Morphologic properties derived from a simple cross‐shore sediment transport model

Abstract

This paper builds on the now classical discussions by Bowen [1980] and Bailard [1981] on the applicability and implications of Bagnold's [1963] sediment transport model to nearshore profile modeling. We focus on the morphologic implications of both the strengths and weaknesses of Bagnold's model, isolating the transport terms that are well predicted (i.e., mean flow terms) from those that are not well predicted (i.e., transport due to correlations between flow and sediment load). We factor Bagnold's model into a dimensional transport magnitude and a nondimensional term. The nondimensional term describes the relative importance of transport due to undertow, gravity, and correlations between flow and sediment load. The transport magnitude largely determines the response time of nearshore profiles. For typical nearshore environments this response time was estimated to vary as a function of incident rms wave height (Hrms) from ∼500 years (Hrms ∼ 0.5 m) to 2 years (Hrms ∼ 3 m). The relative importance of competing transport mechanisms is shown to depend strongly on the relative wave height (defined as the ratio of the rms wave height to the local depth). Simplified nearshore transport parameterizations that are a function of this variable were derived and were interrogated for the existence and form of equilibrium profiles. Several differences from previously computed equilibrium profiles were noted. First, because the relative wave height saturates in natural surf zones, equilibrium profiles converge to a relatively flat profile near the shoreline. Second, under some situations a seaward sloping equilibrium profile may not exist. Third, the long response times combined with unknown stability of an equilibrium profile make it difficult to assess the physical connection between theoretical equilibrium profiles and profiles observed in nature.