Regularity and randomness in the formation of beach cusps

Abstract

Controversy still exists on whether rhythmic features such as beach cusps are the result of the presence of standing edge wave motions in the hydrodynamics or if they are the result of self-organising processes. The compatibility between the two mechanisms is here investigated through the use of a numerical model simulating the formation and development of beach cusps. Simulations characterised by different forcing conditions have been performed. A series of ‘random’ simulations, each individual run simply differing from the others in the seed used in the random number generator, showed the typical self-organisation behaviour with the features appearing at different locations and even with slightly different spacing. ‘Regular’ series of simulations have been run by changing the wavelength of the template superimposed by the hydrodynamic forcing and the number of cycles when the template was present. Results surprisingly indicate that even a minimum number of cycles with a regular forcing can deterministically induce the final shoreline configuration. Furthermore, if the forcing template has the same wavelength as the one resulting from purely random simulations, growth rates are much faster than those obtained with random conditions. Implications for the kind of field measurements necessary to discern which of the two mechanisms is responsible for beach cusp formation have also been considered.