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<br />23 <br /> <br />greater than S. , <br />1 <br />5., and vice versa. <br />1 <br />a tri a 1 and error techni que. Wi dth changes are subject to the <br />physical constraints of rigid banks or the angle of repose of the <br />bank materi a 1. <br /> <br />If Si is <br />decrease <br /> <br />the channel wi dth is reduced so as to <br />The new channel width is determined by <br /> <br />(2) Adjustment in cross-section profile: <br />Deposit i on at an aggradi ng sect i on is assumed to start from the <br />lowest point and to build up the bed in horizontal layers. At a <br />degrading section, the change in cross-section area is distributed in <br />proportion to the local tractive force. These types of adjustment <br />reduce the spatial variation in power expenditure along the channel. <br /> <br />(3) lateral channel migration: <br />The model solves the sediment-cont i nuity equat i on in the transverse <br />direction: <br /> <br />(l-A)ll <br />at <br /> <br />aq' <br />+---i=O <br />ay <br /> <br />....(2-35) <br /> <br />where <br /> <br />q' <br />s <br />a <br /> <br />= <br /> <br />q tan a = transverse sediment-transport rate per <br />s <br />tan-1(IID/r) = angle deviation of transverse <br />direction tangent to the centerline of a <br />Rozovskii(1957) <br />mean flow depth <br />radius of curvature of the bend <br /> <br />unit width <br />flow from <br />bend gi ven <br /> <br />the <br />by <br /> <br />= <br /> <br />D <br /> <br />= <br /> <br />r <br /> <br />= <br /> <br />z = bed elevation <br /> <br />Using a forward-difference scheme in y, aZk is obtained from <br /> <br />q' -q' <br />= _ at sk+l sk <br />aZk a <br />I-A Yk <br /> <br />.... (2-36) <br /> <br />where <br />aYk <br /> <br />= <br /> <br />transverse distance between points k and k+l <br />