Geoscience Reference
In-Depth Information
(a)
(b)
11 10 9 8 7
54321
11
9
7
5 3 1
0.5
0.5
0
6
6
0
0
6
0
0
6
0
-0.5
-0.5
12345
7891011
11
7
9
1
3
5
0.5
0.5
1.8
1.5
1.2
0
0
1.5
0.6
1.8
-0.5
-0.5
0
2
4
6
8 012
0
2
4
6
8 0 2
kx
kx
(c)
0.5
0
-0.5
1
3
5
7
9
11
0.5
0.9
1.2
1.5
0
1.8
-0.5
0
2
4
6
8 0 2
kx
Figure 3.13
Co-tidal and co-range lines for a combination of two Kelvin waves travelling in
opposite directions along a channel which has a width of one Rossby radius Ro. Top panels
shows co-tidal lines along which phase is uniform, at intervals of T
c
/12 where T
c
is the period
of the tidal constituent. Lower panels show the range of the tide relative to 2A
f
the range of the
incident Kelvin wave which is proceeding from left to right. In (a) the incident wave is fully
reflected so that A
b
¼
A
f
; (b) is an example of partial reflection due to frictional losses of wave
energy; (c) shows how the amphidrome becomes degenerate if frictional losses are high.
in
Fig. 3.13b
where you can see that the pattern becomes asymmetric for the case of
A
b
/A
f
¼
0.7 with the amphidrome being displaced to the left side of the gulf looking
into the gulf in the northern hemisphere. In some situations, where frictional losses
are large, the displacement may result in the amphidrome being located on land, in
which case it is referred to as a degenerate amphidrome. Such an extreme displace-
ment is illustrated in
Fig. 3.13c
for a case where A
b
/A
f
¼
0.25.
Before we compare the Kelvin wave theory with examples of real co-tidal charts we
should return to the question, which we deferred, of what happens at the landward end of
the gulf where the Kelvin wave is reflected. Here account must be taken of the condition
of no flow at the landward boundary. A famous analytical solution for the case of
complete reflection in this region was obtained from some difficult mathematics by
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