Equilibrium beach profiles

Various models have been proposed for representing equilibrium beach profiles (EBP). Some of these models are based on examination of the geometric characteristics of profiles in nature and some attempt to represent in a gross manner the forces active in shaping the profile. One approach that has been utilized is to recognize the presence of the constructive forces and to hypothesize the dominance of various destructive forces. This approach can lead to simple algebraic forms for the profiles for testing against profile data.

Dean (1977) has examined the forms of the EBPs that would result if the dominant destructive forces were one of the following:
1) Wave energy dissipation per unit water volume.
2) Wave energy dissipation per unit surface area.
3) Uniform average longshore shear stress across the surf zone.

It was found that for all three of these destructive forces, by using linear wave theory and a simple wave breaking model, the EBP could be represented by the following simple algebraic form

h=Ay^n

in which A, representing a sediment scale parameter, depends on the sediment size D. This form with an exponent n equal to 2/3 had been found earlier by Bruun (1954) based on an examination of beach profiles in Denmark and in Monterey Bay, CA. Dean (1977) found the theoretical value of the exponent n to be 2/3 for the case of wave energy dissipation per unit volume as the dominant force and 0.4 for the other two cases. Comparison of the aforementioned equation with approximately 500 profiles from the east coast and Gulf shorelines of the United States showed that, although there was a reasonably wide spread of the exponents n for the individual profiles, a value of 2/3 provided the best overall fit to the data. As a result, the following expression is recommended for use in describing equilibrium beach profiles