Wave-formed sediment ripples: transient analysis of ripple spectral development

Abstract

A new method has been developed that models the changes a wave-formed rippled sediment bed undergoes as it is actively evolving between two given equilibrium states due to a change in surface wave conditions. The transient analysis of rippled beds has received very little attention within the literature. Dynamic changes within ripple parameters have implications for the estimation of flow dissipation and sediment transport by changing the bottom roughness height. The method uses the spectral density function of the rippled bed and is based on a series of ripple growth and ripple transition experimental tests. The ripple evolution model was developed from the well-known Logistic Growth Law. Fitting the general solution of the logistic nonlinear differential equation to the experimental data enabled the evolution rate of the bed to be determined for each experimental test. It was concluded that there was no difference between the evolution rate determined from the ripple growth tests and the ripple transition tests. This indicated that the two types of growth are special cases of the same evolution processes, which is adequately modeled by the logistic growth equation. A functional dependence was established between the ripple evolution rate and the Shields parameter. This allows the evolution rate to be estimated from flow and sediment properties. The estimation of the rate at which rippled sediment beds evolve under a variable sea state has the potential to lead to significant improvements to the way ripple transition and hence bottom roughness is approximated in coastal wave models.