Long-term equilibrium beach profile based on maximum information entropy concept

This paper presents an application of the maximum information entropy concept to formulate an equilibrium beach profile (EBP) associated with the long-term beach evolution. The model assumes the beach profile is monotonic from a maximum depth at an offshore location to the runup limit or the berm level at the shoreline. The derived equilibrium beach profile has a logarithmic shape in terms of the cross-shore distance and can be either concave or convex depending on the profile shape parameters. If only the underwater portion of the profile is considered, the new EBP in nondimensional form matches the well known 2/3 power profile with the shape parameter S being between I and 1.5. The dimensional form of the profile is controlled by parameter S together with three other parameters which are the beach levels at the two boundaries of the profile and horizontal extent of the profile. These parameters are either directly measurable from the given initial profile and the calculated equilibrium profile or could be estimated using the available empirical formulae appropriate to the sediment properties, wave climate, and the temporal scale considered. As the profile shape comes directly from the use of the maximum information entropy principle without resorting to any assumptions regarding the cross-shore distributions of shear stresses, energy dissipations, or other physical processes the new EBP is applicable to both surfzone and nearshore zone as long as longshore bars are absent or unimportant.