Development of crescentic bars for a periodically perturbed initial bathymetry

Abstract

[1] The development of crescentic bed patterns starting from an ‘undisturbed’ beach (i.e. one only perturbed so as to simulate background noise and thereby initiate morphological development) is compared with that starting from a beach where monochromatic (and in some cases bichromatic) bed patterns pre-exist, using a fully non-linear model (Morfo55). A wide range of different lengthscales and amplitudes is investigated. The findings suggest that the pre-existence of crescentic bed-forms can influence the subsequent morphological development of this beach significantly, but that this development is related to the undisturbed beach development. Whether a pre-existing bed-form remains under certain forcing conditions depends on the position of the pre-existing lengthscale along the undisturbed linear growth rate curve: If the pre-existing mode shows significant linear growth in the undisturbed scenario, this pre-existing lengthscale remains. Otherwise the pre-existing mode will be replaced by a bed-form with a lengthscale closer to the undisturbed fastest growing mode. A pre-existing lengthscale that is significantly longer than the undisturbed fastest growing mode will be replaced by a higher harmonic of the original lengthscale; for shorter pre-existing lengthscales, this will be the linear fastest growing mode. An increased amplitude of the pre-existing bed-form accelerates the development toward a new stable situation. For small initial amplitudes, the initial response of the system to pre-existing bed-forms could theoretically be described using linearized equations alone. The migration rates of both the pre-existing and newly arising modes correspond to the migration rate of these modes in the undisturbed scenario.