TM No. 377 



beach. The inertial subrange is the frequency domain containing the wave 

 motions most closely associated with the response of the sea surface to the 

 wind stress. Thus, the inertial subrange can be thought of as a window 

 (analogous to the green house effect) where wave energy is channeled into the 

 system. Saturation occurs when waves of frequencies f (where f g ^ f %. fj)) 

 attain the maximum height and slope. Then, because of purely physical properties 

 of the water responding under gravity, breaking occurs, providing a new flow of 

 energy into the dissipation range (fp ^ f). 



On the other hand, there is a continuous flow of energy from the inertial 

 subrange to lower frequencies. This transfer has been aptly termed a "red shift" 

 phenomenon by Starr (1961). Starr shows that wave energy tends to move down- 

 frequency because of the inter-relationship of the rate of transport of wave 

 momentum with respect to energy. Evidence of this red shift phenomenon is obvious 

 in the ocean. The previously mentioned transition from smaller (higher frequency) 

 to larger (lower frequency) wind waves and, of course, the occurrence of swells 

 generated from wind waves: both manifestly exhibit the transfer of wind energy 

 through wind waves into low frequency swell. 



It is the wave motions governed by gravity that are capable of projecting 

 energy to lower frequencies; i.e., energy in the inertial subrange. Motions in 

 the turbulent dissipation range or in the capillary wave range, which are governed 

 by viscosity and surface tensions, do not contribute energy to lower frequencies. 

 For example, capillary waves observed on the surface of the ocean (i.e., the 

 cat's paws) vanish almost immediately as the puff of wind subsides. On the other 

 hand, it is suggested (but not proven) that, when swells enter a region of fresh- 

 wind blowing in the same direction as the swells , they do not directly gain wind- 

 imparted energy within the frequency band of the swells. This would be an 

 important measurement to make, since it would further justify the existence of an 

 equilibrium range of energy. 



Munk (19^7) suggested that certain phenomena associated with the air-sea 

 interface, such as wave structure and white caps, wind stress estimates, sea 

 gull soaring, and evaporation data, seemed to point out discontinuities at a 

 critical wind speed of about 7 m sec"-'-. He also considered theoretical evidence 

 related to the Kelvin Helmholtz stability criteria (Thompson, l87l), and predicted 

 instability for winds exceeding 6.5 m sec"!. Munk alludes to the point at which 

 cresting occurs as the transition point. Beyond this point the quasi-laminar 

 stable boundary flow of air over the water is eradicated by the onset of air 

 turbulence at the sea surface, which is reflected by similar turbulent and 

 breaking conditions in the surface of the water. 



The very nature of an equilibrium range is the embodiment of a true non- 

 linear process; i.e., the interaction of motions of different frequencies to 

 effect energy transfer as depicted in figure V-38. If the wave generating process 

 were viewed as a linear system; then, as energy is added to each frequency 

 component, this component would grow independently of adjacent frequency ranges. 

 In this case, the function associated with the wave process could be represented 

 by the infinite series given by equation (lll-l). But the observed phenomena of 



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