Waves and ripples in water, air, and æther

by Sir J. A. Fleming

IT is impossible for the most careless spectator to look at a steam-vessel making her way along a lake, a boy’s boat skimming across a pond, or even a duck paddling on a stream, without noticing that the moving body is accompanied in all cases by a trail of waves or ripples, which diverge from it and extend behind. In the case of a steamer there is an additional irregular wave-motion of the water caused by the paddle-wheels or screw, which churn it up, and leave a line of rough water in the steamer’s wake. This, however, is not included in the true ship-wave effect now to be discussed. We can best observe the proper ship-wave disturbance of the water in the case of a yacht running freely before the wind when the sea is fairly smooth. The study of these ship-waves has led to most important and practical improvements in the art of ship-designing and shipbuilding, and no treatment of the subject of waves and ripples on water would be complete in which all mention of ship-waves was omitted.

In order that we may explain the manner in which these waves are formed, and their effect upon the motion of the ship, and the power required to move it forward, we must begin by a little discussion of some fundamental facts concerning liquids in motion.

Every one is aware that certain liquids are, as we say sticky, or, to use the scientific term, viscous. A request to mention sticky liquids would call up the names of such fluids as tar, treacle, gum-water, glycerine, and honey. Very few people would think of including pure water, far less spirits of wine, in a list of sticky, or viscous liquids; and yet it is quite easy to show by experiment that even these fluids possess some degree of stickiness, or viscosity. An illustration may be afforded as follows: We provide several very large glass tubes, nearly filled respectively with quicksilver, water, alcohol, glycerine, and oil. A small space is left in each tube containing a little air, and the tubes are closed by corks. If we suddenly turn all the tubes upside down, these bubbles of air begin to climb up from the bottom of the tube to the top. We notice that in the quicksilver tube it arrives at the top in a second or two, in the water tube it takes a little longer, in the oil tube longer still, and in the tube filled with glycerine it is quite a minute or more before the bubble of air has completed its journey up the tube. This experiment, properly interpreted, shows us that water possesses in some degree the quality of viscosity. It can, however, be more forcibly proved by another experiment.

To a whirling-table is fixed a glass vessel half full of water. On this water a round disc of wood, to which is attached a long wire carrying a paper flag, is made to float. If we set the basin of water slowly in rotation, at first the paper flag does not move. The basin rotates without setting the contained water in rotation, and so to speak slips round it. Presently, however, the flag begins to turn slowly, and this shows us that the water has been gradually set in rotation. This happens because the water sticks slightly to the inner surface of the basin, and the layers of water likewise stick to one another. Hence, as the glass vessel slides round the water it gradually forces the outer layer of water to move with it, and this again the inner layers of water one by one, until at last the floating block of wood partakes of the motion, and the basin and its contents turn round as one mass. This effect could not take place unless the water possessed some degree of viscosity, and also unless so-called skin friction existed between the inside of a glass vessel and the water it contains.

We may say, however, at once that no real liquid with which we are acquainted is entirely destitute of stickiness, or viscosity. We can nevertheless imagine a liquid absolutely free from any trace of this property, and this hypothetical substance is called a perfect fluid.

It is clear that this ideal perfect liquid must necessarily differ in several important respects from any real fluid, such as water, and some of these differences we proceed to examine. We must point out that in any liquid there may be two kinds of motion, one called irrotational motion, and the other called rotational or vortex motion.

Consider any mass of water, such as a river, in motion in any way; we may in imagination fix our attention upon some small portion of it, which at any instant we will consider to be of a spherical shape. If, as this sphere of liquid moves along embedded in the rest of the liquid, it is turning round an axis in any direction as well as being distorted in shape, the motion of that part of the fluid is called rotational. If, however, our little sphere of liquid is merely being stretched or pulled into an ovoid or ellipsoidal shape without any rotation or spinning motion, then the motion of the liquid is said to be irrotational. We might compare these small portions of the liquid to a crowd of people moving along a street. If each person moves in such a way as always to keep his face in the same direction, that movement would be an irrotational movement. If, however, they were to move like couples dancing in a ball-room, not only moving along but turning round, their motion would be called rotational. Examples of rotational, or vortex motion are seen whenever we empty a wash-basin by pulling up the plug. We see the water swirl round, or rotate, forming what is called an eddy, or whirlpool. Also eddies are seen near the margin of a swiftly flowing river, since the water is set in rotation by friction against objects on the banks. Eddies are likewise created when two streams of water flow over each other with different speeds. A beautiful instance of this may be viewed at an interesting place a mile or two out of the city of Geneva. The Rhone, a rapid river, emerges as a clear blue stream from the Lake of Geneva. At a point called Junction d’eaux it meets the river Arve, a more sluggish and turbid glacier stream, and the two then run together in the same channel. The waters of the Rhone and Arve do not at once mix, but the line of separation is marked by a series of whirlpools or eddies set up by the flow of the rapid Rhone water against the slower Arve water in contact with it.

Again, it is impossible to move a solid body through a liquid without setting up eddy-motion. The movement of an oar through the water, or even of a teaspoon through tea, is seen to be accompanied by little whirls which detach themselves from the oar or spoon, and are really the ends of vortices set up in the liquid. The two facts to notice particularly are that the production of eddies in liquids always involves the expenditure of energy, or, in mechanical language, it necessitates doing work. To set in rotation a mass of any liquid requires the delivery to it of energy, just as is the case when a heavy wheel is made to rotate or a heavy train set in movement. This energy must be supplied by or absorbed from the moving solid or liquid which creates the eddies.

In the next place, we must note that eddies or vortices set up in an imperfect fluid, such as water, are ultimately destroyed by fluid friction. Their energy is frittered down into heat, and a mass of water in which eddies have been created by moving through it a paddle, is warmer after the eddies have subsided than before. It is obvious, from what has been said, that if a really perfect fluid did exist, it would be impossible by mechanical means to make eddies in it; but if they were created, they would continue for ever, and have something of the permanence of material substances.