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<br />amount of se::!iment removal or deposition along the banks within the time <br />step. A river channel undergoing changes usually has nonunifonn spatial <br />distribution in power expenditure or 1QS. Usually the spatial variation in <br />Q is small but that in S is pronounced. An adjustment in width reflects the <br />river's adjustment in flow resistance; that is, in power expenditure. A <br />reduction in width at a cross section is usually associated with a decrease <br />in energy gradient for the section whereas an increase in width is <br />accanpanied by an increase in energy gradient. To detennine the direction <br />of width change at a section i, the energy gradient at this section, Si' is <br />canpared with the weighted average of its adjacent sections, Si' Here <br /> <br />Si = <br /> <br />Si+1Llsi + Si-l~si+l <br />~ si + ,A;i~l----- <br /> <br />(10) <br /> <br />If the energy gradient Si is greater than Si' channel width at this section <br />is reduced so as to decrease the energy gradient. On the other hand, if Si <br />is lower, channel width is increased in order to raise the energy gradient. <br />These changes are subject to the rate of width adjustment and physical <br />constraints. <br /> <br />width changes in alluvial rivers are characterized by widening during <br />channel-bed aggradation (or fill) and reduction in width at the time of <br />degradation (or scour). SUch river channel changes represent the river's <br />adjustments in resistance to seek equal power expenditure along its course. <br />A degrading reach usually has a higher channel-bed elevation and energy <br />gradient than its adjacent sections. Fonnation of a narrower and deeper <br />channel at the degrading reach decreasesi ts energy gradient due to reduced <br />boundary resistance. On the other hand, an aggrading reach is usually lower <br />in channel-bed elevation and energy gradient. Widening at the aggrading <br />reach increases its energy gradient due to increasing boundary resistance. <br />These adjustments in channel width reduce the spatial variation in energy <br />gradient and total power expenditure of the channel. <br /> <br />Rate of Width l\djust:ment <br /> <br />For a time increment, the amount of width change depends on the <br />sediment rate, bank configuration and bank erodibility. The slope of an <br />17 <br />