3 to 4 feet, and under exceptional conditions to 5 feet and even 7 feet.1 There are also the small but constant and ever-present waves derived from the swelling of the tide on the shore, which have a material effect on the movement of beach material. When the tide is rising, the water for some distance from the coast is flowing towards the shore, and when falling is flowing from it. The tidal wave moves along the deep water of the open sea with greater velocity than in the shallow water near the coast. The crest of the wave in the open sea is therefore in advance of that near the shore, resulting in an oblique lateral movement along the shore. The water is also slightly heaped up in the centre of the channel, assuming a convex shape on the flood, and being concave on the ebb. The tidal wave, being a wave of translation, when it encounters the obstruction caused by the shoaling of the shore, is reflected back and a series of small oscillations or waves is set up, which break when they reach the low-water line. Observations of the flowing or ebbing tide, on even the flattest beach, will show that when there is an entire absence of wind or other disturbing cause, the rise and fall of the tide is not effected by a mere vertical swelling and depression, or rising and fall of the water, but is accompanied by a series of small waves varying in height according to the condition of the tide and the beach, from 6 to 24 inches, which break on the beach at the rate of ten to twenty a minute, one of the series reaching a maximum height. These wavelets are never absent from the shore, except when absorbed by the larger waves due to gales. The height of these wavelets is greater when the beach rises rapidly. Up to a certain point, these tidal wavelets are increased by a wind blowing on-shore, but if the wind-force is great, the tidal wave becomes lost in that due to the wind. As these wavelets break on the shore the particles of water assume a horizontal motion, and the wavelet becomes a vehicle for the transmission of mechanical force, and capable of transporting material. 1 "Effect of Wind and Atmospheric Pressure on the Tides," by W. H. Wheeler, M.I.C.E. Paper read at the British Association Meeting, Ipswich, 1895, and Report of Committee, 1896. Wind Waves.-Waves produced directly by the wind blowing on the surface of the sea. These waves are pure undulations. The form of the wave is transmitted towards the shore, but there is no forward progressive movement of the water until the margin of the shore is reached. There are two motions operating in the formation of wind waves -one horizontal, due to the wind which generates the undulation; and the other vertical, due to the force of gravity. These two motions take place within a defined orbit, the limit of which is regulated by the force of the wind which produces the undulation and the depth of the water in which it takes place. The particles of water in the crest or upper half of the undulation, or that above the level of the water when in repose, move upwards and forward in the same direction as the travel of the wave, those contained in the lower portion, or the trough, moving downwards and backwards. The maximum horizontal motion takes place at the top of the crest and bottom of the trough, and is at zero at the centre of the undulation, where the motion is only vertical. The common form of wind waves in the open sea is cycloidal, but the shorter shore waves assume more the form of an ellipse. Although a wave completes its undulation within a given orbit, the height of which is measured from the crest to the trough, the particles of water below the trough must to a certain degree be disturbed, the amount of this disturbance rapidly vanishing as the depth below the trough of the wave increases. Waves moving towards the coast along a shoaling shore show that they feel the effect of the shoaling by altering their shape. The form becomes gradually more abrupt, the crest more raised, the length decreased, the orbit more elliptical, and the whole mass begins to change from a wave of simple oscillation to one of translation. Finally, when the depth is not sufficient for the complete formation of the undulation, the bottom of the wave is retarded by encountering the friction of sea-bed, the top is thrown forward and the vertical oscillation is changed into a horizontal movement, the water contained in the wave being thrown forward on to the beach. A purely oscillating wave cannot cast any material lying seaward of its plunge or breaking-point on to the shore. If two floating substances be thrown into the water, one immediately beyond the wave breaking on the shore, and the other within its range, the former will flow away with the tidal current, while the latter will be thrown on to the beach. Although the wave immediately in the rear of the one that breaks retains its undulating character, any floating substance within its range simply rising and falling and getting no nearer to the shore, while a substance contained in the shoreward wave is thrown forward beyond the water-line, yet the particles of water below the rear wave have a certain amount of translatory movement due to the effect which the shoaling of the bed has on the water below the wave's orbit. This horizontal motion of the particles below the wave in shallow water is proved to be sensible by the broken water that occurs on the surface over a reef of rocks or on the edge of a shoal lying below the orbit of the wave. When a wave meets a barrier projecting from the bed of the sea the water is thrown upward, and the wave which comes in contact with this obstruction attains an increased height. The translatory movement of the particles of water below the wave accounts for substances being thrown, during heavy gales, on to the beach from greater depths than the height of the wave breaking on shore would appear to warrant. This translatory movement, however, only extends for a short distance from the shore-line. Beyond this the waves, being mere undulations, are incapable of conveying material towards the land. In order to find out the depth at which waves act on the seabed, an experiment was made in Lake Ontario, where in storms the waves are of considerable dimensions, by anchoring four empty boxes on the sloping sand-bed of the lake at equal distances over a length of 650 yards, in depths of 6 feet, 12 feet, 18 feet, and 20 feet. After storms it was found that the first box in the shallow water became filled with sand; the box in 12 feet of water half full; in the one at 18 feet there was very little sand; and at 20 feet there was no sand in the box. In storms or heavy ground swells waves will break in depths that are great in comparison with their height, where the bottom is abrupt or uneven, or where there is sudden shoaling. Ground-swell waves which are of great length, although of small height, break in depths where ordinary waves would remain undulations. This translatory movement of the water below the wave itself was termed by Colonel Emy in his treatise on waves1 Flot de Fond, and he considered that the destructive effect of the sea on maritime works was due in a great measure to this action. Although to a certain extent this is the case, it is generally considered that Colonel Emy attached greater importance to this movement than actually prevails. The theory as set out in his treatise is, that as waves approach the shore and begin to feel the effect of the shoaling, the undulatory movement of the lower molecules of the water is changed into a horizontal one, independent of the undulatory movement of the upper part of the wave; and that where the bed of the sea rises abruptly this horizontal or translatory movement accumulates with each successive wave, the wave itself being thus raised above the level which it would otherwise attain. By this means the depth and volume of the water that finally breaks on the shore is increased, and consequently the force and destructive effect with which the wave strikes a cliff or sea-wall against which it is projected. The wave-stroke is much heavier on a steep shore than when the beach consists of a long flat slope. In the latter case the waves are much broken up, the whole space between the shore and deep water becoming a mass of broken water. Tennyson gives a true description of these waves on the flat sands of the Lincolnshire coast : "As the crest of some slow arching wave, Heard in dead night along that table shore, Ground Swell or Rollers.-These are the product of wind waves generated at some distant part of the ocean. When wave-motion is once set up in the ocean, it continues for a considerable interval of time, and extends over a wider space than that covered by the original cause of disturbance, the effect being transmitted beyond the sphere of the gale. Thus frequently there is a heavy ground-swell on the coast without any corresponding gale. Or the wave-motion may travel at a greater rate than that of the movement of the gale which causes Du Mouvement des Ondes et des Travaux Hydraulique Maritime." Paris, 1831. the disturbance, in which case a ground-swell precedes and becomes the harbinger of the coming gale. As waves due to distant gales travel across the ocean shorewards, they coalesce and form long low undulations. The effect of a ground-swell extends to a greater depth than that of ordinary wind waves; and it exerts a greater power of transmission near the bottom than shorter waves in the same depth. As the long waves due to a ground-swell approach shallow water, where the depth is constantly diminishing and the space for their volume is contracted, the momentum contained in the moving water sensibly raises the height of the wave and increases its velocity. These waves are therefore always more powerful and exert a greater percussive effect on a sea-wall or cliff, and the back wash is more destructive to a beach than ordinary wind waves. Breaking Waves.-Waves are said to break when, owing to the water becoming shallow, they are no longer able to complete their undulation; and the water of the wave is thrown forward on the beach with a violence proportionate to the momentum it has acquired. The depth of water in which a wave ceases to be an undulation and breaks varies with circumstances. The least depth in which a wave can complete its undulation is when it reaches water the depth of which in repose is only equal to half the height of the wave from trough to crest. The general result of observation of coast waves shows that as a rule, and under ordinary conditions, a wave breaks when it enters water the depth of which is equal to, or little exceeds, its height from trough to crest. Waves are, however, known to break during very heavy gales, and when the fetch is very extended, in depths considerably greater than their height. As illustrating the effect of the shoaling of the water in changing oscillating to breaking waves, the instance given by Mr. Shield in his book on Harbours1 may be quoted. At Peterhead there is a quay wall resting on a rock base about 2 feet above low water. At a short distance from the wall the rock bed dips, the depth of the water increasing to about 30 feet; there is then a ledge of rocks 160 feet from the wall, on which the "Harbour Constructions," W. Shield. London, 1895. 1 |