Case 02. Windinduced Waves over Slope Bottom Topography
Case 2.Windinduced Waves over Slope Bottom Topography  
1. Analytical Solution Considering an idealized slopingbottom circular lake with water depth given as where is the radius of the lake and is the water depth at the center (Fig. 1).The governing equations shown in Case 1 are applied to this case and an analytical solution was derived by Birchfield and Hickie (BH) (1977). The solution was in the form of a complicated double series characterized by three waves: two for a gravity wave pair and one for a topographic wave. As an initial value problem, the waves are dominated by the first 4 radial modes in the first model day, but higher modes must be taken into account for a longer time period. 
Fig. 1: The illustration of an idealized, sloppingbottom, circular lake 

2. Design of the Numerical Experiment Unstructured triangular and structured rectangular grids used for FVCOM and POM/ECOMsi are similar to those shown in Case 1 except for a radius of 100 km and a maximum depth of 100 m. The analytical solution is derived with a lateral boundary condition at . This condition is allowed in the coordinate transformation system used in FVCOM and POM/ECOMsi until a wet/dry treatment technique is incorporated. In order to make these models run for the case with this idealized sloping bottom, a depth of 0.5 m is added everywhere in , with an understanding that the numerical solution might lead to a bias of BH�s analytical solution for a longtime run. For this reason, the comparison of the models with the analytical solution is limited in the time scale of less than 1 day starting from the initial. 


