Waves and ripples in water, air, and æther

by Sir J. A. Fleming

When an estuary contracts considerably as it proceeds, as is the case with the Bristol Channel, then the range of the tide or the height of the tidal wave becomes greatly increased as it travels up the gradually narrowing channel, because the wave is squeezed into a smaller space. For example, the range of spring tides at the entrance of the Bristol Channel is about 18 feet, but at Chepstow it is about 50 feet.[9] At oceanic ports in open sea the range of the tide is generally only 2 or 3 feet.

If we look at the map of England, we shall see how rapidly the Bristol Channel contracts, and hence, as the tidal wave advances from the Atlantic Ocean, it gets jambed up in this rapidly contracting channel, and as the depth of the channel in which it moves rapidly shallows, the rear portion of this tidal wave, being in deeper water, travels faster than the front part and overtakes it, producing thus a flat or straight-fronted wave which goes forward with tremendous speed.[10]

We must, in the next place, turn our attention to the study of water ripples. The term “ripple” is generally used to signify a very small and short wave, and in ordinary language it is not distinguished from what might be called a wavelet, or little wave. There is, however, a scientific distinction between a wave and a ripple, of a very fundamental character.

It has already been stated that a wave can only exist, or be created, in or on a medium which resists in an elastic manner some displacement. The ordinary water-surface wave is termed a gravitation wave, and it exists because the water-surface resists being made unlevel. There is, however, another thing which a water-surface resists. It offers an opposition to small stretching, in virtue of what is called its surface tension. In a popular manner the matter may thus be stated: The surface of every liquid is covered with a sort of skin which, like a sheet of indiarubber, resists stretching, and in fact contracts under existing conditions so as to become as small as possible. We can see an illustration of this in the case of a soap-bubble. If a bubble is blown on a rather wide glass tube, on removing the mouth the bubble rapidly shrinks up, and the contained air is squeezed out of the tube with sufficient force to blow out a candle held near the end of the tube.

Again, if a dry steel sewing-needle is laid gently in a horizontal position on clean water, it will float, although the metal itself is heavier than water. It floats because the weight of the needle is not sufficient to break through the surface film. It is for this reason that very small and light insects can run freely over the surface of water in a pond.

This surface tension is, however, destroyed or diminished by placing various substances on the water. Thus if a small disc of writing-paper the size of a wafer is placed on the surface of clean water in a saucer, it will rest in the middle. The surface film of the water on which it rests is, however, strained or pulled equally in different directions. If a wire is dipped in strong spirits of wine or whisky, and one side of the wafer touched with the drop of spirit, the paper shoots away with great speed in the opposite direction. The surface tension on one side has been diminished by the spirit, and the equality of tension destroyed.

These experiments and many others show us that we must regard the surface of a liquid as covered with an invisible film, which is in a state of stretch, or which resists stretching. If we imagine a jam-pot closed with a cover of thin sheet indiarubber pulled tightly over it, it is clear that any attempt to make puckers, pleats, or wrinkles in it would involve stretching the indiarubber. It is exactly the same with water. If very small wrinkles or pleats, as waves, are made on its surface, the resistance which is brought into play is that due to the surface tension, and not merely the resistance of the surface to being made unlevel. Wavelets so made, or due to the above cause, are called ripples.

It can be shown by mathematical reasoning[11] that on the free surface of a liquid, like water, what are called capillary ripples can be made by agitations or movements of a certain kind, and the characteristic of these surface-tension waves or capillary ripples, as compared with gravitation waves, is that the velocity of propagation of the capillary ripple is less the greater the wave-length, whereas the velocity of gravitation on ordinary surface waves is greater the greater the wave-length.

It follows from this that for any liquid, such as water, there is a certain length of wave which travels most slowly. This slowest wave is the dividing line between what are properly called ripples, and those that are properly called waves. In the case of water this slowest wave has a wave-length of about two-thirds of an inch (0·68 inch), and a speed of travel approximately of 9 inches (0·78 foot) per second.

More strictly speaking, the matter should be explained as follows: Sir George Stokes showed, as far back as 1848, that the surface tension of a liquid should be taken into account in finding the pressure at the free surface of a liquid. It was not, however, until 1871 that Lord Kelvin discussed the bearing of this fact on the formation of waves, and gave a mathematical expression for the velocity of a wave of oscillatory type on a liquid surface, in which the wave-length, surface tension, density, and the acceleration of gravity were taken into account. The result was to show that when waves are very short, viz. a small fraction of an inch, they are principally due to surface tension, and when long are entirely due to gravity.