Tidal friction

“ It has been shown that the effect of tidal friction is to increase the distance of the satellite from the planet, and to transfer moment of momentum from that of planetary rotation to that of orbital motion. If, then, the direction of the planet's axis of rotation does not change, it follows that the normal to the lunar orbit must approach the axis of resultant moment of momentum. ”

“ Investigation of the Secular Effects of Tidal Friction.—We have indicated in general terms in § 9 that the theory of tidal friction leads to an interesting speculation as to the origin of the moon. We shall therefore investigate the theory mathematically in the case where a planet is attended by a single satellite moving in a circular orbit, and rotates about an axis perpendicular to that orbit. In order, however, to abridge the investigation we shall only consider the case where the planetary rotation is more rapid than the satellite's orbital motion. ”

“ These instruments, although differing considerably in detail from the Indian predictor, are essentially the same in principle.
§ 9. Tidal Friction.—All solid bodies yield more or less to stress; if they are perfectly elastic they regain their shapes after the stresses are removed, if imperfectly elastic or viscous they yield to the stresses. We may thus feel certain that the earth yields to tide-generating force, either with perfect or imperfect elasticity. ”

“ We have dwelt upon the rate at which the heat increases with the descent, this rate being about one degree every sixty-six feet. Now the distribution of the heat, if it had come from the tidal action, would be quite different from the distribution which would result from the gradual efflux of heat from the centre in the process of cooling. And, speaking quite generally, we may surmise that the heat produced by tidal friction would be distributed rather more towards the exterior of the earth than at its centre. ”

“ The difference appears to lie in the genesis of the moon close to the present surface of the planet, and we shall see below that solar tidal friction may be assigned as a reason to explain how it has happened that the terrestrial planet had contracted to nearly its present dimensions before the genesis of a satellite, but that this was not the case with the exterior planets. The efficiency of solar tidal friction is very much greater in its action on the nearer planets than on the farther ones. ”

“ It was assumed for the purposes of the stability theorems that the bodies of the solar system are perfectly rigid; in other words, the motions relative to one another of the parts of any one body were ignored. Both the ordinary tides of the ocean and the bodily tides to which modern research has called attention were therefore left out of account. Tidal friction, though at present very minute in amount (§ 287) , differs essentially from the perturbations which form the main subject-matter of gravitational astronomy, inasmuch as its action is irreversible. ”

“ Tidal friction upon the planets.—The satellites of the outer planets are equally subject to influences of this kind, and there appears to be independent evidence that some of them, at least, turn always the same face toward their respective planets, indicating that the work of tidal friction has here been accomplished. ”

“ The facts with regard to the rate of increase with depth thus show that, whatever the tides may have done in producing internal heat, there has been another and a still more potent cause in operation. The important conclusion for our present purpose is that our argument may justly proceed without taking account of the effect of tidal friction. ”

“ There are tides which sway to and fro in the waters on the earth’s surface; there are tides in any molten or viscous matter that the earth may contain, and there are even certain small tidal displacements in the solid material of our globe. Tides of any kind will generate friction, and friction produces heat, and the energy of the earth’s rotation, which we have not been able to account for otherwise, has been thus transformed into heat. Throughout the whole interior of the earth heat has been produced by the tidal displacement of its parts. ”

“ However this matter may stand, it does not follow that, because the changes produced by tidal friction in a man's lifetime or in many generations of man are almost insensible, the same must be true when we deal with millions of years. ”

“ If the rapidity of the earth's rotation is diminishing, it is not certain how much of that retardation is due to tidal friction, how much to meteors, how much to possible excess of melting over accumulation of polar ice, during the period covered by observation, which amounts, at the outside, to not more than 2,600 years. ”

“ These humps are pulled at by the moon, and the earth rotates on its axis against this pull. Hence it tends to be constantly, though very slightly, dragged back.
In so far as the tidal wave is allowed to oscillate freely, it will swing with barely any maintaining force, giving back at one quarter-swing what it has received at the previous quarter; but in so far as it encounters friction, which it [Pg 387] does in all channels where there is an actual ebb and flow of the water, it has to receive more than it gives back, and the balance of energy has to be made up to it, or the tides would cease. ”

“ Tidal force would raise bulges, and these, not being carried round with the planet's rotation except to a certain distance, due to viscosity, must necessarily act as brakes upon the planet's spin. In consequence of the friction they would thus exert, energy of motion must be lost. So long, then, as tidal forces can come into play, the energy of the system is capable of decrease. ”

“ For it would make a vast effort to cause the earth to cease rotating. All this effort is, as it were, stored up in the revolving earth. as the tidal waters, then, rub along the bed of the sea, or the waters on which they rest and the adjacent coasts, this friction tends to make the earth move faster or slower, according to the direction in which the tidal flow is. ”

“ These two halves ma be described as moon and anti-moon, and such a substitution will facilitate the explanation. Let M and M' be the projections of the moon and anti-moon on to the terrestrial sphere. If the fluid in which the tides are raised were perfectly frictionless, [39] or if the earth were a perfect fluid or perfectly elastic, the apices of the tidal spheroid would: be at M and M'. If however, there is internal friction, due to any sort of viscosity, the tides will lag, and we may suppose the tidal apices to be at T and T'. ”

“ The motion of a liquid of which the particles move among each other with friction, can only be sustained by the incessant degradation of energy from the mechanical form into the lower form of diffused heat. Thus the very fact that the tides are ebbing and flowing, and that there is consequently incessant friction going on among all the particles of water in the ocean, shows us that there must be some great store of energy constantly available to supply the incessant draughts made upon it by the daily oscillation of the tides. ”

“ Tides or currents driven powerfully and constantly against a rocky shore, and bringing with them hard materials, may produce blunt, smooth surfaces, such as the repeated blows of a hammer on stone would cause; but they never bring it to a high polish, because, the grinding materials not being held steadily down, in firm, permanent contact with the rocky surfaces against which they move, as is the case with the glacier, but, on the contrary, dashed to and fro, they strike and rebound, making a succession of blows, but never a continuous, uninterrupted pressure and friction. ”

“ But as their huge bulks come nearer, the chains that bind them become stronger and stronger, and the tremendous pull of the one gargantuan fire ball on the other raises titanic tides of flame. Great streamers of gas shoot out, and all the space about is lighted by the flaming suns. The pull of gravity becomes more and more intense, and as the one circles the other, the tide is pulled up, and the mighty ball of fire, which, for all its existence has been practically motionless as far as rotation goes, begins to acquire a greater and greater rotational speed as the tidal drag urges it on. ”

“ There is indeed another way of demonstrating that a condition of the system in which the day has assumed equality with the month must necessarily be one of dynamical equilibrium. We have shown that the energy which the tides demand is derived not from the mere fact that there are high tides and low tides, but from the circumstance that these tides do rise and fall; that in falling and [125] rising they do produce currents; and it is these currents which generate the friction by which the earth's velocity is slowly abated, its energy wasted, and no doubt ultimately dissipated as heat. ”

“ The friction of the wind combines with the tide in agitating the surface of the ocean, and, according to the theory of undulations, each produces its effect independently of the other. Wind, however, not only raises waves, but causes a transfer of superficial water also. Attraction between the particles of air and water, as well as the pressure of the atmosphere, brings its lower stratum into adhesive contact with the surface of the sea. If the motion of the wind be parallel to the surface, there will still be friction, but the water will be smooth as a mirror ”

“ That this wave ‘does work,’ no one can doubt who has watched its effects. The mere rise and fall in open ocean may not be strikingly indicative of ‘work done;’ but when we see the behaviour of the tidal wave in narrow channels, when we see heavily-laden ships swept steadily up our tidal rivers, we cannot but recognise the expenditure of force. Now, where does this force come from? Motion being the great ‘force-measurer,’ what motion suffers that the tides may work? We may securely reply, that the only motion which can supply the requisite force is the earth’s motion of rotation. ”

“ The tides were then far more violent.
Halving the distance would make them eight times as high; quartering it would increase them sixty-four-fold. A most powerful geological denuding agent. Trade winds and storms were also more violent.
If ever the moon were close to the earth, it would have to revolve round it in about three hours. If the earth rotated on its axis in three hours, when fluid or pasty, it would be unstable, and begin to separate a portion of itself as a kind of bud, which might then get detached and gradually [Pg 380] pushed away by the violent tidal action. ”

“ Placing a stick into the ground, in a few moments a heap of sand would accumulate on the windward side. These sand storms fill up all the mouths of the Alt, and pile the sand up in big banks. If there was no correcting force these sand storms would quickly fill up the shallow shores and destroy their capacity to impound the tidal water which assists the scouring power of the main stream; but at high water with a westerly gale the waves churn up these deposits of sand, and the ebb tide carries them out to sea. ”

“ The levels are, however, liable to be affected by winds. A wind blowing towards the shore raises the level of both high and low water; a wind blowing off shore lowers both levels. A severe storm in the North Sea has caused a double tide at London Docks, by accelerating the North Sea tidal wave. 191
In a funnel-shaped estuary, especially if it faces the direction of the tidal wave in the sea, the tide in going up the channel increases in velocity, and the momentum of the water causes it to rise higher and higher as the width decreases. ”

“ So long as the velocity of the wind remains constant, the velocity of the current which the wind-waves generate is less than that of the wind, and there is always a differential movement of the water, each layer moving faster than the one beneath. The friction is thus distributed through the whole vertical column of the water in movement, and is even borne in part by the sea-bottom if the movement extends so far down. The greater the depth, the smaller the share of the friction each layer of water is called upon to bear, and the greater the velocity of the current generated by a given wind. ”

“ We might as well try to get a steam-engine which would produce enough heat by friction not only to supply its own boilers, but to satisfy all the thermal wants of the whole parish. We must therefore adopt the other alternative. The tides do not draw their energy from the moon; they draw it from the store possessed by the earth in virtue of its rotation. ”

“ Again, when the tidal swelling is increased in height by the convergence of the shores between which it moves, it is no longer a mere oscillation or pulsation of the great ocean, but the water acquires a true motion of translation, and rushes past headlands and through narrow channels with tremendous force and speed—a phenomenon well known along the west coasts of Scotland and Scandinavia. In some cases the advancing tide on entering a narrow inlet or estuary gathers itself into one or more large waves, and rushes up between the converging shores. ”

“ The disruption occurs from the well-known law of differential gravitation on the two sides of a body leading to tidal deformation in a liquid, and to unequal strain in a solid. When the changes of gravitative force take place slowly, and are also small in amount, the tides in liquids or strains in solids are very small, as in the case of our earth when acted on by the sun and moon, the result is a small tide in the ocean and atmosphere, and no doubt also in the molten interior, to which the comparatively thin crust may partially adjust itself. ”