Iwagaki and Noda (1962) tested this theory by using both Ho/Lq and 

 H0/D50 as parameters to determine the criterion for the formation of 

 longshore bars. Nayak (1970) extended this work to include material of 

 a different specific weight than sand and proposed another criterion for 

 the formation of longshore bars based on the parameters Hq/Lq and 

 Hq/y'D5o (Fig. 2). The literature on equilibrium beach profiles was also 

 discussed by Nayak (1970) . 



Some investigators also attempted to find empirical equations to 

 describe the beach equilibrium profile. Rector (1954) derived empirical 

 power-law equations to describe the average beach slope, using laboratory 

 data. Eagleson, Glenne, and Dracup (1963) derived an empirical equation 

 for the offshore profile where the shear velocity was based on laminar 

 flow in the boimdary layer. Yalin (1963) derived a model-law relation- 

 ship for the offshore zone also using a bed velocity based on laminar 

 boundary layer conditions. Larras (1961) determined an empirical relation 

 for the profile in the breaker zone in the form of a power-law relation- 

 ship which has not been found to be very useful. Many investigators tried 

 to quantify some of the most important characteristics of a beach profile. 

 This requires a choice of parameters useful to define the beach profile. 

 The work of Sitarz (1963) appears to be the most comprehensive, although 

 other investigators, including this study, have not found very close agree- 

 ment with his proposed relationships (see Fig. 3, and Bonnefille and 

 Pemecker, 1965). 



Nicholson (1968) showed that certain beach profile parameters are 

 apparently a function of Hq/Lq only within certain ranges of Hq/Lq, but 

 for other ranges of Hq/Lq the beach profiles are influenced by the fall 

 velocity of the sediment particles. Figure 4 shows that for small Hq/Lq 

 (less than 1.5 X lO'^) and for large Hq/Lq (greater thkn 6 X 10"^), 

 beach profiles can be produced in similitude using sand; i.e., if Ys, 

 the vertical distance from beach crest to step or bar is proportional 

 to Hq, modeling is feasible. However, Nicholson's (1968) experiments 

 cover only a relatively narrow range of beach parameters for prospective 

 scale models and the results from the present studies do not confirm 

 the results for sand alone. 



3. Dimensional Analysis . 



Keulegan (1948), Rector (1954), Kemp (1960), Nicholson (1968), Paul, 

 Kamphuis, and Brebner (1972), Kamphuis (1972), and other investigators 

 listed governing parameters for the sediment-water interaction on a beach 

 and derived many dimensionless groups for defining beach processes. 

 Rector (1954) presented one of the most complete set of groups and even 

 included wave sorting in his initial formulation but dropped these terms 

 during subsequent analysis. Generally, the dimensionless groups are 

 considered in three subgroups: (a) Waves, (b) sediment, and (c) inter- 

 action. The wave subgroup includes terms such as Hq/Lq, d/LQ, and P/T, 

 whereas the sediment subgroup has many single terms such as a^, Iq, and 

 Y'; wave-sediment interaction subgroup includes F*, R*, and Hq/Dsq (see 

 following definitions). By various cross products, it follows that the 



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