4. MODEL EVALUATION TESTS 



4.1 Computer Simulation of Vicksburg Tidal Flume 



Ippen and Harleman (1961) conducted experiments at the Waterways 



Experiment Station in Vicksburg, Mississippi to study the influence of various 

 parameters on tidal motion. The experiments were performed in a uniform 



rectangular flume with one end closed while another end was connected to a 



large reservoir where sinusoidal tides were generated. The flume was 100 m 



long, 22.86 cm wide, and 15.24 cm deep. For their Test No. 29, the tidal 

 forcing was: 



M 



?(0,t) = ^o COS ^1 (4.1) 



where ? = 1.52 cm and T = 600 sec. For both high water and low water 

 conditions, the water level at selected points along the flume are plotted in 

 Figure 4.1. 



To test our three-dimensional numerical model, we ran a simulation of the 

 Vicksburg flume. The parameters used are: A^ = 1 cm^sec, C^j = 0.004, 

 Ax = 5 m, Ay = 4.56 cm, Az = 0.3 cm. As shown in Figure 4.1, the results 

 obtained with At = 5 sec agree very closely with the measurements. Even at 

 At = 30 sec, the results are only slightly off. 



4.2 Comparison with Analytical Results 



In this section, the vertically-averaged version of our model was used to 

 simulate the tidal flow in a rectangular bight and the results were compared 

 with the analytical solution. 



Consider a square basin of constant depth h and length L. The basin has 

 vertical walls along the West (x=0) and the South (y=0), while open boundaries 

 along the East (x=L) and the North (y=L). Neglecting the non-linear terms and 

 horizontal diffusion terms, and also linearizing the bottom friction terms, 

 one obtains the following governing equations in dimensional form: 



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