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<br />reservoir volume. The bottom profile and elevations were <br />detennined from sediment investiaation cross sections. Con- <br />ditions that existed in the reservoir during the last week <br />of March, 1966 were used to provide the boundary conditions <br />for the simulation. Water temperature profiles, water surface <br />elevations, and flows into and out of the test reach were <br />obtained from the TVA (1969) data. The reservoir was strati- <br />fied and was approximately 108 m (353 ft.) deep'at the dam. <br />Surface heat exchange, wind velocity, and tributary inflows <br />were all assumed to be zero for the purposes of this investi- <br />gation; a steady inflow and outflow of 140 ems (5000 cfs) was <br />used. <br /> <br />Di s cus s i on <br />The-fiITIe--and effort necessary to describe the reservoir <br />geometry for both the FDM and FEM models were comparable. To <br />achieve calculated results at comparable locations in space, <br />optional quadrilateral elements were used so that the finite <br />element network (Fig. 10) was almost identical to FDM grid <br />(not shown). It is recognized that this network does not <br />exploit the capability of the FEM model to allow increased <br />geometric resolution where desired, such as near the reservoir <br />outflow point, but this simplification was useful for com- <br />parison of results. <br />The convergence of the FEM solution was noted to be <br />somewhat more sensitive to the magnitude of the turbulent <br />exchange coefficients than the FDM model. The ranges of values <br />of the coefficients over which convergent solutions can be <br />obtained for the two models have not yet been firmly estab- <br />lished. Additional sensitivity investigations shall be under- <br />taken at a later time. Ariathurai, et al (1977) examined <br />similar equations and found that stability and convergence of <br />the solution could be related not only to spatial and temporal <br />step sizes but also to the Peclet number which is the ratio of <br />convective transport to diffusive transport. <br />The flow fields calculated with the FDM and FEM models <br />are shown in Figs. 11 and 12 respectively. The vertical scale <br />of Figs. 10-12 is exaggerated by a factor of 100. Coefficients <br />used (refer to equations 4-7) were: Exx=24, Exz=4.8xlO-3, <br />Ez~=240, Dx=23, Dz=9.3xlO-7 m2jsec (260,0.05, 2600, 250, 10-s <br />ft jsec). Although the models have numel'OUS detailed differ- <br />ences, particularly in the description of boundary conditions, <br />the calculated flow fields are similar and reasonable. For the. <br />test application, the reservoir was thermally stratified, with <br />the incoming fluid cooler and more dense than the fluid in the <br />surface layers. The stable density gradient in the region of <br />the thermocline tends to inhibit vertical momentum and material <br />transport, yet circulation appears in the upper layers. The <br />circulation in the surface layers is driven by internal hori- <br />zontal shearing between the cool water flowing toward the <br />outlet and the warmer water above. A similar flow pattern is <br />also observed in the bottom region below the main flow in the <br /> <br />" <br />