Modelling the impact of a time-varying wave angle on the nonlinear evolution of sand bars in the surf zone

Sandy beaches are often characterized by the presence of sand bars, whose characteristics (growth, migration speed, etc.) strongly depend on offshore wave conditions, such as wave height and angle of wave incidence. This study addresses the impact of a sinusoidally time-varying wave angle of incidence with different time-means on the saturation height, migration speed and longshore spacing of sand bars. Model results show that shore-transverse sand bars (so-called TBR bars) eventually develop under a time-varying wave angle. Depending on the time-mean, amplitude and period of the varying angle of wave incidence, the mean heights and mean migration speeds of the bars can be larger or smaller than their corresponding values in the case of time-invariant angles. Bars might not even form when the wave angle varies around a too large oblique mean value, whereas bars exist in the case of a time-invariant wave angle. The oscillations in both bar height and migration speed are large if the period of the time-varying wave angle is close to the adjustment timescale of the system and if large differences in the local growth and migration rates of the bars occur during one oscillation period. The oscillations in bar height are a combination of harmonics with the principal period and half the period of the time-varying wave angle, whereas those of migration speed contain only the principal period. Bars that are subject to time-varying wave angles have larger longshore crest-to-crest spacings than those which form under fixed wave angles. Physical explanations for these findings are given.