Logarithmic Spiral Coastlines

Abstract

The 45 km stretch of coastline between Mapelane and Cape Vidal is an offset coastline which is subject to a dominant wave attack from the south-east. This section of coastline is characterized by long stretches of sandy beach alternating with rocky headlands. Each headland is recessed or offset behind its neighbour and so has an asymmetrical seaward concave plan shape where radius of curvature becomes greater with increasing distance from the headland. The seaward concave plan shape results from erosion caused by wave refraction and diffraction into the shadow zone behind the headland.

In order to determine the amount of wave refraction occurring, wave refraction diagrams were compiled. These diagrams were also used to indicate areas of increased and decreased wave energy and the presence of possible longshore currents.

Increasing radius of plan curvature with distance from the headland suggested using a log spiral curve as an approximation of the shape of these asymmetrically offset bays. Using the log spiral curve four sections of coastline were selected for testing “goodness of fit” to the log spiral curve. A computer was programmed to generate a best fitting log spiral curve to each section of coastline. Once the plan shape of the offset coast was defined by the best fitting log spiral curve the coastline was evaluated in terms of wave refraction and diffraction, areas of erosion and accretion, changing beach morphology and coastal orientation and equilibrium.