Physics of nearshore bed pattern formation under regular or random waves

We present an investigation into the growth of nearshore, rhythmic patterns. A comprehensive linear stability model of the surf and shoaling zones is used to examine which type of pattern, transverse or crescentic bar, is likely to form under different wave conditions. In contrast to earlier studies we examine normal and near-normal incidence on a plane beach. In doing so we reproduce results of earlier, more restricted studies and thereby identify the physical mechanisms leading to the growth of different patterns. This paper also focuses on the role of random wave height distribution compared with regular waves and identifies conditions likely to lead to pattern growth. To this end, an amended wave height dissipation function is presented, which allows us to move between random and regular regimes. It is found that a sharply defined surf breakpoint leads to larger growth rates and crescentic-bar-type features. In contrast, a large spread in breaking gives rise to transverse bar patterns with reduced growth rates. Transverse bar alongshore spacing is typically about 1/4 to 1/2 the width of the surf zone, while crescentic bar spacing is larger, up to twice this width. It is also shown that pattern types are influenced by the wave height to depth ratio in the surf zone. This indicates that sites with substantial inner surf zone wave energy and thus greater energy available to move sediment will give rise to transverse bar patterns. A new, propagating mode is identified in such cases, which exists for normal wave incidence. Finally, the role of wave shoaling and wave refraction, either on the bed or on the currents is examined. Crescentic bars seem to be a very robust feature as they stem from the model even if those three effects are ignored. Thus the only essential feedback for their formation is the coupling between depth-controlled breaking and the evolving bathymetry. In contrast, transverse bar formation is very sensitive to wave refraction being enhanced by refraction over the bed and weakened by refraction over the current