CHAPTER 3 

 THEORETICAL DESCRIPTION 



I. HISTORICAL SUMMARY 



1. Before 1967 . 



All the relevant theories proposed to predict longshore current velocity 

 before 1967 have been thoroughly reviewed by Galvin (1967). At least 12 

 different equations existed and were derived by the following methods: 



(a) Continuity of water mass, 



(b) energy flux, 



(c) momentum flux, and 



(d) empirical correlations. 



Galvin (1967) concluded that all were oversimplified models and the empirical 

 methods lacked sufficient data. For example, the Inman-Quinn (1951) theory 

 used momentum conservation principles modified by empirical data. It was shown 

 to be based on an untenable assumption, supported by inappropriate data and 

 found to be only a fair predictor for just one of the three data sets then 

 available. No adequate theory was felt to exist at that time (Galvin, 1967). 



A summary of most of these longshore current formulas is included as Ap- 

 pendix C (from Thornton, 1969). It lists an additional empirical equation 

 based on multiregression analysis as found by Harrison (1968) at Virginia 

 Beach, Virginia. Such equations are only roughly tenable for the location and 

 range of variables observed. Equations based on the conservation laws of 

 physics are much preferred for general usage. Additional analysis and discus- 

 sion of the theories before 1967 can be found in Horikawa (1978a) who includes 

 some Japanese formulas not previously referenced. The formula of Shadrin 

 (1961), based on measurements at a barred coastline of the Black Sea (Anapa 

 coast), is also discussed by Horikawa (1978). There are also recent original 

 summaries by Komar (1976) and Gourlay (1978) of most theoretical attempts befoi 

 1967. 



In retrospect, all these theories were doomed to failure for a number of 

 reasons. Those based solely on mass conservation and kinematics omitted the 

 crucial dynamics and interplay among forces and fluid accelerations. The 

 amount of energy dissipation in the surf zone is a significant percentage of 

 the total available and difficult to estimate. Energy flux theories rely on 

 that small fraction remaining which represents' a second-order phenomenon 

 (Galvin, 1967). Momentum conservation principles were simply not applied pro- 

 perly and neglected the influence of the streamline curvature present in short 

 waves on the vertical pressure distribution. They all predicted one mean 

 longshore current velocity for the entire surf zone width. They neglected 

 important factors such as breaker type, beach profile, and bottom roughness. 

 They were all for longshore current estimates and no theories to handle near- 

 shore circulations and rip currents existed at that time. 



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