the area of the maximum longshore current and the slope Increased with sand 

 fall velocity and wave period. 



90. Hughes and Chiu (1981) studied dune recession by means of small- 

 scale movable-bed model experiments. The amount of dune erosion was found by 

 shifting the barred profile horizontally until eroded volume agreed with 

 deposited volume (Vellinga 1983). Geometric properties of the equilibrium bar 

 profile were expressed in terms of dimensionless fall speed. 



91. Sawaragi and Deguchi (1981) studied cross -shore transport and beach 

 profile change in a small wave tank and distinguished three transport rate 

 distributions. They developed an expression for the time variation of the 

 maximum transport rate and discussed the relation between bed and suspended 

 load. 



92. Gourlay (1981) emphasized the significance of the dimensionless 

 fall speed (Gourlay 1968) in describing equilibrium profile shape, relative 

 surf zone width, and relative uprush time. 



93. Hattori and Kawamata (1981) developed a criterion for predicting 

 the direction of cross-shore sediment transport similar to Dean (1973), but 

 including beach slope. The criterion was derived from the balance between 

 gravitational and turbulent forces keeping the grains in suspension. 



94. Watanabe, Riho, and Horikawa (1981) calculated net cross-shore 

 transport rates from the mass conservation equation (van Hijum 1975, 1977) and 

 measured profiles in the laboratory, arriving at a transport relationship of 

 the Madsen and Grant (1977) type. They introduced a critical Shields stress 

 below which no transport occurred and assumed a linear dependence of the 

 transport rate on the Shields parameter. 



95. Moore (1982) developed a numerical model to predict beach profile 

 change produced by breaking waves. He assumed the transport rate to be 

 proportional to the energy dissipation from breaking waves per unit water 

 volume above an equilibrium value (Dean 1977). An equation was given which 

 related this equilibrium energy dissipation to grain size. The beach profile 

 calculated with the model approached an equilibrium shape in accordance with 

 the observations of Bruun (1954) if exposed to the same wave conditions for a 

 sufficiently long time. 



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