CAUSES OF SURF 109 



special situations where the slope of the bottom steepens very 

 abruptly from deeper water, as in the case of cliffs and of breakwaters. 

 Masses of water may then spout high into the air, or up on the shore, 

 as happens frequently against isolated rocky islands or ledges, along 

 the steeper parts of the offshore faces of coral reefs, against light- 

 houses, against breakwaters, over submerged ledges, and also against 

 the nearly vertical walls of the antarctic ice barrier, where the depth 

 of the water may be measured in hundreds of fathoms. In fact, it is 

 not unusual for sheets of water — not just foam — to spout more than a 

 hundred feet into the air under such circumstances (for examples, 

 see page 120). 



Alteration in steepness. — A wave advancing into shoal water not 

 only becomes steeper as a consequence of its decrease in length, com- 

 bined in most cases with an increase in height, but it does so very 

 abruptly just before it finally breaks. Anyone who has occasion to 

 come in through the surf in a small boat has this fact impressed upon 

 him, for his boat, which may merely rise and fall bodily with the 

 longer swell offshore, is pitched up more and more steeply as it rides 

 in on the back of a chosen roller, until her bow may be lifted far above 

 her stern just before the breaker develops. This point is discussed in 

 further detail on page 110. 



Alteration in the orbital velocities of the water particles. — The 

 orbits around which the water particles move are circles in deep water, 

 but become elliptical, with their larger axis horizontal, when a wave 

 runs into water shoaler than one-half its own initial length (p. 00, 

 fig. 3), and the ellipses become more and more flattened as the water 

 shoals, until the water particles in contact with the bottom simply 

 move to and fro in straight lines. The velocity at which the water 

 particles move around their orbits — uniform while these are circular — 

 is no longer so after they are transformed into ellipses, but is greatest 

 near the crest and the trough. This discrepancy between the velocities 

 along different parts of the elliptical orbits increases as the eccentricity 

 of the orbits increases with the advance of the wave into shoaler and 

 shoaler water, for it is proportional to the length of the major (hori- 

 zontal) axis of the ellipse. 35 And since the transformation of the 

 orbits from circles to ellipses consists in an expansion of their hori- 

 zontal axes, with their vertical axes changing only as much as the 

 height of the wave, the velocity with which the water particles ad- 

 vance in the crests and recede in the troughs grows greater and greater 

 as the wave advances into shoaler and shoaler water. The orbital ve- 

 locities, for example, in the crests and troughs of a wave 15 times as 



35 According to the equation V"= — ~r- where V" is the orbital velocity along the part 

 of the ellipse where it is at its maximum, a' the half-length of the major axis of the 

 ellipse, and T the period of the wave. 



