becomes shallow enough to initiate breaking; this depth is usually denoted as 

 dv and termed the breaking depth. Munk (1949) derived several relationships 

 from a modified solitary wave theory relating the breaker height E^, the 

 breaking depth d^, the unrefracted deepwater wave height H', and the 

 deepwater wavelength I^. His expressions are given by 



\ 1 



H' 3.3(H'/L )l/3 

 o o o 



(2-90) 



and 



■^= 1.28 (2-91) 



The ratio H^/H^ is frequently termed the breaker height index. Subsequent 

 observations and investigations by Iversen (1952, 1953) Galvin (1969), and 

 Goda (1970) among others, have established that H^/Hq and d^/H^ depend on 

 beach slope and on incident wave steepness. Figure 2-72 shows Coda's empiri- 

 cally derived relationships between H^^/H^ and H^/^ for several beach 

 slopes. Curves shown on the figure are fitted to widely scattered data; how- 

 ever they illustrate a dependence of H^/Hq on the beach slope. Empirical 

 relationships derived by Weggel (1972) between dt^/Hv and Hv/gT^ for various 

 beach slopes are presented in Figure 2-73. It is recommended that Figures 2- 

 72 and 2-73 be used, rather than equations (2-90) and (2-91), for making esti- 

 mates of the depth at breaking or the maximum breaker height in a given depth 

 since the figures take into consideration the observed dependence of ^u/^w and 

 Hl/H' on beach slope. The curves in Figure 2-73 are given by 



d 



T = b-(aH /gT2) ^^"^^^ 



D D 



where a and b are functions of the beach slope m, and may be approxi- 

 mated by 



a = 43.75(1 - e-^^'") (2-93) 



1.56 

 (1 + e'l^-^"") 



b = ., ■ '-l^.Sm, (2-94) 



Breaking waves have been classified as spilling, plunging, or surging 

 depending on the way in which they break (Patrick and Wiegel, 1955) , and 

 (Wiegel, 1964). Spilling breakers break gradually and are characterized by 

 white water at the crest (see Fig. 2-74). Plunging breakers curl over at the 

 crest with a plunging forward of the mass of water at the crest (see Fig. 2- 

 75) . Surging breakers build up as if to fonn a plunging breaker but the base 

 of the wave surges up the beach before the crest can plunge forward (see Fig. 

 2-76). Further subdivision of breaker types has also been proposed. The term 

 collapsing breaker is sometimes used (Galvin, 1968) to describe breakers in 

 the transition from plunging to surging (see Fig. 2-77). In actuality, the 



2-130 



