88
4 Long Waves in a Channel
4.6.8 Co-oscillations in Bays
Semi-enclosed oceanic regions, such as bays or long gulfs, do not exhibit free
natural oscillations as they are connected with the ambient ocean. Nevertheless,
these regions can experience co-oscillations forced by sea-level oscillations near
the entrance. Co-oscillations of large amplitudes are exited if a wave node is located
in vicinity of the entrance, such that water is pumped into and out of the bay in an
oscillatory fashion. Figure 4.21 illustrates such co-oscillations that occur for forcing
periods of:
T ≈
λ
c
≈
4
m
L
c
for m = 1, 3, 5, . . .
(4.30)
where c is the phase speed of surface or internal gravity waves.
Fig. 4.21 Examples of co-oscillations in a semi-enclosed channel
4.6.9 Additional Exercise for the Reader
The task is to employ the shallow-water model with two layers to explore cooscillations in a semi-enclosed bay. Figure 4.22 displays the physical settings. As
in Exercise 5, forcing is provided by placing a wave paddle near the left end of the