For practical purposes, a sea-state scale based on visual 

 estimates relating wave height, wind speed, and sea surface appear- 

 ance has been quite useful. One, based on the Naval Oceanographic 

 Office code, is given in figure 6-5. 



An important application of the sea-state code to underwater 

 sound is the Knudsen curves for average ambient noise in water shown 

 in figure 6-6. The curves fall off at the rate of about 5 dB/octave. 



Another application of the sea-state code in terms of crest-to- 

 trough wave height occurs in the propagation of sound involving ray 

 paths that bounce off the sea surface. Propagation loss per bounce 

 (ttg) is given as a function of the product of mean wave height, h(f t) , 

 and acoustic frequency, f(kHz). 



0-3 = 1.64 (fh) 1/2 dB/bounce 



This relation is plotted in figure 6-7. 



b. Energy Spectrum of the Wind Waves 



Actual waves on the sea surface are irregular, aperiodic, and 

 short crested. The wave spectrum concept may be used to describe 

 distribution of energy among waves of different frequency or wave 

 number. Wave spectrum must be studied in terms of probabilistic models 

 and measured and analyzed by statistical techniques. A wave model is 

 used to describe fluctuation in wave height at any point in terms of a 

 statistically invariant gaussian function of time. 



As the wind blows and as waves grow, turbulent variations and 

 varying amounts of internal eddy viscosity — as well as the interaction 

 of one wave with another — set an individual limit to the growth of 

 each individual component wave train in the developing sea. They do 

 this by initiating the energy-dissipating, breaking, or "white-cap" 

 process, whenever a momentarily high crest reaches an unstable configu- 

 ration. In classical theory, this occurs when the height-to-length 

 ratio of waves in a train reaches the critical value of 1/7 at which 

 point in a wave's development its crest is sharply peaked. Thus, the 

 total energy present in all waves on a developing sea progressively 

 distributes itself over a range of frequencies, each frequency charac- 

 terizing a particular wave train. As waves continue to grow and as new 

 trains continually develop, this range extends more and more to lower 

 frequency — or longer period — waves. In brief, a spectrum of ocean 

 waves is formed (fig. 6-8), in which — for any given wind velocity 

 and for fully developed waves — energy distribution over a narrow band 

 of wave frequencies from 0.05 to 0.3 Hz is distinctive. 



The accepted expression for the energy spectrum of wind-driven 

 gravity waves is that of Pierson and Moskowitz (PM) . It is a directional 

 spectrum and is given by: 



20 



