SCIENCE AND THE SEA 



All water particles in the long-crested deep-water waves of Fig. 4, 

 whatever their depth and regardless of their orbital diameter, com- 

 plete one orbit in the same period taken by the wave itself to advance 

 one wavelength. But the particles don't all reach the same points in 

 their orbits — the top for instance— at the same instant. Rather, like 

 the valves in an engine opening and closing at just the right instant 

 in the combustion cycle, the water particles phase in and out of the 

 appropriate positions in their respective orbits so as to fill the wave 

 form as it progresses laterally. 



Waves travel this way ■ 



Water particles travel this way /""^ 



Wave form and particle distribution at one instant 



Wave form and particle distribution V2 period later 



Fig. 4. Instead of traveling with the waves, the water 

 particles themselves move in nearly stationary orbits 

 whose diameters decrease exponentially with depth 

 beneath the surface Each particle cycles into the 

 appropriate position m its orbit so as to sustain the 

 wave form as it progresses, carrying energy across 

 the sea. 



The energy spectrum of the sea 



The ideal wave train pictured in Fig. 4 has infinitely long crests 

 that are somewhat more narrow, and equally long troughs that are a 

 bit wider than those of a sinusoidal wave; its form more nearly 

 approaches the curve called a trochoid. And as wind-generated waves 

 grow steeper their form departs even more from the sinusoidal ideal. 



No one has ever seen— and no one ever will see— a sea that be- 

 haves in the classical way just outlined, not even for a finite time 

 over a finite area of the ocean. Yet for many years attempts were 

 made to force real waves to fit this restrictive oversimplified theo- 

 retical model, at least locally. 



But actual waves on the surface of the sea are irregular, aperiodic, 

 and short crested. The realization that the classical theoretical 

 structure was untenable came gradually. Some features of real waves 

 were discovered, written up in classified reports, and so successfully 

 buried they had to be rediscovered by others several times before the 

 knowledge became available to those studying ocean waves. 



The essential feature of wind waves, and of their swell progeny 

 which usually have distinctive frequencies (see Fig. 5), is that in 

 practice they must be studied in terms of probabilistic models and 

 measured and analyzed by statistical techniques. To do this now- 

 a-days, we use an extremely useful but still not fully accurate model 

 of the waves that describes their fluctuation in height at any point 

 in terms of a statstically invariant Gaussian (i.e., normally distributed) 

 function of time. Such functions were studied originally in communi- 

 cations theory to evaluate noise variation as a function of time. 



When the function that describes the fluctuating height of waves 

 (the "noise") at a fixed point is generalized to cover many points 

 over the sea surface, we obtain a function— a model of the sea 

 surface— that closely approximates reality. This model sea surface 

 is a characteristically short-crested, Gaussian surface that moves in a 

 convincing way through time. 



SEA AND SWELL DIFFER CLEARLY.. .SOMETIMES 



Sea 



60 sec 



Intermediate 



Swell 



Fig. 5. Waves stilt in the area of 

 the winds that generated them — 

 "sea" — are typically but not always 

 higher, more sharply peaked, more 

 disorderly, and shorter-period than 

 waves — ""sweM" — that have trav- 

 eled out of their generating area. 



12 



