Exploring the sensitivities of crenulate bay shorelines to wave climates using a new vector-based one-line model

We use a new exploratory model that simulates the evolution of sandy coastlines over decadal to centennial timescales to examine the behavior of crenulate-shaped bays forced by differing directional wave climates. The model represents the coastline as a vector in a Cartesian reference frame, and the shoreface evolves relative to its local orientation, allowing simulation of coasts with high planform-curvature. Shoreline change is driven by gradients in alongshore transport following newly developed algorithms that facilitate dealing with high planform-curvature coastlines. We simulated the evolution of bays from a straight coast between two fixed headlands with no external sediment inputs to an equilibrium condition (zero net alongshore sediment flux) under an ensemble of directional wave climate conditions. We find that planform bay relief increases with obliquity of the mean wave direction, and decreases with the spread of wave directions. Varying bay size over 2 orders of magnitude (0.1-16 km), the model predicts bay shape to be independent of bay size. The time taken for modeled bays to attain equilibrium was found to scale with the square of the distance between headlands, so that, all else being equal, small bays are likely to respond to and recover from perturbations more rapidly (over just a few years) compared to large bays (hundreds of years). Empirical expressions predicting bay shape may be misleading if used to predict their behavior over planning timescales.