Computational models for dune time-lag: Population structures and the effects of discharge pattern and coefficient of change

Abstract

An earlier model for dune time-lag in periodically varying unidirectional flows (J.R.L. Allen, 1976) is modified so as to treat more realistically the stochastic behaviour of dunes and the ability of the individual to change in height during its life-span. The improved model shows that hydrograph shape could substantially influence dune behaviour in unsteady flows. For the same flow period and extreme discharge values, a reduction in the relative duration of the high-water stages causes an increase in the phase differences between dune dimensions and flow, and an increase in the dimensions averaged over the flow cycle as compared with the similarly averaged dimensions given no lag. The relative range of dimensions over the flow cycle is little affected. The time-dependent structure of the dune populations is explored using histograms of the instantaneous values of dune wavelength, height and age. At small values of the time ratio (ratio of characteristic dune life-span to flow period), the dunes invariably are unimodally distributed in wavelength, height and age, and the relative dispersion of these properties is small. At intermediate ratios, dune properties are bimodally distributed and moderately to highly dispersed over much of each flow cycle, usually the later part and sometimes the whole of the low-water phase. Dune properties are at all times highly dispersed and, broadly, unimodally distributed when the time ratio is large. There is a close correlation between the patterns in time of dune creation rate, population structure, the average values and relative dispersions of dune dimensions, and the phase difference evaluated for each instant. An increase of the coefficient of change of dune height decreases the equivalent phase difference for height, diminishes the calculated wavelength and height averaged over the flow cycle, but increases the ranges of height and wavelength. Increasing the coefficient has no apparent effect on the equivalent phase difference for wavelength.