Equilibrium Shape Of Headland Bay Beaches For Engineering Design

The equilibrium shoreline form of crenulate or headland-bay beaches was identified in the 1940s and is widely accepted by coastal geomorphologists and engineers. However, little quantitative verification of the standard functional shoreline forms, the logarithmic-spiral shape and parabolic shape, has been made. In addition, limited guidance is available for applying the functional shapes in engineering practice. In this paper, we investigate the two shapes by fitting to 46 beaches in Spain and in the North America covering from large regional scale to small project scale. Software is described which automates the fitting. A new function, called the hyperbolic-tangent shape, is introduced for engineering applications. The hyperbolic-tangent shape is easy to fit, and its controlling parameters have simple geometric, interpretation. Guidance is given for interpreting and fitting the three headland-bay beach functions, with background data listed.