Another important parameter defined by Ahrens is the spectral (or 

 modified) stability number A^ defined as: 



N . m "mo S (3 1) 



where H mo is the zero-moment wave height of the incident wave spectrum and 

 L is the Airy wavelength calculated using the peak wave period T and the 

 local water depth h at the toe of the structure. 



The reduced crest height of a reef breakwater is estimated by: 



h c = ft, I a exp(AO < 32 ) 



where "a" is a coefficient and A t is the structure's cross-sectional area. 



Ahrens (1989) gives several equations for the coefficient "a". Van der 

 Meer (1988) tested several structures with crest heights, water depths, bulk 

 numbers, and slope angles different than Ahrens. Van der Meer (1990) re- 

 analyzed the data of Ahrens (1987) and Van der Meer (1988), and derived a 

 new equation for the coefficient "a." The resulting equation is similar to 

 Ahrens, but valid for a wider range of conditions. The resulting equation for 

 the coefficient "a" is given by: 



"a"= -0.028 + 0.045C + 0.034 h c '/h - 6x1 a 9 B n 2 (33) 



and h c = h c ' if h c in Equation 32 > h c ' . 



where 



C" = average structure slope "as built" (normal range: 1.5 < C'< 3.0) 



B n = bulk number, A, I D^ 2 (34) 



A, = Bh c ' + C'h c ' 2 (35) 



B = crest width (normally taken as 3 median stones wide, 3 D^q) 



Crest height reduction of a reef breakwater as shown in Figure 50 can be 

 calculated using Equations 32 and 33. Design curves can also be produced 

 from these equations which give the crest height as a function of H s (Fig- 

 ure 51) or even a£ (Figure 52) for a given water level, structure slope, initial 

 crest height, and bulk number. Bulk number can be described as the 

 equivalent number of median stones per median stone width in the breakwater 

 cross section. The reefs tested by Ahrens and Van der Meer have relatively 

 high bulk numbers (B n greater than 200) compared to many structures that are 

 actually being built in the United States. Therefore, bulk numbers for a given 

 design should be checked against the valid ranges of the above equations to 

 assure accurate results. 



Chapter 4 Structural Design Guidance 



87 



