Numerical Model Formulation Sample Clauses

Numerical Model Formulation. The hydrology model developed in the previous section was integrated to a high- resolution depth-integrated two-dimensional model of estuarine circulation for the Barataria Basin. It was assumed that the use of two-dimensional depth-integrated equations for conservation of mass and momentum was adequate, considering the typically well-mixed water column due to wind and tidal stirring of the system (Inoue et al., 1998). The model used here is based on the model initially developed for other neighboring estuaries including Terrebonne- Timbalier Basin (Inoue and Xxxxxxx, 2000), Fourleague Bay (Xxxxxxx and Xxxxx, 1994), as well as Barataria Basin (Park, 1998). The description of the numerical model formulation being presented here comes from Xxxxx et al. (2001). The model equations for conservation of mass and momentum including baroclinic pressure gradient written in Cartesian coordinates in terms of depth-integrated transport (e. g., Xxxxxxxxxx, 1967; Xxxxxxx and Xxxx, 1976) are; U ⎧⎪⎛ U ⎞ 2 ⎛ V ⎞2 ⎫⎪ 2 ⎨⎜ ⎟ + ⎜ ⎟ ⎬ ∂U ∂ U 2 ∂ UV ∂ζ 1 2 ∂ρ H ⎪⎩⎝ H ⎠ ⎝ H ⎠ ⎪⎭ τ x 2 (8) + ∂t ∂x H + ∂y H − fV = − gH − gH − g ∂x 2 ∂x C 2 + + A∇ U ρ ⎜ ⎟ Figure 1-10. Function defined by f (t ) = 5 exp⎜− t ⎝ ⎟ used in this study to estimate the t ⎠ shape of a unit hydrograph for various drainage basins in the Barataria Basin. V ⎧⎪⎛ U ⎞2 1 ⎛ V ⎞2 ⎫⎪ 2 ⎨⎜ ⎟ + ⎜ ⎟ ⎬ ∂V ∂ UV ∂ V 2 ∂ζ 1 2 ∂ρ H ⎪⎩⎝ H ⎠ ⎝ H ⎠ ⎪⎭ τ y 2 (9) + ∂t ∂x H + ∂y H + fU = −gH − gH − g ∂y 2 ∂y C 2 + + A∇ V ρ ∂ζ + ∂U + ∂V = 0 (10) ∂t ∂x ∂y ⎛ ∂S ∂H ∂S ⎞ ∂HS + ∂HS + ∂HS ⎜ ∂H = DS ⎜ ∂x + ⎟ ∂y ⎟