g + CO. 



In contrast with the case of an Infinitely long basin where there is a 

 single oscillation with a period between T„ and J , the flow in a finite 

 enclosed basin consists of the superposition of two different sets of waves as 

 the result of interaction between the inertial oscillations and the surface 

 gravity waves. Lamb (1932) analyzed the normal modes in a circular basin and 

 found that the period of one of these waves is on the order of T , while the 

 period of the other wave goes from T to about 2T where g goes from » to 0. 

 Analytic solution in such a square basin, driven by a uniform wind stress, was 

 obtained by Haq, Lick, and Sheng (1974) and was found to be quite similar to 

 the solution in a circular basin. These important time scales are very useful 

 for checking the accuracy of numerical results. 



Comparison With Numerical Results 



A free-surface model has been applied to examine the response of a square 

 basin, with a constant depth of 10 m, to an impulsive wind stress of 



2 2 



1 dyne/cm . Constant vertical eddy viscosity of 25 cm /sec was assumed such 

 that Ey = 0.025. Simulations were carried out in a number of basins with 

 varying horizontal lengths, ranging from 40 km to 100 km, such that 6 varied 

 from about 4 to about 0.01. In all the cases, due to the relatively small 

 viscous effect, the transient results exhibited two distinct time scales 

 indicating the interaction of two waves in the basin. For large values of 5b, 

 as shown in Figure 4.4, one of the waves has a period (T ) that corresponds 

 exactly to the period of gravity waves (!„) while another wave has a period 

 (T ) slightly larger than the inertial period (2TrTj). As g is decreased, t 

 becomes larger than T„ and asymptotes to approximately 2Tq, while T is 

 increased only slightly. This agrees with the approximate analytical results 

 discussed above. 



58 



