OCEAN 



WAVES 



^^^--^: 



By WiUard J, Pierson, Jr. 



Their rarietif und ntnifihxitii h bewildering 



and rej'itnj to det^iijne/s of ship^i, radar, and nonar— 



hut their enenjij apectra are being uvrareled 



by trickij iinnlifscs of neir records from the sea 



Prehistoric man in his childHke simplicity probably threw stones 

 into placid pools of water and watched with keen and uncomplicated 

 pleasure as ridges and depressions on the surface radiated from the 

 satisfying splash in ever-widening circles. More than a century ago 

 hydrodynamicists, perhaps with a more sophisticated sense of pleasure, 

 developed the mathematics for analyzing ideal periodic and 

 aperiodic waves in a fluid bounded by a free surface. Today those 

 who study real waves on water— for pleasure or for profit— must 

 combine the mathematical methods of time-series analysis with those 

 for analyzing nonlinear oscillations, and both of these with elaborate 

 statistical methods, to describe and predict the wave-torn configura- 

 tion of the sea surface. 



These mathematical procedures are formidable, But they have 

 not deterred studies of ocean waves. On the contrary, the number of 

 investigators has been growing rapidly. And it increasingly includes 

 not only oceanographers, but designers and operators of ships, hydro- 

 foil craft, submarines, harbor and other coastal installations, offshore 

 drilling platforms, and similar structures— and still others whose 

 prime concerns are radar return from the sea surface, or the ambient 

 noise background against which underwater sonar systems must 

 operate. A few of the practical reasons for studying ocean waves 

 are suggested in Fig. 1. 



Investigators of ocean waves are not all motivated by either 

 practical reasons or mathematics. To some the challenge lies in the 

 art of making difficult measurements. And precision instruments, 

 now being used instead of scattered visual observations to record 

 waves at sea, also have played an increasingly prominent role in recent 

 progress. 



What accounts for the need for such an impressive arsenal of 

 observational and analytical tools? Two things— the internal complex- 

 ity and diversity of waves, and the many ways they can combine to 

 create that confused, chaotic, worldwide geometric entity called the 

 surface of the sea. 



The surfncp of the sea is a mess 



At any instant, this surface covering three-quarters of the earth 

 exhibits an amazingly complex and thoroughly random shape. Its 

 geometric irregularities span horizontal distances ranging from 

 centimeters or less to thousands of kilometers, a range of 9 orders of 

 magnitude. Irregularities in the vertical direction are much less, 

 however: they span several tens of meters at most. 



The complex pattern created by intersecting waves is not static. 

 It changes endlessly through time, and it never repeats itself exactly 

 in totality. But individual elements of the total pattern — individual 

 kinds and groups of waves— do repeat themselves; they are periodic, 

 over a tremendous range in time. The periods of the smallest 

 "capillary" ripples, for instance, so important in radar work at sea, 

 are less than a second, while a single cyclic oscillation in worldwide 

 sea level sometimes takes geologic ages to complete. Few periods of 

 ordinary wave motions on water, however, exceed several hours and 

 most are much less. 



Small wonder, in the face of this chaos extending over such long 

 spans of space and time, that many scientists and engineers came to 

 feel prior to the last war that real ocean waves— unlike the ideal waves 

 of classical hydrodynamic theory— lay beyond the bounds of possible 

 understanding. Yet in the last 15 years, under the stimulus initially 

 provided by the need for knowledge of sea and surf conditions during 

 World War II. we have partly broken through the "chaos" barrier to 

 a reasonably clear understanding of the behavior of several kinds of 

 waves. We even can— and routinely do— forecast the heights, periods, 

 distribution, and travel paths of the dominant kind of ocean waves, 

 those generated by turbulent fluctuations in the wind. Such forecasts 

 are even accurate, sometimesi 



Does this mean we truly understand ocean waves? Of course not, 

 no more than the weather forecaster truly understands the dynamics 

 of the atmosphere. To understand waves fully we must know how 

 they begin, how they travel, how they interact with other waves, 

 with the air above, and with the water and bottom below. And we 

 must know how they die. We know none of these to our satisfaction, 

 but we do know enough to draw clear distinctions among various kinds 

 of waves. 



