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5. Tides
a lunar day and is the time for successive passages of the Moon across a given
meridian. It is longer than the solar day of 24 hours. In other words, the high
tides at many locations are almost an hour later each successive day.
Under the equilibrium concept, two tide bulges can only maintain the same
position relative to the Moon when they travel around the Earth at the same
rate (but in the opposite direction) as the Earth rotates with respect to the
Moon. Using the value of 40000 km for the length of the Earth's circumference,
the bulges speed should be:
40000 km
40000 km
km
m
C =
=
= 1610- = 447-.
24hr50.47min
24.841hr
hr
s
(5.22)
As the tide bulge movement can be considered as the movement of very long
wave, the velocity of such waves is C = ygh. Therefore, the required water
depth becomes h = C 2 /g. So, h = 44762/9.81 = 20.4 km. However, such
water depth does not occur on the Earth, and thus, the tidal bulges are unable
to follow the Earth's rotation. Only around the Antarctica, at 60 0 S, where
circumference is shorter and the water is sufficiently deep, the semi-diurnal
tides can be considered as free shallow water waves. As will be shown in
Sect. 5.3.3, the actual tides behave differently and more complex approach is
required to predict them. However, the important conclusion follows from the
equilibrium theory of tides that the fundamental period of tides due to the
attraction of the Moon is 12 hours and 25 minutes.
Influence of Moon Declination. The actual tides behave differently to what
is described above, as the relative position and orientation of the Earth and
the Moon vary in time. In particular, the axis about which the Earth rotates
is not perpendicular to the plane of the Moon's orbit, but is tilted by about
28.5° (Fig. 5.6). Therefore, a line joining the centre of the Earth with that of
the Moon ranges up to 28.5° either side of the equatorial plane. The period of
revolution of the Moon along its orbit is equal to 27.2 days. This period should
not be confused with the 27.3 day period of the Earth-Moon system's rotation.
Let us now consider a few points on the Earth's surface at various latitudes.
In particular, let the latitude of points A and A' be 60 0 N. An observer at
point A would experience a higher tide than that at point A'; 12 hours and 25
minutes later, their position would be reversed. Thus, the water level at points
A and A' would be high twice a day and also low twice a day. However, these
maxima (minima) will not be equal, i.e. there will be a higher high tide and a
lower high tide and similarly, a higher low tide and a lower low tide. The daily
inequality becomes even larger at the maximum Moon declination of 28.5°, i.e.
at points Band B'. On the other hand, at the minimum declination, when the
Moon is vertically above the Equator, there is no daily variation in tide heights
at points C and C'.
When observations at points A, Band C (also A', B' and C') last for an extended period of time, other periodic variations in tide heights will be recorded.
These variations are due to eccentricity of the Moon's orbit around the Earth
5. Tides
a lunar day and is the time for successive passages of the Moon across a given
meridian. It is longer than the solar day of 24 hours. In other words, the high
tides at many locations are almost an hour later each successive day.
Under the equilibrium concept, two tide bulges can only maintain the same
position relative to the Moon when they travel around the Earth at the same
rate (but in the opposite direction) as the Earth rotates with respect to the
Moon. Using the value of 40000 km for the length of the Earth's circumference,
the bulges speed should be:
40000 km
40000 km
km
m
C =
=
= 1610- = 447-.
24hr50.47min
24.841hr
hr
s
(5.22)
As the tide bulge movement can be considered as the movement of very long
wave, the velocity of such waves is C = ygh. Therefore, the required water
depth becomes h = C 2 /g. So, h = 44762/9.81 = 20.4 km. However, such
water depth does not occur on the Earth, and thus, the tidal bulges are unable
to follow the Earth's rotation. Only around the Antarctica, at 60 0 S, where
circumference is shorter and the water is sufficiently deep, the semi-diurnal
tides can be considered as free shallow water waves. As will be shown in
Sect. 5.3.3, the actual tides behave differently and more complex approach is
required to predict them. However, the important conclusion follows from the
equilibrium theory of tides that the fundamental period of tides due to the
attraction of the Moon is 12 hours and 25 minutes.
Influence of Moon Declination. The actual tides behave differently to what
is described above, as the relative position and orientation of the Earth and
the Moon vary in time. In particular, the axis about which the Earth rotates
is not perpendicular to the plane of the Moon's orbit, but is tilted by about
28.5° (Fig. 5.6). Therefore, a line joining the centre of the Earth with that of
the Moon ranges up to 28.5° either side of the equatorial plane. The period of
revolution of the Moon along its orbit is equal to 27.2 days. This period should
not be confused with the 27.3 day period of the Earth-Moon system's rotation.
Let us now consider a few points on the Earth's surface at various latitudes.
In particular, let the latitude of points A and A' be 60 0 N. An observer at
point A would experience a higher tide than that at point A'; 12 hours and 25
minutes later, their position would be reversed. Thus, the water level at points
A and A' would be high twice a day and also low twice a day. However, these
maxima (minima) will not be equal, i.e. there will be a higher high tide and a
lower high tide and similarly, a higher low tide and a lower low tide. The daily
inequality becomes even larger at the maximum Moon declination of 28.5°, i.e.
at points Band B'. On the other hand, at the minimum declination, when the
Moon is vertically above the Equator, there is no daily variation in tide heights
at points C and C'.
When observations at points A, Band C (also A', B' and C') last for an extended period of time, other periodic variations in tide heights will be recorded.
These variations are due to eccentricity of the Moon's orbit around the Earth