Modelling the response of a double-barred sandy beach system to time-varying wave angles

Sandy beaches typically have one or more shore-parallel bars with superimposed smaller-scale three-dimensional (3D) bars. Knowledge of their morphodynamic behaviour under more realistic wave conditions is limited. This study investigates the response of beaches with two shore-parallel bars to sinusoidally time-varying angles of incidence, using a non-linear morphodynamic model. Different periods and amplitudes of this sinusoidal variation are considered, as well as different time-mean wave angles. For time-invariant and normally incident waves, results show that alongshore rhythmic 3D bars form in the domains of inner and outer shore-parallel bars. The 3D bars in the inner domain are coupled at half the outer-bars wavelength. This phase coupling breaks up when the wave angle varies in time. Initially, regular 3D bars form in the inner domain (free behaviour), which become irregular when 3D bars develop in the outer domain (forced behaviour). The heights of the 3D bars oscillate with time, reaching maximum values when the forcing period is comparable to the system adjustment time scale (∼ 10–20 days). For a time-varying wave angle around an oblique mean, alongshore migrating 3D bars emerge in both inner and outer domains. In contrast, for an oblique (constant) wave angle, 3D bars only form in the inner domain and they hardly migrate alongshore. For any forcing period, the dominant response period of the oscillating bar heights is at half the forcing period when waves are (on average) normally incident, and it equals the forcing period when waves are on average obliquely incident. Compared with time-invariant angles, heights of inner and outer 3D bars are (on average) smaller and larger, respectively, when the angle varies with time, particularly for forcing periods in the order of the system adjustment time scale. Increasing the amplitude of the time-varying wave angle weakens bar growth. Explanations of these results are also provided