A dynamical attractor governs beach response to storms

Abstract

Sandbars are ubiquitous, yet not well understood beach features that change their position and shape in response to changing wave conditions. We propose and test a simple empirical model consisting of two coupled linear differential equations that represents bar dynamics in terms of wave forcing and two other state variables: (1) the mean cross‐shore bar position and (2) the alongshore variability about that mean. Model coefficients are constrained by fitting to a 2‐month data set, and the modeled behavior is examined with a stability analysis. The system is found to be stable and, hence, predictable. Rates of change of the bar position and its alongshore variability are found to be significantly coupled, such that prediction of one variable requires information about the other. The system response time is slow compared to the storm wave cycle such that the bar response continually orbits time‐varying equilibrium points in the state variable phase plane.