V. SPIRAL BEACHES 



Hooklike beaches (Fig. 16) are common along exposed coasts and are 

 formed by the long-term combined effects of refraction and diffraction 

 around headlands. Yasso (1965) discovered that the planimetric shape of 

 many of these beaches could be fitted very closely by a segment of log- 

 arithmic spiral; the distance, r , from the beach to the center of the 

 spiral increasing with the angle according to 



exp 



cot e (49) 



in which 3 is the spiral angle. 



Bremmer (1970) has shown the logarithmic spiral to give an excellent 

 fit for the profile of a recessed beach between two headlands. 



The evolution of spiral beaches belongs to the geographical time- 

 scale domain (Sylvester and Ho, 1972) . However, similar evolution has 

 also been observed over smaller time scales in consonance with the 

 definition of long-term shoreline evolution adopted in this study. 



So far, only empirical rather than theoretical mathematical repre- 

 sentations of spiral beaches are available. The empirical approach has 

 been fruitful in providing the spiral coefficients 3 as function of 

 wave angle, a , with the headland alinement (Fig. 16) (Sylvester and 

 Ho, 1972). The "indentation ratio" (depth of the bay to width of open- 

 ing) also depends upon a and, in most cases, varies between 0.3 and 

 0.5 (Fig. 17). 



There have been many attempts to explain this peculiar beach forma- 

 tion (Leblond, 1972; Rea and Komar, 1975). Leblond assumed that the 

 rate of sediment transport is proportional to the longshore currents as 

 given by the theory of Longuet-Higgins (1975) . He also assumed that the 

 beach profile is not modified by erosion or accretion so that the con- 

 tinuity equation from the one-line theory can be used in a two-dimen- 

 sional coordinate system. 



Thus, the variation in longshore current intensity with wave angle 

 will yield the rate of erosion or accretion. 



Difficulties arise in expressing this variation of longshore current 

 in areas subjected to wave diffraction. Leblond (1972) points out that 

 classical wave diffraction theories are too complicated to be used in 

 his theoretical scheme. Another difficulty arises from the fact that 

 the barrier (headland) is not thin as it is assumed in the theory of 

 diffraction of Putnam and Arthur (1948). To account for this effect, 

 Leblond introduces an empirical correction coefficient to the theory 

 of Putnam and Arthur over a two-dimensional network. The results of 



42 



