104
3 An Introduction to Surface Waves
antinode
water surface
length of container I
half the wavelength of the seiche JI2L
antinode
0:
Fig. 3.15: Vertical profile of idealized standing wave in a container
the oscillation is damped out by friction. The main body of water may oscillate
longitudinally or laterally at different periods, while water in a separate bay or
harbour may oscillate at its own natural period. Coastal seiches are more often
forced by direct action of wave energy at the mouth of a gulf or the entrance
of a harbour. The resulting sea surface can be unimodal (as in Fig. 3.15) or
multimodal. If the water depth in a basin of rectangular shape is constant, the
periods of seiches, T, are given by the Merian formula (Massel, 1989):
2l
T - - -
11. -
nV9h'
(3.21 )
in which l is the length of the basin, h is the water depth, 9 is the acceleration
due to gravity, and n = 1,2, ... denotes the number of nodes in the basin.
The periods, Tn, are known as the resonance periods or natural periods of
oscillation.
When the seiche is unimodal (n = 1) as is shown in Fig. 3.15, the period of
the seiche is given by:
(3.22)
Therefore, the wavelength of the seiche becomes:
(3.23)
When the seiche is bimodal (n = 2), we obtain from (3.21):
(3.24)