
Table
Having made this distinction let us consider a storm centre moving across the sea. The velocity of the centre is the velocity at which the energy of the system moves, i.e. the group velocity. Individual waves will travel outwards at twice this velocity, and if sufficiently large will travel a considerable distance without the need for maintenance by wind. They may approach a shore in still air, thus indicating the approach of a storm From their rate of arrival, we can measure their period. We can thus estimate their length (by an empirical relation) and hence their velocity. The storm is then advancing at half this velocity.
Waves which have travelled ahead of their parent " group " are termed " swell " and provide a disturbed surface on which fresh waves may be generated and maintained, probably at an angle to the swell.
Swell is a long-crested wave motion. The resultant swell which may be experienced at any point is produced by several swells from different sources, interfering and beating to give an irregular motion.
Table I gives some empirical values for wind and wave measurements at sea :
I
Beaufort
No.
Wind m.p.h.
Waves m.p.h.
Period sees.
Length ft.
Height ft.
Length Height
6i
31
24.8
7.0
251
21.7
11.6
7
35
28.0
8.0
328
24.7
13.3
8
42
33.6
9.6
472
29.4
16.0
9
50
40.0
11.4
666
35.0
19.0
10
59
47.2
13.5
934
41.3
22.6
11
68
54.2
15.5
1231
47.6
25.9
= 8/10
of wind
speed
= 2/7
of wind
speed
= 5J
x (Period)2
= 7/10
of wind
speed
= If x period