Surface gravity water waves 163
Example 6.5
This exercise considers a one-dimensional basin subject to a sudden
excitation (Dirac function) of the water surface at a certain location.
The data utilized for the simulation and the Fourier series analysis are
as follows:
Basin length = 1000 m
Undisturbed water depth = 5 m
Excitation amplitude = 0.5 m
Bed friction coefficient = 0.001
Number of Fourier series components = 40
The excitation occurred at a distance of 980 m. Data were collected
at two points, one at a distance of 200 m and another at a distance
of 500  m (mid-point). The spatial step was taken as 10 m while the
time step as 0.1 s. The simulation was conducted for a period of 1000
seconds.
The time series of the free surface oscillation at the mid-point of the
basin is presented in Figure 6.10. From this figure, the primary eigen
period of natural oscillation (T o ) of about 275 seconds is easily recognizable. From the same figure, the attenuation in time of the oscillation
due to frictional and other effects is also evident. It should be emphasized that the evolution of the various eigen periods depends on the
type of excitation (i.e. Dirac function in this example).
0.15
0.05
–0.05
–0.1
0.1
0
0
200
400
600
800 1000 1200 1400 1600 1800 2000
Time steps × 0.5 (s)
Free surface excitation at midpoint of the basin (m)
Figure 6.10 Free surface excitation at the midpoint of the basin.