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

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

“…Our results show that in the limit of narrow distributions of wave direction, including diffraction rules in a numerical model is required to produce realistic crenulate bay shapes (consistent with the findings of Daly et al []). Outwith this limit, diffraction still influences the morphology of the bay, resulting in bays that are more curved along their length, yet in contrast to previous studies [ Rea and Komar , ; Weesakul et al , ], diffraction is not essential to understand the formation of crenulate bays (consistent with the findings of Littlewood et al []). Comparison to empirical formulations for static bay morphology reveal differences in predicted bay planform morphology driven primarily by the spread of wave approach angles, suggesting that engineering solutions based on the static bay concept should consider the variability of waves impinging on the coast within a modeling framework when designing coastal interventions.…”

“…The experiments were run on bays with l b =2 km and we simulated 100 years in order that all model runs attain a morphological steady state, defined by the condition that the coastal length tends to a constant value and mean change in coastline position fluctuates about zero. We ran these ensembles for the condition where wave properties in the shadow zone were diffracted following equations and , or where there was no diffraction so that shadowed regions of the coast were not subject to sediment transport for a particular wave approach angle (similar to Littlewood et al []). Additionally, we ran an ensemble of experiments in which the wave climate was held constant ( θ mean =025° and θ std =30°, respectively), and l b was varied over 2 orders of magnitude to explore the influence of spatial scale on bay evolution and morphology.…”

“…One‐line models of shoreline evolution can reproduce embayed beach morphology in the lee of a headland or promontory [ LeBlond , ; Rea and Komar , ; Hanson , ; Littlewood et al , ; Iglesias et al , ; Weesakul et al , ; Barkwith et al , , ]. Rea and Komar [] used simple rules to describe the adjustment in wave height and direction due to diffraction in the shadow of a promontory and demonstrated that the resulting bay forms were similar in form to a logarithmic spiral.…”

“…Both of these studies examined the formation of bays under the influence of a single dominant wave direction, with the morphology of the highly curved portion of the bay controlled by diffraction of waves into the shadowed region. The study by Littlewood et al [] neglected wave diffraction in the shadow zone yet demonstrated that a crenulate‐shaped bay can still develop when there is variation in the approaching wave angles. Sediment transport in the shadow of the dominant wave direction only occurs when waves approach from the leeside of the crenulate bay.…”

Unraveling the dynamics that scale cross‐shore headland relief on rocky coastlines: 1. Model development

“…The equilibrium shape of log‐spiral or headland‐bay beaches on kilometer scales has received considerable attention [e.g., Silvester , ; Yasso , ; Littlewood et al ., ; Weesakul et al ., ; Jackson and Cooper , ; Hsu et al ., ]. These studies are mostly concerned with the curved, crenulate shape of the sandy bay that results from wave interactions with a stationary headland (either refraction/diffraction using a single wave condition or wave‐shadowing effects with a mix of wave directions) [ Littlewood et al ., ] rather than the understanding of how headland amplitude evolves. The equilibrium amplitude of log‐spiral coasts has been addressed [ Hsu et al ., ], but it is found empirically [ Hsu et al ., ] rather than through a dynamical process‐based approach as is presented here.…”