An Alternative Explanation for the Shape of 'Log-Spiral' Bays

We present a simple numerical model capable of producing distinctive scalloped bays of a form found when a sandy coastline extends downdrift of a rocky headland. The shape of such bays can often be approximated by a log-spiral—a curve for which the radius of curvature increases logarithmically with distance from the headland or ‘pinning point.' A considerable body of work has been published attributing this shape to the pattern of refraction and/or diffraction created as waves approaching from a dominant direction interact with the pinning point. Here, we present a fundamentally different explanation for these shapes. We use an existing one-line numerical model of wave-driven alongshore transport which includes shoaling and refraction over contours assumed to parallel local shoreline orientations. Rather than assuming a single wave angle, it generates new waves repeatedly according to an input wave climate. It does not include refraction or diffraction around the pinning point; thus, the log-spiral-like shape evolves as simply as a result of alongshore transport driven by a distribution of deep-water wave approach angles.