Evaluation of statistical analysis techniques for developing bedforms recorded in 3D

Abstract

This study investigated the development of bedforms from a flattened sand bed to equilibrium conditions in laboratory flumes. Experiments were undertaken in two flumes at The University of Auckland, a narrow 11.9-m-long, 0.38-m-deep and 0.44-mwide glass-sided open-channel flume and a wide 45-m-long, 1.2-m-deep and 1.5-mwide glass-sided open-channel flume. A fine uniform sand with D50 = 0.24-mm and a coarse uniform sand with D50 = 0.85-mm were used for the experiments. Flow velocities ranging from 0.35-m/s to 0.81-m/s and water depths between 0.15-m and 0.52-m were used. The development of bedforms was recorded with an array of 30 Multiple Transducer Arrays (MTAs) from Seatek. The acoustic sensors were arranged in a grid structure, covering the centre 40% of the flume width for the narrow flume and 90% of the flume width for the wide flume. A motorised carriage traversed the grid over a distance of 6.25-m for the narrow flume and 18.5-m for the wide flume, enabling 3D sand-bed elevation measurements every 1-min, and 2-min respectively, resulting in quasi-4D bedform development records. Moving sensor measurements (47 experiments all together) were used until the bedforms were fully developed, ranging from 2.5-hrs up to 7.5-hrs for individual flow conditions. Recorded data post-processing techniques and general bedform development observations are presented. Continuous analysis tools are introduced, treating sand-bed elevations as a random field, compared to the conventional discrete analysis methods. Continuous analysis tools are applied to study topographical changes during the dune development in fine sand and the 2D-3D dune transition for coarse sand. Analysis of experiments showed that 3D ripples have on average a skewness value similar to that for a normal distribution, with a slight negative trend. The average kurtosis value also resembles that of a normal distribution. Conversely, 2D dunes feature neutral to negative skewness as well as neutral to negative kurtosis. The skewness values show a correlation with the flow strength for dune beds. For dunes developed in fine sand, both visual observations and analysis with the help of highorder distribution moments, do not support the existence of a pronounced ripple bed when dunes develop from a flattened sand bed. Fine sand dunes exhibit less steep topographies than dunes developed under similar conditions in coarse sand. A new approach to analyse 3D textures of sand-bed elevation fields is presented. 2D structure function and 2D autocorrelation function analysis is successfully applied to the recorded bedform data set obtained in the wide flume. It is shown that a significant trend removal is important before application of the analysis technique. An ellipticity analysis is introduced, the results defining analytically the restricting boundaries for bedform development. For the wide flume experiments, the analytical results of the ellipticity analysis show that either the flume walls or the flow depth act as a restricting force to further growth of bedforms. A flume comparison study between the narrow and the wide flume was carried out. Individual experiments with similar flow conditions are compared in regards to bedform development. It is shown that characteristic height and length values display similar trends to discrete height and length values. Minor deviations in the definition of saturation values and scaling regions can result in slight variations for the growth parameters when applying the intersection technique, often even substantial variations. The determination of parameters associated with characteristic height values seems to be less susceptible to those problems than those associated with characteristic length values. It is shown that dunes in the wide flume display larger height and length features than dunes developed under the same flow conditions in the narrow flume. Scaling relations are analysed and discussed. Equilibrium parameters of characteristic height and length and their corresponding time parameters, are obtained for each experiment and used for normalisation. It is shown that although the growth deviation across the flume is substantial for wide flume experiments, once normalised, growth parameters show a better agreement for all recorded dune development data. Double scaling analysis is adversely affected by the difficult determination of temporal equilibrium parameters.