Unexpected Property of Dean-Type Equilibrium Beach Profiles

It has been demonstrated that, for the majority of beach profiles with multiple bars, the only beach parameter that controls the total nearshore wave energy dissipation, which was obtained by the integration of a constant dissipation rate in a unit water volume over Dean-type equilibrium beach profiles, is the depth at which Dean's regime is initiated. This does not depend on the Dean coefficient (A), and, therefore, the wave breaking index (y) remains the only morphodynamic parameter that controls the magnitude of that dissipation. However, A serves as a more accurate proxy of the beach state when applied with data-driven empirical beach equilibrium profiles, because it better describes the state of the seabed between the shoreline and the depth down to which the Dean concept is valid. Two exceptions to this general behavior of beaches with multiple bars have been identified: one with two zones of saturated energy dissipation, which was induced by a large offshore-most bar (which requires the introduction of the outer Dean function), and one where the bars are small and shallow, and the morphology offshore the bar zone closely resembled the equilibrium profile shape. These outliers will be discussed in detail.