British Kinematography (1953)

,90 BRITISH KINEMATOGRAPHY Vol. 23, No. 4 Fig. 8. Flow of wafer through a pipe of varying cross-section. We can now attribute the breaking of waves on a beach to a combination of two effects at least : (a) Due to shallowness, translation in the surface layers is proportionately greater than in the bottom layers and induces a falling forward of any wave travelling up the beach ; (b) Due to slope, the front wall of the wave is in shallower water than the rear wall : the front portion of the wave therefore tends to travel more slowly than the rear portion, which induces a tendency to fall forwards. Origin of Waves at Sea We will next consider the origin of waves at sea. As stated in the opening paragraph, it is not sufficient to create waves : they must be maintained or they will rapidly die out by loss of energy in the friction of the orbital movements of the water particles and to a lesser extent in. the " heave." When two immiscible fluids in contact possess different relative velocities, wave motion is generated at the interface. This can be proved by the following considerations. Consider the flow of water through a pipe of the shape shown in Fig. 8. Let it be supposed that the cross-section of the pipe at the planes a — a is the same, but is larger at b, then the velocity of the water at b will be lower than at a — a. It will be found by experiment that the pressure at b will be greater than at a — a. This is in fact a property of fluids in motion, that a decrease in velocity is accompanied by an increase in pressure. Consider now the interface between the air and the sea where the air (wind) is moving Fig. 9. Generation of a disturbance in a water-surface. over the sea at a certain mean velocity. Now the wind is never of exactly the same velocity at all points on the earth's surface, owing to local currents, obstructions, etc. Hence there is an uneven distribution of pressure over the surface of the sea and the sea is thus depressed locally into small troughs and waves, so a disturbance is generated (Fig. 9). At the position a, the cross-section of the air stream has been increased and the pressure therefore increases, tending to depress further the water surface. Thus the depression is unstable and once formed it tends to be increased until the displacement is balanced by gravity. We have the same effect when a flag is flying. It is the interface between two adjacent streams of air. Given a small depression in one side, e.g. in Fig. 9 at a the pressure increases and at b it decreases (since the air-stream here must increase in velocity). The depression is unstable and the flag flaps without any control until the depression extends beyond the end of the flag and the surface becomes sensibly flattened. Then the conditions reverse and the flag flaps back the other way and so on. Having obtained a disturbed surface on the sea, consider the action of the wind on the waves as in Fig. 10. The wind blowing over the tops of waves strikes the crests and produces eddies on the far side. This is a common phenomen, that a fluid flowing past an obstruction causes eddies to form on the sheltered side. The air is thus in quicker motion in the sheltered troughs behind the as yet stationary wave than on the exposed wall where, owing to the slope, a pressure is developed with a component normal to the water surface. The