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(a)
(b)
8
4
9
3
.4
10
2
.6
.8
1
11
1.0
1.0
1.2
1.2
1.4
1.4
12
0
.8
.6
.4
1
11
2
10
.4
3
9
.8
.6
1.0
4
1.2
8
1.4
1.8
1.6
5
6
7
Figure 3.14
G. I. Taylor's solution to a Kelvin wave reflecting at the end of a gulf, from (Taylor,
1922
), courtesy of the London Mathematical Society. (a) shows the co-phase (solid) and co-range
(dashed) lines, (b) shows the tidal current ellipses. Numbers on the outside of (a) indicate the
times of the co-phase lines in intervals T/12; co-range contours are labeled with a measure of the
tidal range. The mouth of the gulf is at the top, and rotation is anticlockwise.
G. I. Taylor (Taylor,
1922
). You can see the results in
Fig. 3.14
. There is some significant
modification of the co-range lines extending to a distance of
l/2 from the end of the
∼
gulf. Along the landward boundary the range increases by
60% relative to the next
antinode. The tidal currents in the first amphidromic system from the head of the gulf
are also modified. In contrast to the simple Kelvin wave model, there are substantial
cross-gulf flows as indicated by the more circular tidal current ellipses in this region.
An example of an amphidromic system in the real ocean is shown in
Fig. 3.15
for the Yellow Sea, a large, shallow gulf between China and Korea driven by the
ocean tide which enters from the East China Sea. This gulf can be regarded (with
some imagination!) as being approximately rectangular with a length of
∼
1000 km.
For the main lunar tidal constituent M
2
,
Fig. 3.15a
shows that there are four
clearly defined amphidromes within the gulf spaced at intervals of
∼
l/2, i.e. half a
tidal wavelength. In each amphidromic system the tide rotates in an anticlockwise
sense and, as in our Kelvin wave model, the phase changes 180
between adjacent
systems, so that when it is HW on the coast of China at one amphidrome it is low
∼
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