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<br />flow and sediment transport processes exhibited in the process of adjust- <br />ments are outside the scope of regime approach but they are included in the <br />mathematical modeling. This manual addresses the IIIOre rapid process- <br />response or the transient behavior of alluvial rivers. The subject is on <br />unsteady flow and sediment transport in river channels with a changing <br />boundary under given physical constraints. In the following, the physical <br />foundation and numerical techniques for the transient process-response of <br />the FLUVIAL model are described. The input/output instructions are <br />provided. Applications of the FLllVIAL model are illustrated by examples <br />given in the appendixes. <br /> <br />III. PHYSICAL l!alNIWfiC>>l CR J!'t\JVIAL PII(Jt""C'''- JK'C">(IISE <br /> <br />Mathematical modeling of river channel changes requires adequate and <br />sufficient physical relationships for the fluvial processes. While the <br />processes are governed by the principles of continuity, flow resistance, <br />sediment transport and bank stability, such relations are insufficient to <br />explain the time and spatial variations of channel width in an alluvial <br />river. Generally, width adjustment occurs concurrently with changes in <br />river bed prOfile, slope, channel pattern, roughness, etc. These changes <br />are closely interrelated; they are delicately adjusted to establish or to <br />maintain the dynamic state of equilibrium. While any factor imposed upon <br />the river is usually absorbed by a canbination of the above responses. The <br />extent of each type of response is inversely related to the resistance to <br />change. <br /> <br />The dynamic equilibrium is the direction toward which each river <br />channel evolves. The transient behavior of an alluvial river undergoing <br />changes must reflect its constant adjustment toward dynamic equilibrium, <br />although, under the changing discharge, the true equilibrium may never be <br />attained. For a short river reach of uniform discharge, the conditions for <br />dynamic equilibrium are: (1) Equal sediment discharge along the channel, <br />and (2) uniformity in power expenditure "YOS, where 'Y is the unit weight of <br />the water-sediment mixture, 0 is the discharge, and S is the energy grad- <br />ient. If the energy gradient is approximated by the water-surface slope, <br />then unifODll power expenditure or energy gradient is equivalent to the <br />4 <br />