High‐angle wave instability and emergent shoreline shapes: 1. Modeling of sand waves, flying spits, and capes

TLDR

The updated numerical model incorporates a barrier overwash formulation that maintains a minimum barrier width by widening overly thin barriers. The study shows that a high proportion of oblique deep‑water waves triggers a high‑wave‑angle instability that drives the self‑organization of shorelines into regular, quasiperiodic shapes, with symmetric wave climates producing increasingly pointed cuspate coasts, asymmetric climates generating downdrift migration into sand waves or flying spits, and the high‑angle wave fraction controlling the offshore‑versus‑alongshore aspect ratio, while the rate of alongshore scale merging follows a diffusional temporal scale independent of wave angle.

Abstract

Contrary to traditional findings, the deepwater angle of wave approach strongly affects plan view coastal evolution, giving rise to an antidiffusional “high wave angle” instability for sufficiently oblique deepwater waves (with angles between wave crests and the shoreline trend larger than the value that maximizes alongshore sediment transport, ∼45°). A one‐contour‐line numerical model shows that a predominance of high‐angle waves can cause a shoreline to self‐organize into regular, quasiperiodic shapes similar to those found along many natural coasts at scales ranging from kilometers to hundreds of kilometers. The numerical model has been updated from a previous version to include a formulation for the widening of an overly thin barrier by the process of barrier overwash, which is assumed to maintain a minimum barrier width. Systematic analysis shows that the wave climate determines the form of coastal response. For nearly symmetric wave climates (small net alongshore sediment transport), cuspate coasts develop that exhibit increasing relative cross‐shore amplitude and pointier tips as the proportion of high‐angle waves is increased. For asymmetrical wave climates, shoreline features migrate in the downdrift direction, either as subtle alongshore sand waves or as offshore‐extending “flying spits,” depending on the proportion of high‐angle waves. Numerical analyses further show that the rate that the alongshore scale of model features increases through merging follows a diffusional temporal scale over several orders of magnitude, a rate that is insensitive to the proportion of high‐angle waves. The proportion of high‐angle waves determines the offshore versus alongshore aspect ratio of self‐organized shoreline undulations.