Eh = [ Eni(f,h)df = I ag2 f^ $(a)h)/(2Tr)'* df ^3) 



The depth-limited significant wave height (spectral) is then 



H^ = 4.0 (Eh) 1/2 (14) 



In shallow water, Ho is expected to be different from H1/3, but how differ- 

 ent is uncertain. Although H1/3 has a long tradition of use in coastal engi- 

 neering, the wave height H£ defined in equation (14) appears to be a more 

 consistent parameter because it is directly related to the energy of the wave 

 field. 



Figure 4 provides curves of H£ as a function of cutoff frequency, f^., 

 and depth, h, for a = 0.0081. If a is different an estimate of H£ for 

 that a can be made by 



H^ = H^(a/0.0081)l/2 (15) 



where H| is H„ estimated with a of 0.0081. 



Clearly the cutoff frequency and the value of a are crucial for obtaining 

 estimates of H£. An examination of storm spectra indicates that the spectral 

 peak is quite sharp. Consequently, a reasonable choice for fc would be about 

 90 percent of fp. If there is evidence of more energy on the forward face of 

 the spectrtnn, fc could be estimated by using a lower percentage. The param- 

 eter a can be obtained by fitting equation (4) to observed data if available. 

 For field engineers, most often this may not be possible in which case a can 

 be estimated by knowledge of the peak frequency, fp, and windspeed, U, 

 through the relationships developed by Hasselmann, et al. (1973). The values 

 of fp and U can be obtained from hindcasts or measurements. Figure 5 

 provides values of (a/0.0081) ^'^ ^g a function of fp and U. 



When the primary frequency components containing the major part of the 

 energy are in shallow water, as determined by the condition tuh < 1 , then Em 

 is given by equation (9). This can be integrated analytically to give an 

 estimate of H for a = 0.0081 



H£ = ^ (agh)l/2 f^-1 (16) 



Equation (16) has the remarkable consequence of suggesting that H^ defined 

 as 4.0(E) V2 varies with the square root of depth when the primary spectral 

 components are depth limited. The monochromatic depth-limited wave height, 

 Hjj, varies linearly with h. 



V. FIELD AND LABORATORY EVIDENCE FOR DEPTH-LIMITED SIGNIFICANT HEIGHT, H^ 



In order to test the applicability of equations (15) and (16) in predicting 

 H£ in shallow water, laboratory data taken by Seelig and Broderick (1981) in 



15 



