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cycle with a period of 14.79 days in which the tides alternate between the large
spring tides and small neap tides. This fortnightly modulation in the strength of
the tides is easily understood in terms of the positions of the Moon and Sun
relative to the Earth. If the Earth, Moon and Sun are in line (at new Moon and
full Moon) then the tidal ellipsoids generated by the Moon and the Sun are
aligned. Thus the Moon HW and the Sun HW add together to produce a very
high tide. Conversely, with the Moon-Earth-Sun forming a right angle, the
Moon's HW coincides with the Sun's LW, resulting in a smaller HW. This
spring-neap cycle, which can be extreme when the amplitudes of M 2 and S 2 are
similar, has an important role in modulating mixing processes, as we shall see in
Chapters 7 , 8 and 9 .
2.5.2
Tidal energy supply to the shelf seas
Most of the energy input to sustain the tides occurs in the deep ocean, but a
large majority of the energy is dissipated in the shallower waters of the shelf seas
where frictional forces are much greater. The tidal forces acting directly on the
waters of the shelf seas also contribute but are responsible for only a small
fraction of the energy input to the shelf seas. The majority of the energy input to
the shelf seas comes from the deep ocean in the form of waves of tidal period.
These waves cross the shelf break on to the shelf, where they are reflected
and amplified before losing much of their energy in dissipation by frictional
stresses acting at the seabed. We shall look more closely in Chapter 3 at
the behaviour of these waves and the way that the shelf seas react to the tidal
forcing which they bring, but for the moment we shall concentrate on the large
scale budget of energy supply to the tides.
The Moon tides supply power to the Earth as a whole at the rate of
3.2 TW
10 12 W) with a further
(1 TW
¼
0.5 TW coming from the tides generated by the Sun.
Tides in the solid earth (
0.02 TW) make minimal
contributions to energy dissipation, so that most of the total power supply (
0.2 TW) and in the atmosphere (
3.5 TW)
is accounted for by energy dissipation in the ocean. Until quite recently it was thought
that almost all dissipation was concentrated in the shelf seas, but as knowledge of more
remote seas improved, it became increasingly difficult to account for all the power
input in terms of the observed and modelled tidal dissipation. It now appears that
about 75% of the ocean's dissipation occurs in the shallow seas, with the rest (0.9TW)
being consumed in the deep ocean partly through the generation of internal tides
and waves (Munk and Wunsch, 1998 ).
In Fig. 2.13 you can see that the distribution of the tidal energy input within
the world's oceans and shelf seas is rather uneven, with a relatively small number of
shelf sea areas accounting for a high proportion of the total. The large shelf region
of Western Europe experiences particularly high dissipation, as do the comparable
areas of the Yellow Sea and the large shelf area of northern Australia. In some
cases, extremely high dissipation rates occur in relatively small regions, e.g. in the
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