spray. When waves move out of the area where they are directly affected 

 by the wind, they assume a more ordered state with the appearance of 

 definite crests and troughs and with a more rhythmic rise and fall. These 

 waves may travel hundreds or thousands of miles after leaving the area in 

 which they were generated. Wave energy is dissipated internally within 

 the fluid by interaction with the air above, by turbulence on breaking, 

 and at the bottom in shallow depths. 



Waves which reach coastal regions expend a large part of their energy 

 in the nearshore region. As the wave nears the shore, wave energy may be 

 dissipated as heat through turbulent fluid motion induced by breaking and 

 through bottom friction and percolation. While the heat is of little 

 concern to the coastal engineer, breaking is important since it affects 

 both beaches and manmade shore structures. Thus, shore protection measures 

 and coastal structure designs are dependent on the ability to predict wave 

 forms and fluid motion beneath waves, and on the reliability of such 

 predictions. Prediction methods generally have been based on simple waves 

 where elementary mathematical functions can be used to describe wave motion, 

 For some situations, simple mathematical formulas predict wave conditions 

 well, but for other situations predictions may be unsatisfactory for 

 engineering applications. Many theoretical concepts have evolved in the 

 past two centuries for describing complex sea waves; however, complete 

 agreement between theory and observation is not always found. 



In general, actual water-wave phenomena are complex and difficult 

 to describe mathematically because of nonlinearities, three-dimensional 

 characteristics and apparent random behavior. However, there are two 

 classical theories, one developed by Airy (1845) and the other by Stokes 

 (1880), that describe simple waves. The Airy and Stokes theories gener- 

 ally predict wave behavior better where water depth relative to wavelength 

 is not too small. For shallow water, a cnoidal wave theory often provides 

 an acceptable approximation of simple waves. For very shallow water near 

 the breaker zone, solitary wave theory satisfactorily predicts certain 

 features of the wave behavior. These theories will be described according 

 to their fundamental characteristics together with the mathematical equa- 

 tions which describe wave behavior. Many other wave theories have been 

 presented in the literature which, for some specific situations, may pre- 

 dict wave behavior more satisfactorily than the theories presented here. 

 These other theories are not included, since it is beyond the scope of 

 this Manual to cover all theories. 



The most elementary wave theory, referred to as small-amplitude or 

 linear wave theory, was developed by Airy (1845). It is of fundamental 

 importance since it not only is easy to apply, but is reliable over a 

 large segment of the whole wave regime. Mathematically, the Airy theory 

 can be considered a first approximation of a complete theoretical descrip- 

 tion of wave behavior. A more complete theoretical description of waves 

 may be obtained as the sum of an infinite number of successive approxima- 

 tions, where each additional term in the series is a correction to preced- 

 ing terms. For some situations, waves are better described by these 

 higher order theories which are usually referred to as finite amplitude 



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