Fig. 299.—Figure illustrating the decrease in the amount of wave-movement with increase of depth. (Fenneman.)
At the surface, the radius of the circular orbit which a particle of water in a wave tends to describe is half the height of the wave. At a depth equal to one wave-length, the radius of the circle described by a particle is ¹⁄₅₃₅ as great as at the surface, and at a depth equal to two wave-lengths, ¹⁄₃₀₀₀₀₀. If the height of a wave be 43 feet, the radius of the circle described by a surface particle is 21½ feet. If the length of the wave be 300 feet, the radius of a particle at a depth of 300 feet is only about ⁴⁄₁₀ of an inch, and at 600 feet ¹⁄₁₂₀₀ of an inch.[152] These figures make it clear that effective agitation of the water does not extend to great depths.
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. But while the wave-motion extends indefinitely downward, the lower limit of agitation effective in erosion is soon reached. Engineering operations have shown that submarine structures are little disturbed at depths of five meters in the Mediterranean and eight meters in the Atlantic.[153] On the other hand, débris as coarse as gravel, which is transported by rolling on the bottom, is not infrequently carried out to depths of 50 feet, and sometimes even to 150 feet. Fine sediment, like silt, is disturbed at still greater depths, for ripple-marks, which indicate agitation of the water, are said to have been found at depths of 100 fathoms.[154]
When a wave approaches a shelving shore, its habit is changed. The velocity of the undulation is diminished, while the velocity of the advancing particle of water in the crest is increased; the wave-length, measured from trough to trough, is diminished, and the wave-height is increased; the crest becomes acute, with the front steeper than the back, and these changes culminate in the breaking of the crest, when the undulation proper ceases. Waves of a given height break in about the same depth of water, and the line along which incoming waves break is the line of breakers. The line of breakers is in deeper water and farther from shore when the waves are strong than when they are weak. Waves are reported to have broken in 100 fathoms of water,[155] but this must be regarded as very exceptional. The return of the water thrown forward in the crests of waves is accomplished by a current along the bottom called the undertow. The undertow is sensibly normal to the coast when uninfluenced by oblique waves, and is efficient in removing the products of erosion.
Since the incoming wave affects water which is at the same time under the influence of the undertow, it gives to that current a pulsating character, for the wave-motion sometimes supports and sometimes opposes the undertow, and thus endows it with a higher transporting power than belongs to its mean velocity. Near the breaker-line, the oscillations communicated by the wave may momentarily overcome and even reverse the movement of the undertow. Inside the breaker-line, irregular oscillation only is communicated. The broken wave-crest, dashing forward, overcomes the undertow and throws it back, and the water returns as a simple current descending a slope. The power of the undertow diminishes rapidly from the breaker-line outward as the depth of the water increases.
Fig. 300.—Diagram showing relative directions of wave, undertow, and shore-current.
When waves advance on the shore obliquely, a shore-current is developed as illustrated by [Fig. 300], where ab represents the direction of the incoming wave, bc the direction of the littoral current, and bd the direction of the undertow. Where they strike the borders of land, the wind-waves, therefore, generate two other movements, the undertow and the littoral current. Any particle of water near shore may be affected by any two or by all three of these movements at the same moment. The effect of littoral current and undertow is to give a particle of water on which both are working a direction between the two, as be. The effect of other combinations can be readily inferred. These various combinations are of consequence in the transportation of débris.