Instability and finite-amplitude self-organization of large-scale coastline shapes

Author Posting. © The Author(s), 2012. This is the author's version of the work. It is posted here by permission of The Royal Society for personal use, not for redistribution. The definitive version was published in Philosophical Transactions of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences 371 (2013):20120363, doi:10.1098/rsta.2012.0363.Recent research addresses the formation of patterns on sandy coastlines on alongshore scales that are large compared with the cross-shore extent of active sediment transport. A simple morphodynamic instability arises from the feedback between wave-driven alongshore sediment flux and coastline shape. Coastline segments with different orientations experience different alongshore sediment fluxes, so that curvatures in coastline shape drive gradients in sediment flux, which can augment the shoreline curvatures. In a simple numerical model, this instability, and subsequent finite-amplitude interactions between pattern elements, lead to a wide range of different rhythmic shapes and behaviours—ranging from symmetric cuspate capes and bays to alongshore migrating ‘flying spits’—depending on the characteristics of the input wave forcing. The scale of the pattern coarsens in some cases because of the merger of migrating coastline features, and in other cases because of non-local screening interactions between coastline protrusions, which affect the waves reaching other parts of the coastline. Features growing on opposite sides of an enclosed water body mutually affect the waves reaching each other in ways that lead to the segmentation of elongated water bodies. Initial tests of model predictions and comparison with observations suggest that modes of pattern formation in the model are relevant in nature