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October, 1953
MOULT : WATER EFFECTS
89
known as capillary waves and possess different properties from gravity waves. Their shape is not trochoidal but more nearly sinusoidal and their velocity increases as their length decreases. They are generally of very short length and period and are to be seen in puddles in which rain-drops are falling. We have the condition, then, that as we reduce the length of gravity waves, their velocity decreases up to the point at which they turn into capillary waves owing to their small size. Thereafter the velocity increases as the wave length is decreased. These effects are shown in the graph in Fig. 6.
K X
Fig. 6. Relation of velocity to wavelength of water-waves.
There is thus a minimum value for V which we denote Vm. At this velocity the wavelength is denoted by Am. For water :
A^-0-68 ins. -1-73 cm (2)
Kw=0-78 ft./sec. =23-2 cm./sec.
= 0-45 knots (3).
In practice capillary waves are indentified with ripples. The significance of this is that gravity waves cannot be produced with a smaller velocity than 0'45 knots.
So far we have considered waves in deep water, that is water whose depth is greater than the wavelength. We will now consider the effect of shallow water.
If the depth is decreased to the extent that
the orbits of the particles tend to interfere with the bottom, then these orbits become distorted and the wave motion modified. Water (or any fluid) is deemed to move in layers in the presence of a stationary surface. Consider the flow of water in a trough, a section of which is shown in Fig. 7.
It is considered (and can be justified) that the layer of water in contact with the bed is at rest. The layer on the surface is certainly in motion. The intervening layers move with different velocities, depending on their depth. Thus, when a wave motion passes through shallow water, the orbits next to the bed must degenerate to points and the remainder must be compressed so that the movement of the water is restricted by the friction resulting from the nearness of the bed. The lower orbits become ellipses. When very shallow, the velocity of the wave
Fig. 7. Flow of water in a trough. ceases to depend on the wavelength and is governed by the depth, d, the velocity decreasing as d decreases.
Another factor to be considered is that which causes the " heave " of the sea and the setting up of surges in tanks used for wave-making. The motions of a fluid under the action of a wave can be divided into three kinds :
(i) Translation (ii) Strain (iii) Vorticity.
So far we have considered the most pronounced motion of water in waves, its orbital motion or vorticity (iii). One should also consider the elasticity of the fluid and the wave-motions arising from strain (ii). Water, however, is so very incompressible that this factor is ignored. The third kind of motion, translation (i) is a bodily surge of the water in the direction in which the waves are travelling. This is an inescapable consequence of wave-motion ; it diminishes with depth.