Table 3. Variation of Ho with depth for ocean, large 

 lake, and small lake generation cases. 



Depth 



Monochromatic 



Ocean 



Large lake. 



Small lake. 





wave, H^ ^ 



H£^ 



H£ ' 



H£ ' 



(m) 



(m) 



(m) 



(m) 



(m) 



1 



0.78 



1.55 



l.l5 



0.95 



3 



2.2 



2.65 



1.9 



1.6 



5 



3.9 



3.4 



2.5 



1.9 



8 



6.2 



4.2 



3.0 



2.3 



10 



7.8 



4.7 



3.3 



2.6 



^Estimated by lower limit of 0.78 h. 



2f_ = 0.08, fp = 0.07, (a/0. 0081)1/2 = 1.20. 



3fp = 0.12, f^, = 0.11, (a/0. 0081)1/2 = ^ 37^ 

 '*f„ = 0.16, f- = 0.14, (a/0. 0081)1/2 = 1.44. 



^Larger than H^j. 



one gage will show considerable scatter because of the time variation of a 

 and f^. The evaluations of the method in this report have removed this 

 constraint by using a series of gages across the nearshore zone. 



The use of the method at the beginning of this report was restricted to 

 spectra of some breadth such as storm seas. It is clear that nearly mono- 

 chromatic waves follow the linear depth relationship, yet it is increasingly 

 clear that irregular waves do not. A question of major importance not yet 

 resolved is how wide must a spectrum be before the waves follow the relation- 

 ships in this report. Equally important is the isolation of the physics of 

 wave motion that determine these differences. In a shoaling monochromatic 

 wave, nonlinearities arise which force the development of harmonics in the wave 

 frequency and tend to broaden the spectrum, yet the absence of other wave 

 components may reduce the transfer energies by resonant interactions. If the 

 bottom slope is sufficiently steep, the evolution of the swell waves may be 

 markedly different from irregular waves which may more easily exchange energy 

 due to resonant interactions. 



VII, SUMMARY 



A method for estimating depth-limited significant wave height, H£, 

 based on a theoretical form for the shape of shallow-water storm wave spectra 

 was presented. The method requires an estimate of the peak frequency of the 

 wave spectrum, fp; knowledge of the Phillips' equilibrium coefficient, a; 

 and water depth, h. A method for estimating a based on information about 

 the peak frequency of the sea spectrum is also given. The results indicate 

 that the depth-limited significant wave height, H£, based on the energy of 

 the sea state is generally less than the depth-limited monochromatic wave 

 height, H(j. The depth-limited wave height defined as 4.0(E) 1/^ appears 

 to be related to the square root of depth. 



22 



