2. Energy Reduction in Shallow Water . 



As an irregular wave train enters transitional and shallow-water depths, 

 the presence of the sea bottom causes changes in wave steepness which, due to 

 the limitation on wave steepness, lead to a loss of wave energy. Kitaigorodskii, 

 Krasitskii, and Zaslavskii (1975) suggest that an upper limit of energy exists 

 at a given frequency which is a function of depth and a: 



E(f) = ag2 f-5 (2u)-'+ (A-2) 



where 



C^ tanh (w^ C^) = 1 



d = water depth 



a = 0.0081 



^ = Ch{l + [2a){i Ci^/sinh(2aJh C^) ] i 



OJ^j = 2TTf /d/i 



This equation represents a stability limit or "limiting form criterion" on a 

 wave component. Kitaigorodskii, Krasitskii, and Zaslavskii used a value of 

 a of 0.0081 based on field data. Recent work at the U.S. Army Engineer 

 Waterways Experiment Station (WES) has indicated that another mechanism, non- 

 linear wave-wave interaction, has an equivalent effect but that a would vary 

 with dimensionless fetch (gF/U^) . The application of this theory is further 

 outlined by Vincent (1981) . 



Shoaling of a wave in shallow water also changes wave energy. A shoaling 

 coefficient can be calculated as in the Shore Protection Manual (App. C in 

 U.S. Army, Corps of Engineers, Coastal Engineering Research Center, 1977) for 

 each frequency component according to linear theory: 



and can be multiplied by the deepwater energy at each frequency band to obtain 

 a "shoaled" spectrum, 



E(f) shoaled = Ks(f) E(f) deep (A-4) 



3 . Determination of Shallow-VJater Energy Spectrum . 



Figure A-1 is a flow chart describing the solution process used in produc- 

 ing the design curves presented in this paper. 



16 



