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<br />(5) <br /> <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br /> <br />equations for turbulent flows. The forms of the depth-integrated equations of fluid mass <br />and momentum conservation in two directions are shown below. <br /> <br />(3) <br />8u 8u 8u h( 02U 02U) (oa Oh~ gun2 (2 2).!. <br />h Ot + hu Ox + hv 0' - p E;a Ox2 + Exy 0'2 + gh Ox + Ox) + ( .!.) 2 + U + v 2 = 0 <br />1.486h6 <br /> <br />(4) <br />iJv iJv iJv h (02V 02V) (oa Oh) gvn2 (2 2).!. <br />h Ot + hu Ox + hv 0' - p Eyx Ox2 + Eyy 0'2 + gh 0' + '0' + ( .!.) 2 + U + v 2 = 0 <br />1.486h6 <br /> <br />Oh + h( Ou + iJv) + u Oh + v Oh. = 0 <br />Ot Ox 0' Ox 0' <br /> <br />where: h = depth <br />u,v = velocities in cartesian directions <br />x,y,t = cartesian coordinates and time <br />a = density of fluid <br />E = eddy viscosity coefficient <br /> for xx = normal direction on x axis surface <br /> for yy = normal direction on y axis surface <br /> for xy and yx = shear direction on each surface <br />g = acceleration due to gravity <br />a = elevation at bottom <br />n = Mannings roughness coefficient <br /> <br />Equations 3, 4, and 5 are solved by the finite element method using the Galerkin <br />Method of weighted residuals. Elements may be two-dimensional quadrilaterals or <br />triangles and each may have curved sides. Integration in space is performed by <br />Gaussian integration and derivatives in time are replaced by a non-linear finite <br />difference approximation. Solutions are fully implicit and the set of simultaneous <br />equations is solved by Newton-Raphson non-linear iteration. RMA2 permits wetting <br />and drying within the grid either through elemental elimination or gradual wetting and <br />drying through the consideration of marsh porosity (King 1997). <br /> <br />Surface-Water Modeling System (SMS) is a commonly used interface for <br />RMA2. SMS is a pre- and post-processor for RMA2 which allows for the creation of <br />the finite element mesh and associated boundary conditions with a Gill. <br /> <br />HABITAT AVAILABILITY <br /> <br />On September 15, 1999, at a flow of287 cfs, aerial photographs were taken at a <br />scale of 1"=600'. The aerial photography included the survey site and the representative <br /> <br />8 <br />