I 



OCEAN WAVES 



9 orders of magnitude. 



Seiches and storm surges — generated either by hurricanes, tropical 

 cyclones, or, in the right circumstances, by frontal squall lines— are 

 also of more than passing practical interest. The heights of these 

 sporadically occurring wind-driven waves can easily reach 10 ft or 

 more in harbors; they differ from each other primarily in that the 

 seiche is a storm surge which, because it occurs in a landlocked lake 

 or partially inclosed harbor, enters into a standing-wave oscillation 

 that persists after the generating wind dies down. The effects of 

 both on coastal and harbor installations on occasion compare with 

 those of the less frequent but more spectacular tsunamis, which are 

 generated by some of the seismic disturbances that occur in ocean 

 areas. 



Tsunamis are the moat awesome waves on the surface of the sea. 

 The modest 1-2 ft heights that characterize them in the open sea 

 rapidly piles up to nearly vertical walls of onrushing water— as much 

 as 100 ft high — along coast lines and beaches of appropriate config- 

 uration near their area of generation, in the Kamchatka Peninsula, 

 the Aleutian Islands, the Kuriles and the South Pacific. 



In the family of ocean waves the smallest are the capillary waves. 

 They have sharp troughs that point downward into the water, in 

 contrast to ordinary wind-driven waves which have sharp crests that 

 point up into the air. This difference in form is a consequence of the 

 capillary's very short wavelengths; below wavelengths of about 

 2.44 cm, waves on water show puzzling nonlinear properties, which 

 are somehow related to the large local curvature of the water surface. 

 Under these conditions the effect of water's surface tension in 

 controlling the wave's form and height becomes more important than 

 the factors of gravity and water depth that are the controlling 

 parameters for other waves raised on the sea by winds. 



It's these other wind waves whose wavelengths range up to 

 thousands of feet, however, that make ships heave, pitch, roll, surge, 

 sway and yaw that limit ship speed; and that routinely travel as 

 "swell" thousands of miles out of the storm areas in which they are 

 bom, across the oceans, to break with mostly gentle but unending and 

 deadly erosional efficiency on the shores. Let's concentrate on them. 



Birth and developinent of wind waves 



If wind waves were perfectly periodic, simple harmonic progres- 

 sive waves with infinitely long crests — as shown in the lower part of 

 Fig. 3— or if this standard assumption of classical wave theory were 

 even approximately true, they would have been understood for more 

 than a century. But wind effects on the sea surface are not this simple, 

 (lecause turbulance and viscosity in both sea and air introduce com- 

 plex nonlinear effects. 



Wind turbulance creates a moving pattern of minute fluctuations 

 in air pressure over the water; these can generate the initial tiny 

 ripples that eventually become fully developed waves. Viscosity and 

 turbulence also create a distribution of pressure differences in the 

 air that is out of phase with the waves, and these pressure differences 

 feed in the energy needed to grow bigger waves. 



Fjg. 3. The infinitely complex, reat sea surface is 

 closely approximated in wave studies by a model 

 surface vvtiich, as shown, is made up of a large 

 number of randomly superimposed, simple harmonic, 

 progressive sine waves — each having its own amp. 

 lltude. direction of travel, and frequency. 



Measuring the amount of energy fed into waves by the wind is 

 a severe and unsolved instrumentation problem. However, we can 

 attain one important practical end— forecasting sea states— by 

 treating the character of the sea surface statistically, after the energy 

 being fed into the waves equals the energy dissipated by breaking at 

 the wave crests, so the waves are no longer growing. This point of 

 dynamic equilibrium— where the sea is said to be "fully developed"— 

 limits the height wind waves can achieve, even under forcing 

 conditions of strong winds in severe storm areas. Classical hydro- 

 dynamic theory, although it cannot really explain this limiting process, 

 nevertheless is useful in appreciating what seems to be going on 

 physically. 

 Witid waves limited by blowing their tops 



The ideally organized motion of water particles beneath a regular 

 train of waves, moving in water deep enough so bottom effects don't 

 enter the picture, is shown in Fig. 4. Perhaps surprisingly, the water 

 particles do not move en masse with the waves above them which 

 carry the vrind-supplied energy from one parcel of the ocean to 

 another. It's fortunate that they don't. If you recall standing inshore 

 of the breakers along a beach, where, after breaking, the water 

 particles do move en masse, you'll realize instantly that no ship could 

 sail if a 10- ft wave on the open sea, for example, represented a wall 

 of water that high moving along with the waves. 



Instead of traveling with the waves, the particles move in nearly 

 stationary circular orbits which lie in the vertical plane. Orbits of 

 particles at the surface have a diameter equal to the height of the 

 wave from crest to trough. Below the surface, orbits grow smaller 

 with increasing depth, by a factor of about 1/2 for a depth equal to 

 l/9th the wavelength, 1/4 for a depth equal to 2/9ths the wavelength, 

 and so on. Water particle motion effectively is nil for all practical 

 purposes, such as submarine operation, at a depth of about 1/2 wave- 

 length. 



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