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<br />cross sections in the study reach toward establishing uniformi ty in power <br />eXpenditure. <br /> <br />IX. SDIJLA'lIQI CP ~ IN OWlNEL-Bm PRa!'ILE <br /> <br />After the banks are adjusted, the remalnlng correction for Ab is <br />applied to the bed. Distributions of erosion and deposi tion, or fill and <br />scour, at a cross section are usually not uniform. Generally speaking, <br />deposition tends to start fran the low point and it is more uniformly dis- <br />tributed because it tends to build up the channel bed in nearly horizontal <br />layers. This process of deposition is often accompanied by channel <br />widening. on the other hand, channel-bed erosion tends to be more confined <br />wi th greater erosion in the thalweg. This process is usually associated <br />with a reduction in width as the banks slip back into the channel. Such <br />characteristic channel adjustments are effective in reducing the streamwise <br />variation in stream power as the river seeks to establish a new equilibrium. <br />In the model, the allocation of scour and fill across a section during each <br />time step is assumed to be a power function of the effective tractive force <br />'1"0 - f1"c, i.e. <br /> <br />("0 - f1C) n <br />l::1 z = ----------- LlAj, <br />! ~ - rrc)nAY <br />B <br /> <br />(11) <br /> <br />wherell.z is the local correction in channel-bed elevation,rr; (given by j'DS) <br />is the local tractive force, rrc is the critical tractive force, n is an <br />exponent, and y is the horizontal coordinate, and B is the channel width. <br />The value of /f;; is zero in the case of fill. <br /> <br />'!he n value in Eq. 11 is generally between 0 and 1; it affects the <br />pattern of scour-fill allocation. For the schematic cross section shown in <br />Fig. 3, a small value of n, say 0.1, would mean a fairly uniform distribu- <br />tion of Llz across the section; a larger value, say 1, will give a less <br />uniform distribution of ~z and the local change will vary with the local <br />tractive force or roughly the depth. The value of n is determined at each <br />time step such that the correction in channel-bed profile will result in the <br />most rapid movement toward uniformity in power expenditure, or linear water- <br /> <br />19 <br />