4.5 Comparison of Vertically-Integrated Model 

 versus Three-Dimensional Model 



As a comparison between the two-dimensional, vertically-integrated and 

 the three-dimensional models, surface elevations computed by the 

 two-dimensional model at selected locations are also shown in Figure 4.5. The 

 quadratic stress law, as shown by Eq. (2.40), with a Manning's n of 

 0.035 cm ' , was used in the computation. The computed surface elevations of 

 the two-dimensional model agreed well with those of the three-dimensional 

 model. Of course, the two-dimensional model cannot compute the vertical 

 structure of horizontal velocities, as shown in Figure 4.6. 



The computed currents over the entire basin are also shown in Figures 

 4.7. While the vertically-integrated mass fluxes in all three cases exhibit a 

 counter-clockwise gyre, the detailed vertical structure of velocities show 

 appreciable differences. The three-dimensional model with quadratic stress 

 law gives the strongest bottom currents over much of the basin. The 

 near-surface currents in this case are quite weak along the deep end and at 

 some points are opposite to the wind direction. The three-dimensional model 

 with no-slip condition gives weaker currents and somewhat different current 

 structures. The two-dimensional model gives identical current structures at 

 all levels. The corresponding results of surface elevation and bottom shear 

 stress are shown in Figure 4.8. Hence it appears that in the unstratified 

 case, by choosing a proper bottom friction coefficient, the 

 vertically-integrated model can provide a reasonable estimate on the surface 

 elevation and volume transport. Due to the lack of vertical resolution, 

 however, the vertically-integrated model is not suitable for predicting 

 transport of contaminants which are strongly influenced by the 

 three-dimensional flow structures. 



4.6 Tidal Response in the Mississippi Sound - Idealized Basin 



The three-dimensional model has been applied to simulate the purely tidal 

 currents in the Mississippi Coastal Waters. A 51 x 51 (3 km grid spacing) 

 grid is applied over the idealized coastal area as shown in Figure 4.9. 

 Idealized bottom topography is represented by the contour lines with an 

 interval of 3 meters. Depth within the entire Mississippi Sound is less than 



63 



