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The Analysis of Exponential Beach Profiles

1994; Coastal Education and Research Foundation; Volume: 10; Issue: 1 Linguagem: Inglês

1551-5036

Paul D. Komar, William G. McDougal,

Coastal wetland ecosystem dynamics

The overall form of many beach profiles has an exponential shape where the depth h is given by h = S 0 / k) (1-e -kx ) with S 0 the beach-face slope at x = 0 and k is an adjustable coefficient that determines the degree of concavity. The cross-shore variation in beach slope is then S = S 0 e –kx or S = S 0 - kh. Beach profiles can be analyzed in terms of both the cross-shore variations in hand S. Based on previous studies, the beach-face slope S 0 is predictable as a function of the sediment grain size and wave parameters. The evaluation of k can be based on best-fit comparisons with the measured profile depths or from bottom slope variations across the profile. Equations are derived for the evaluation of k from the offshore closure depth of the envelope of profile changes, or from some arbitrarily selected coordinate of the profile. An example of the analysis approach is provided by a beach profile from the Nile Delta coast of Egypt. This measured profile shows good agreement with the exponential form for cross-shore variations in both the absolute depth h and local bottom slope S. There is poor agreement with the h = Ax 2/3 profile relationship, in part because this Nile Delta profile is more reflective and has a greater concavity than allowed by the x 2/3 dependence. The failure of the x 2/3 profile form is still more evident in analyzing the beach-slope variations since it predicts an infinite slope at the shoreline. The exponential beach profile is a convenient mathematical relationship that should be useful in many applications.