Propagation of bed waves in rivers: ELV simulations

Sustainable river management can be supported by models predicting long-term morphological developments. Even for one-dimensional morphological models, run-times can be up to several days for simulations over multiple decades. Alternatively, analytical tools yield metrics for propagation and damping of sediment waves, which might be used as rapid assessment tools for future morphological development. We present a linear stability analysis of the St. Venant-Exner equations and derive an analytical relation for sediment waves with spatial scales much larger than the length scale of bedforms such as dunes. With a one-dimensional morphological model, we assess the validity range of the analytical approach. The comparison shows that the propagation of small bed perturbations is well-described by the analytical approach. For Froude numbers over 0.3, diffusion becomes important and bed perturbations celerities reduce in time. The linear stability analysis based on spatial modes then provides an upper limit for the bed perturbation celerity. For longer and higher bed perturbations, the dimensions relative to water depth and the backwater curve length determine whether the analytical approach yields realistic results. For higher bed wave amplitudes, non-linearity becomes important. For Froude numbers ≤ 0.3, the celerity of bed waves is then increasingly underestimated by the analytical approach. The degree of overestimation is proportional to the relative amplitude (ratio of amplitude to water depth) of the sediment wave and the Froude number. For Froude numbers exceeding 0.3, the net impact on the celerity de pends on the balance between decrease due to damping and the increase due to non-linearity.

In this paper with the title \"Propagation of bed waves in rivers: analytic approach and comparison to numerical modelling\" simulations with 1D morphological modelling code ELV have been performed to generate Figures 8, 10 and 12. The input and output files of these simulations are stored here.

Explanation of the files:
beddev.xlsx - bed level as a function of time and space
beddev_dyn_'name'.xlsx - analysis of beddev.xlsx to assess celerities and generate graphs
cpu.txt - output cpu time simulation
input.mat - Matlab input file for ELV
log.txt - log file simulation
output.mat - matlab output file ELV