Edinburgh Napier University

  The primary purpose of this work was to study the morphological change of river-bed
sediment surfaces over time using wavelet transform analysis techniques. The wavelet
transform is a rapidly developing area of applied mathematics in both science and
engineering. As it allows for interrogation of the spectral made up of local signal
features, it has superior performance compared to the traditionally used Fourier
transform which provides only signal averaged spectral information. The main study of
this thesis includes the analysis of both synthetically generated sediment surfaces and
laboratory experimental sediment bed-surface data. This was undertaken using
two-dimensional wavelet transform techniques based on both the discrete and the
stationary wavelet transforms.
A comprehensive data-base of surface scans from experimental river-bed sediment
surfaces topographies were included in the study. A novel wavelet-based
characterisation measure - the form size distribution ifsd) - was developed to quantify
the global characteristics of the sediment data. The fsd is based on the distribution of
wavelet-based scale-dependent energies. It is argued that this measure will potentially
be more useful than the traditionally used particle size distribution (psd), as it is the
morphology of the surface rather than the individual particle sizes that affects the near
bed flow regime and hence bed friction characteristics.
Amplitude and scale dependent thresholding techniques were then studied. It was found
that these thresholding techniques could be used to: (1) extract the overall surface
structure, and (2) enhance dominant grains and formations of dominant grains within
the surfaces. It is shown that assessment of the surface data-sets post-thresholding may
allow for the detection of structural changes over time.