5.3 Dynamic Model of Tides
169
A specific configuration of the Earth, Moon and Sun produces exceptionally
high tides when the Earth is at perihelion, the Moon is at perigee, the Sun and
the Moon are in declination. This combination produces the greatest possible
tidal range. However, such an occurrence is very rare, and happens about every
1 600 years. The last occurrence took place in about the year A.D. 1400.
5.3 Dynamic Model of Tides
5.3.1 Brief Overall
A comparison of the equilibrium tide theory, developed by Newton, with observed tides immediately shows various discrepancies. High tide often occurs
at the wrong time, with the range of the tide not properly predicted by equilibrium theory. For example, the equilibrium theory predicts that high tide
at Monterey and at the Golden Gate, in California, should occur at the same
time, but in fact high tide at the Golden Gate occurs 45 minutes after Monterey
(Denny, 1988). There are many other examples of discrepancies between the
equilibrium theory of prediction and observations. According to equilibrium
theory, semidiurnal tidal ranges would reach their maximum value of about
10.5 m at equatorial latitudes. In fact, observed tides in the ocean have mean
ranges of 0-1 m.
When tides propagate into the relatively shallow waters of the continental
shelf, their heights increase. At locations within bays and embayments, the
tidal range becomes much higher. For example, in shelf areas of the Bay of
Fundy, the Bristol Channel, and the Kimberley Coast (North Australia), the
spring tidal ranges exceed 10 m. In Fig. 5.9, an example of such very high tides
is shown for the Bay of Le Mont-Saint-Michel (Normandy, France). The MontSaint-Michel Benedictine Abbey stands high on the summit of granite rock out
in the Bay. The Bay surrounding the rocky island is known for its quicksands
and extremely fast rising tides, with the speed of tidal currents exceeding 10
m/s.
There are several reasons for discrepancies between observations and predictions by the equilibrium theory. The most important may be summarized as
follows (Pugh, 1987):
1. The Earth is not uniformly covered with the water. The average depth
of the oceans is much smaller than the depth of 20 km which is required
to allow the tidal bulges to travel as shallow water free waves at the
equatorial zone. Only around the Antarctica, at 60 0 S, can the semidiurnal tides be considered as free shallow water waves.
2. The presence of continents prevents the tidal bulges from propagating
around the Earth and complex ocean bathymetry constrains the direction
of tidal flows.
3. As we showed in Sect. 3.7, the ocean basins have their own natural modes
of oscillation, with many resonant frequencies. These oscillations interact
169
A specific configuration of the Earth, Moon and Sun produces exceptionally
high tides when the Earth is at perihelion, the Moon is at perigee, the Sun and
the Moon are in declination. This combination produces the greatest possible
tidal range. However, such an occurrence is very rare, and happens about every
1 600 years. The last occurrence took place in about the year A.D. 1400.
5.3 Dynamic Model of Tides
5.3.1 Brief Overall
A comparison of the equilibrium tide theory, developed by Newton, with observed tides immediately shows various discrepancies. High tide often occurs
at the wrong time, with the range of the tide not properly predicted by equilibrium theory. For example, the equilibrium theory predicts that high tide
at Monterey and at the Golden Gate, in California, should occur at the same
time, but in fact high tide at the Golden Gate occurs 45 minutes after Monterey
(Denny, 1988). There are many other examples of discrepancies between the
equilibrium theory of prediction and observations. According to equilibrium
theory, semidiurnal tidal ranges would reach their maximum value of about
10.5 m at equatorial latitudes. In fact, observed tides in the ocean have mean
ranges of 0-1 m.
When tides propagate into the relatively shallow waters of the continental
shelf, their heights increase. At locations within bays and embayments, the
tidal range becomes much higher. For example, in shelf areas of the Bay of
Fundy, the Bristol Channel, and the Kimberley Coast (North Australia), the
spring tidal ranges exceed 10 m. In Fig. 5.9, an example of such very high tides
is shown for the Bay of Le Mont-Saint-Michel (Normandy, France). The MontSaint-Michel Benedictine Abbey stands high on the summit of granite rock out
in the Bay. The Bay surrounding the rocky island is known for its quicksands
and extremely fast rising tides, with the speed of tidal currents exceeding 10
m/s.
There are several reasons for discrepancies between observations and predictions by the equilibrium theory. The most important may be summarized as
follows (Pugh, 1987):
1. The Earth is not uniformly covered with the water. The average depth
of the oceans is much smaller than the depth of 20 km which is required
to allow the tidal bulges to travel as shallow water free waves at the
equatorial zone. Only around the Antarctica, at 60 0 S, can the semidiurnal tides be considered as free shallow water waves.
2. The presence of continents prevents the tidal bulges from propagating
around the Earth and complex ocean bathymetry constrains the direction
of tidal flows.
3. As we showed in Sect. 3.7, the ocean basins have their own natural modes
of oscillation, with many resonant frequencies. These oscillations interact