Bars, bumps, and holes: Models for the generation of complex beach topography

TLDR

In shallow water, two waves of the same frequency generate complex drift‑velocity patterns, and when their longshore wave‑number components differ, the resulting steady flows exhibit a longshore periodicity equal to the difference of those components regardless of propagation direction. The study investigates the detailed interaction between two edge‑wave modes. Drift velocities are computed and a simple sediment‑transport model is applied to predict the beach topography that would be in equilibrium with these flow patterns. The model predicts crescentic sand bars for standing edge waves, while other combinations produce complex transverse and offshore bars resembling observed rhythmic topography; extending the model to three or more waves yields increasingly irregular patterns that repeat only over very long distances relative to bar scale.

Abstract

In shallow water, any two waves of the same frequency are shown to produce complex patterns of drift velocity above the sea bed. If the longshore components λ 1 , λ 2 of the wave numbers of the two waves are different, these steady flow patterns exhibit a longshore periodicity of wave number (λ 1 ‐ λ 2 ) irrespective of whether the waves propagate in the same direction (say λ 1 , λ 2 positive) or in opposite directions (λ 2 negative). The interaction of two edge wave modes is examined in detail. The drift velocities are calculated and a simple sediment transport model is used to predict the beach topography that would be in equilibrium with these flow patterns. As expected, crescentic sand bars are produced by the special case of standing edge waves (λ 1 = −λ 2 ). Intriguingly, for all other cases a combination of complex transverse bars plus meandering or straight offshore bars result, patterns that are surprisingly reminiscent of many published descriptions of complex, rhythmic topography. The extension of the model to three or more waves produces topography that appears to be very irregular. Although the pattern should repeat over sufficiently long distances along the beach, even with only three waves these distances may be very large compared to the scale of the bars.