a flume 44 meters long and 0,45 meter wide with a maximum water depth of 0.6 

 meter and a bottom slope of 1:30 at one end were examined. Seelig and Broderick 

 ran a variety of spectral shapes and energies. Figure 6 is a plot of H^ 

 calculated, as in equation (1), from a Fourier analysis of their wave data 

 against h^/^. Typically, the wave appear to shoal with decreasing depth, 

 thereby increasing in height until a point is reached at which the wave height 

 decreases linearly with the square root of depth. Figure 7 is an estimate of 

 H/, based on equation (15), for two forms of f c . A plot of the maximum 

 individual wave, ^ax> ^^ plotted as is the monochromatic breaking limit which 

 Hmax appears to follow. H£ is much less than the monochromatic breaking 

 limit in this case. Figure 8 provides plots of H£ versus h^'^ for wave data 

 at FRF on 25 October 1980. The value of h is estimated by an average of 

 profiles before and after the storm and includes the tide and the wave setup. 

 The curves are approximately linear with h}'^. 



VI. DISCUSSION 



An examination of the characteristics of spectral shape in shallow water 

 has led to a method of estimating the upper bound on wave energy as expressed 

 by a depth-limited wave height. It is shown that in the shallow-water limit 

 this leads to an approximate variation of H£ with the square root of depth. 

 Frequently, the monochromatic limiting value Hd is used to provide an upper 

 bound on the wave height in shallow water. This report indicates that such an 

 approach can significantly overestimate the significant wave height. The tra- 

 ditional method of estimating wave conditions in shallow water has been to 

 obtain an estimate of Hj 73 in some depth of water, then refract and shoal 

 it into the shore. At some point Hj/3 becomes larger than H^, in which 

 case Hw3 is set to H^j. This report indicates, however, that the wave 

 height H£, which is directly related to the wave energy, varies with h^/^ 

 and is normally much less than H^j. Consequently, when the energy in the sea 

 is of concern, H£ should be used rather than H^. If the maximum individual 

 wave that can occur is of concern then H^j is appropriate. 



The method in this report also indicates that the maximum significant wave 

 height, H£, in shallow water in lakes and bays can be different than that in 

 the open ocean because the cutoff frequency, f , in the smaller water bodies 

 is normally much higher than f^, for large ocean storms. Table 3 provides 

 esimtates for H£ as a function of h for an ocean, a large lake, and a small 

 lake for the same windspeed, U, of 25 meters per second but for different 

 frequencies. Longer waves in an ocean are expected to develop than in small 

 lakes; consequently, f^ is higher in the short fetch cases. The coefficient 

 a increases in short fetch cases, but it enters H£ through a square root 

 relationship. 



Estimates of depth-limited wave conditions have traditionally been based 

 on linearity of wave height and depth. This linear relationship is well estab- 

 lished for monochromatic waves by both laboratory and theoretical studies. 

 Extensions to irregular wave conditions have relied on this linear relationship 

 but with a coefficient of about 0.4. Figure 8 is a plot of this variation for 

 25 October 1980 and shows that in slope and magnitude this form is a poor 

 predictor. The method in this report is based on a theory about spectral shape 

 and appears to be a better predictor. It should be noted, however, that 

 evaluations of the newer method must account for variations in a and fc 

 as wave conditions change. Hence, simply plotting H£ versus h or h^/^ for 



18 



