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<br />and channel width described in the following sections. <br />Sediment rate is computed separately for cases of erosion and depo- . <br />sition using different size fractions of the bed material. For a particular <br />size, transport capacity is obtained from a sediment equation. In the case <br />of deposition, sediment rate is controlled by the transport capacity but, <br />in the case of erosion, sediment rate is availability controlled. Simulation <br />of sediment transport and accounting of bed-material composition by <br />tracking river channel evolution are similar to those developed by Ben- <br />nett and Nordin (2). Materials eroded from the channel banks, excluding <br />that portion in the wash load size range, are included in the accounting. <br />Bed armouring develops if bed shear stress is too low to transport any <br />available size. <br />Changes in Channel Width.-Simulation of width variation is based <br />upon the concept of minimum stream power. At a time step, width cor- <br />rections for all cross sections are such that the total stream power (or <br />rate of energy expenditure) for the reach is minimized; these corrections <br />are subject to the physical constraint of rigid banks and limited by the <br />amount of sediment removal or deposition along the banks within the <br />time step. Total stream power of a channel reach is <br /> <br /> <br />p = i'lQSdx ..........,............,.......................... (4) <br /> <br />in which P = total stream power of the reach; L = length of the reach; <br />and 'I = specific weight of water and sediment mixture. Written in finite <br />difference form, this equation becomes <br /> <br />N-' I <br />P = 2: - '1(Q,S, + Qi+1Si+,)Ax, . ... ... .., ...... ... .... .. .... .... .. (5) <br />i-I 2 <br /> <br />in which N = total number of cross-sections for the reach; i = cross <br />section index counted from upstream to downstream; and Ax, = distance <br />between Sections i and i + 1. Previous studies (5,12,13) have established <br />that minimum stream power for an alluvial river is equivalent to equal <br />power expenditure per unit channel length, that is, constant 'IQS along <br />the reach. A river channel undergoing changes usually has uneven spa- <br />tial distribution in power expenditure or '1QS. Usually the spatial vari- <br />ation in Q is small but that in 5 is pronounced. Total stream power of <br />a reach decreases with the reduction in spatial variation in QS (or 5 if <br />Q is nearly uniform) along the reach. Adjustments in channel widths <br />are made in such a way that the spatial variation of QS is minimized <br />subject to the constraints and limitations aforementioned. An adjust- <br />ment in width reflects the river's adjustment in flow resistance, that is, <br />in power expenditure. A reduction in width at a cross section is usually <br />associated with a decrease in energy gradient for the section whereas an <br />increase in width is accompanied by an increase in energy gradient. Us- <br />ing these guidelines, a technique for width correction has been devel- <br />oped as described in a previous publication (5). <br />Width changes in alluvial rivers are characterized by the formation of <br />small widths at degrading reaches and widening at aggrading reaches <br />(4,5,11,13,15). This type of width formation represents the river's ad- <br /> <br />159 <br /> <br />8 <br />