H(i,j,0) = .1 + .2 (i - 1) , (93) 



i = 1,2 ••• 45 , 



j = 2,3 ' • ' 22 i . 



The initial condition of constant azimuthal slope and no radial vari- 

 ation of H along a line of constant 9 implies that there are 

 several modes of seiching present; however, the dominate mode is for 

 m = and n = 2. This is indicated by Figures 54 and 55 which show 

 the simulated surface topography at 27 hours in the rectilinear and 

 polar grid systems, respectively. The solution in the polar grid 

 is more representative of the analytical solution than that shown 

 in the Cartesian system. 



The hydrograph at 9 = 0° and r = r i is shown in Figure 56 (a) 

 where the water elevation as determined from the polar grid is the 

 solid line and that from the rectilinear mesh is the dashline. 

 Figure 56 (b,c) shows the hydrographs along 9=0° for r = r 

 (the average radius of the annulus) and r = r 2 , respectively. The 

 three hydrographs along 9 = tt/2 and the same r positions are shown 

 in Figure 57 (a,b,c) and along the nodal line by Figure 58 (a,b,c). 

 The average period of oscillation as determined from the hydrographs 

 of Figures 56 and 57 is approximately 26 hours in the polar system 

 and 28 hours in the rectilinear grid. The error in the period of 

 oscillation (about 8 percent) for the rectilinear system is most 

 evident in the figures by noting the lag of the dashline with 

 respect to the solid line. The longer period of oscillation is 

 directly related to the stairstep boundary. Effectively, the length 

 of the basin is increased by the reflections introduced by these 

 boundaries. This distortion is more than academic since many recti- 

 linear grid models of enclosed irregular bays require adjustments 

 to reproduce the fundamental seiching mode. 



The analytical solution at any point is a smooth function of 

 time. The solid lines in the various hydrographs portray this 

 feature better than the dashlines which are contaminated by high- 

 frequency spurious oscillations. The nodal line in the polar grid 

 solution as evidenced by Figure 58 (a,b,c) remains fixed at 9 = it/4 

 which agrees with the theory. This is not observed in the recti- 

 linear system. Although the hydrographs in the rectilinear grid 

 are not positioned exactly on 9 = tt/4 (actually, about 44°), the 

 magnitude of the oscillation about it/4 is approximately 2 to 4 

 times larger than expected. 



97 



