Hysteresis in the evolution of beach profile parameters under sequences of wave climates - Part 2; Modelling

Disequilibrium-type models for two beach profile parameters, P, the shoreline position and net bulk sediment transport, are developed for laboratory experiments that demonstrate morphological hysteresis in the evolution to equilibrium of beach profiles under sequences of different wave climates. The model principle follows the classical disequilibrium approach but with non-monotonic relationships between the forcing and the chosen beach profile parameter at equilibrium, Peq, previously verified and presented in part 1 of this work (Baldock et al., 2017). Two such relationships are required to model beach profile evolution that exhibits morphological hysteresis. The model coefficients are derived for monochromatic and random wave experiments and subsequently used to model data obtained from cyclic erosive and accretive wave conditions of shorter durations, alternating through multiple cycles. In these conditions equilibrium conditions were not reached and hysteresis does not occur. The model is used to investigate the morphological feedback between the outer and inner bars and the resulting behaviour of the bulk transport, and the relative depth over the bar crest is shown to be an attractor in this case. The model coefficients and morphological time-scales derived from the cyclic experiments are very similar to those derived from the equilibrium experiments for the bulk transport. Normalised mean square model errors range from 1% to 20% when applied to independent data. The data from the cyclic wave conditions can be inverted to derive the conditions expected at equilibrium, which match those observed, indicating a robust model relationship between the forcing and Peq. The relationship between the forcing and Peq can also be determined directly from the cyclic experiments. This approach may be more robust than determining the relationship from periods where P is stationary since, in a time-series of P versus the forcing, stationary points can occur due to changes in wave conditions, in addition to the instances when P=Peq.