Coastline evolution due to a high-wave-angle instability
Deep-water waves obliquely approaching a coast with angles between wave crests and the shoreline greater than approximately 45° (from 'high angles') produce an instability in the planview shape of a shoreline. Although previously overlooked, this instability merely requires a maximum in alongshore sediment transport for a given deep-water wave angle; this maximum, often obscured by wave refraction, arises in many relationships for alongshore sediment transport. A one-contour-line numerical model predicts that wave climates with a majority of high-angle waves develop large-scale rhythmic shoreline features resembling naturally occurring coastal landforms, including capes, cuspate forelands, and alongshore sandwaves. Addressing the instability and the resulting complex behaviors required refining the traditional one-line approach, and the numerical model, which can attain arbitrarily sinuous configurations, includes the process of barrier overwash. Model behaviors, which include alongshore translation and offshore spit growth, depend on the characteristics of the wave climate. Although the proportion of high-angle waves does not affect the approximately diffusional rate of wavelength growth of shoreline features, the aspect ratio of the features increases with increasing high-angle waves. Using metrics to characterize wave climates in terms of net coastal stability, model results are compared to natural examples, including Long Point, on Lake Erie, Ontario, Canada, and the Carolina Capes along the southeastern coast of the United States of America, revealing similar trends in wave climate instability as coastal orientation changes. Additional comparisons are made between models and measurements for alongshore sandwaves measured along the Dutch coast and the North Carolina Outer Banks coast, showing that trends in shoreline behavior with changing orientation are consistent with numerical predictions.